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#21

--- In FREEvpFREE@yahoogroups.com, "rsing1111" <rsinger1111@c...>
wrote:

--- In FREEvpFREE@yahoogroups.com, "rgmustain" <rgmustain@a...>

wrote:

> The method I use for the 40 credit win is to look at the any win
40
> credits. If that win is enough to cover the loss at the previous
> level then I subract that amount from the win and reset to the
> previous level. I continue along that path until I can no longer

get

> to another level and pocket what's left. This may get me to

either a

> 100 or 300 credit game. If you only reset to the 100 credit games
> then I will need to make a change.

For clarity, the only times I retreat back to a lower level is when

I

have a hit that recovers all lost credits in the current

denomination,

and recovers 400 credits in the previous denomination--and

sometimes,

but not often, it retreats more than one. I also must pocket at

least a

40-credit profit he same time I'm doing the retreat, meaning, if I
recover all lost credits as just stated then I still can't retreat
until I also make at least a 40-credit profit at the current level.

I added in these changes and I changed the output to give averages in
all cases. I used the 5 level progression instead of 6.

Run 1)

seed = 12102
8-5BP 0.99166 10-7DB 1.001725 8-5BP 0.99166 10-7DB 1.001725 8-5BP
0.99166 10-6DDB 1.00067 8-5BP 0.99166 9-5TB+ 0.998033 8-5BP 0.99166 9-
5TB+ 0.998033
Average hands at level 1 = 3257
Average hands at level 2 = 3185
Average hands at level 3 = 862
Average hands at level 4 = 937
Average hands at level 5 = 286
Average hands at level 6 = 340
Average hands at level 7 = 162
Average hands at level 8 = 196
Average hands at level 9 = 83
Average hands at level 10 = 110
Number of wins = 62 averaging 5812.983871
Number of losses = 38 averaging 15096.710526
Subgoal hits = 49 Level resets = 36 Level losses = 41
Average wagered = 108075.2 for payback of 98.026652
Expected payback = 99.611553 Total hands per session = 9423.23

Run 2)

seed = 0
8-5BP 0.99166 10-7DB 1.001725 8-5BP 0.99166 10-7DB 1.001725 8-5BP
0.99166 10-6DDB 1.00067 8-5BP 0.99166 9-5TB+ 0.998033 8-5BP 0.99166 9-
5TB+ 0.998033
Average hands at level 1 = 3218
Average hands at level 2 = 3336
Average hands at level 3 = 881
Average hands at level 4 = 879
Average hands at level 5 = 294
Average hands at level 6 = 346
Average hands at level 7 = 132
Average hands at level 8 = 181
Average hands at level 9 = 82
Average hands at level 10 = 84
Number of wins = 79 averaging 6571.772152
Number of losses = 21 averaging 15274.52381
Subgoal hits = 49 Level resets = 38 Level losses = 41
Average wagered = 102972.65 for payback of 101.926774
Expected payback = 99.612359 Total hands per session = 9436.98

I think it is now possible to discuss this system. Even though this
is not exactly the system Rob uses (no special plays), some of the
points I will make should be applicable to any progressive approach.
I'll be upfront with my opinion: No finite progressive system can
change the expected return of the games played unless it can change
the expected return of the individual hands. Now for some random
thoughts ...

1) The small number of hands played at the high denominations is
probably responsible for the high variance of this approach. This has
the effect of making either hugh wins or hugh losses possible. It
also pretty much negates any hope of ever reaching the "long term" EV
of the games played for most players. The bell curve would be
somewhat flattened and wider than non-progressive VP approaches. This
is extremely evident when you quadruple the bet in a progression,
like going from $25 to $100.

2) One way to look at this approach is too consider each progessive
level as a single bet. You either win the bet (win some amount and go
home or revert to a previous level) or you lose the bet and go on to
the next level. Therefore, it may be useful (or may not) to play
these levels with a different goal and a different strategy (A
strategy that optimizes around reaching the goals). If this is the
case it would be interesting to research what this strategy would
look like. Would it look like Robs' special plays? Of course, the
play at the first level would not follow this strategy and most
likely follow a max-EV or min-risk strategy.

If a new strategy is required it seems counterproductive to extract
sub-goals at the highest level of the progression since that would
reduce the likelihood of gaining a big win at that level. What is the
best strategy for the highest level? Maximizing the chances of
returning to a lower level will clearly sacrifice EV. However, that
seems unimportant if you plan on losing a set amount and then
quitting. But then, what is the real advantage of getting to a lower
level. Playing more hands improves the chances of reaching the final
goal so that, in and of itself, would seem to take precedent over
maximizing EV. On the other hand, if that lower level is played on a
negative EV machine won't that just mean you'll lose that money over
time anyway?

So, what would be the best strategy at the intermediate levels? On
one hand you still want to obtain sub-goals to help reach the overall
win goal with the understanding that the credits at that level may be
restored by a win at a higher level. On the other hand, anything you
use will descrease the liklihood of returning to a previous level. Do
these conflicting goals cancel each other?

3) Using a progression on a positive set of machines with the goal of
producing more session wins also has its' risks. You pay for the
additional wins with a higher bankroll requirement. For example,
assumed you could play FPDW for 3 levels (.25, .50 and 1.00). I did
some runs and the percentage of session wins went up to 52% (for a
$200 goal). The average win was around $650 and the average loss
around $600. The average bet in this progression was $2.00 (.40
credits). Hence, you would receive points, comps, CB, etc. as if you
were playing a .40 machine while needing a bankroll closer to the
1.00 level. If you played exclusively at the .50 level the session
win rate with a $200 stake would be closer to 20% while requiring the
standard bankroll for this denomination.

Unless some way of "improving" the EV can be demonstrated by changes
in strategy at various levels of a denomination progression then it
is impossible to change the overall EV using this approach. The
overall EV would be the EV for each game played times the number of
hands played for each game averaged out over all the hands. While I'm
still open to other possibilities (along the lines I described
above), I can't see any strategy that would accomplish these results.

4) It may be possible to come closer to Robs' special plays. I don't
own FVP but I realize that strategy variations can be used. If anyone
could create a strategy that encompasses the special plays for each
game then all I need the average number of hands for each outcome to
update my simulator.

Dick

#22

Questions & comments:

1) Does your analysis tell you at which level(s) the RF's are hit?

2) I think I understood your comment about the 6th level. With a 4:1
ratio at the last level, I believe that would significantly increase
the chances of winning more and more often.

3) When the special plays that deviate from expert strategy were
incorporated, they were not analyzed as part of the entire strategy,
but rather, as part of certain individual hands. True, using them
decreases the long-term EV, but in the short-term it counts on
receiving the luck to make the medium to big hits---only when a
smaller and more probable (and higher EV hold) win will not attain an
immediate goal. These overall have been the difference-makers over
the 8+ years, as many or most of my largest hits (other than royals,
but the 1 RF I hit on the $25 machine was one of those plays) were
the result of seizing the opportunity. I do not tall anyone that I
have a skill beyond all others. I readily come out and say I take
maximum advantage of all the good luck afforded me. That means,
taking advantage of the "really, not all that many" hands that may
allow a big winner when optimal play will not, and packing up the
ship and going home when a goal is reached.

I added in these changes and I changed the output to give averages

in all cases. I used the 5 level progression instead of 6.

Run 1)

seed = 12102
8-5BP 0.99166 10-7DB 1.001725 8-5BP 0.99166 10-7DB 1.001725 8-5BP
0.99166 10-6DDB 1.00067 8-5BP 0.99166 9-5TB+ 0.998033 8-5BP 0.99166

9-5TB+ 0.998033

Average hands at level 1 = 3257
Average hands at level 2 = 3185
Average hands at level 3 = 862
Average hands at level 4 = 937
Average hands at level 5 = 286
Average hands at level 6 = 340
Average hands at level 7 = 162
Average hands at level 8 = 196
Average hands at level 9 = 83
Average hands at level 10 = 110
Number of wins = 62 averaging 5812.983871
Number of losses = 38 averaging 15096.710526
Subgoal hits = 49 Level resets = 36 Level losses = 41
Average wagered = 108075.2 for payback of 98.026652
Expected payback = 99.611553 Total hands per session = 9423.23

Run 2)

seed = 0
8-5BP 0.99166 10-7DB 1.001725 8-5BP 0.99166 10-7DB 1.001725 8-5BP
0.99166 10-6DDB 1.00067 8-5BP 0.99166 9-5TB+ 0.998033 8-5BP 0.99166

9-

5TB+ 0.998033
Average hands at level 1 = 3218
Average hands at level 2 = 3336
Average hands at level 3 = 881
Average hands at level 4 = 879
Average hands at level 5 = 294
Average hands at level 6 = 346
Average hands at level 7 = 132
Average hands at level 8 = 181
Average hands at level 9 = 82
Average hands at level 10 = 84
Number of wins = 79 averaging 6571.772152
Number of losses = 21 averaging 15274.52381
Subgoal hits = 49 Level resets = 38 Level losses = 41
Average wagered = 102972.65 for payback of 101.926774
Expected payback = 99.612359 Total hands per session = 9436.98

I think it is now possible to discuss this system. Even though this
is not exactly the system Rob uses (no special plays), some of the
points I will make should be applicable to any progressive

approach.

I'll be upfront with my opinion: No finite progressive system can
change the expected return of the games played unless it can change
the expected return of the individual hands. Now for some random
thoughts ...

1) The small number of hands played at the high denominations is
probably responsible for the high variance of this approach. This

has

the effect of making either hugh wins or hugh losses possible. It
also pretty much negates any hope of ever reaching the "long term"

EV

of the games played for most players. The bell curve would be
somewhat flattened and wider than non-progressive VP approaches.

This

is extremely evident when you quadruple the bet in a progression,
like going from $25 to $100.

2) One way to look at this approach is too consider each progessive
level as a single bet. You either win the bet (win some amount and

go

home or revert to a previous level) or you lose the bet and go on

to

the next level. Therefore, it may be useful (or may not) to play
these levels with a different goal and a different strategy (A
strategy that optimizes around reaching the goals). If this is the
case it would be interesting to research what this strategy would
look like. Would it look like Robs' special plays? Of course, the
play at the first level would not follow this strategy and most
likely follow a max-EV or min-risk strategy.

If a new strategy is required it seems counterproductive to extract
sub-goals at the highest level of the progression since that would
reduce the likelihood of gaining a big win at that level. What is

the

best strategy for the highest level? Maximizing the chances of
returning to a lower level will clearly sacrifice EV. However, that
seems unimportant if you plan on losing a set amount and then
quitting. But then, what is the real advantage of getting to a

lower

level. Playing more hands improves the chances of reaching the

final

goal so that, in and of itself, would seem to take precedent over
maximizing EV. On the other hand, if that lower level is played on

a

negative EV machine won't that just mean you'll lose that money

over

time anyway?

So, what would be the best strategy at the intermediate levels? On
one hand you still want to obtain sub-goals to help reach the

overall

win goal with the understanding that the credits at that level may

be

restored by a win at a higher level. On the other hand, anything

you

use will descrease the liklihood of returning to a previous level.

Do

these conflicting goals cancel each other?

3) Using a progression on a positive set of machines with the goal

of

producing more session wins also has its' risks. You pay for the
additional wins with a higher bankroll requirement. For example,
assumed you could play FPDW for 3 levels (.25, .50 and 1.00). I did
some runs and the percentage of session wins went up to 52% (for a
$200 goal). The average win was around $650 and the average loss
around $600. The average bet in this progression was $2.00 (.40
credits). Hence, you would receive points, comps, CB, etc. as if

you

were playing a .40 machine while needing a bankroll closer to the
1.00 level. If you played exclusively at the .50 level the session
win rate with a $200 stake would be closer to 20% while requiring

the

standard bankroll for this denomination.

Unless some way of "improving" the EV can be demonstrated by

changes

in strategy at various levels of a denomination progression then it
is impossible to change the overall EV using this approach. The
overall EV would be the EV for each game played times the number of
hands played for each game averaged out over all the hands. While

I'm

still open to other possibilities (along the lines I described
above), I can't see any strategy that would accomplish these

results.

4) It may be possible to come closer to Robs' special plays. I

don't

own FVP but I realize that strategy variations can be used. If

anyone

could create a strategy that encompasses the special plays for each
game then all I need the average number of hands for each outcome

to

···

--- In FREEvpFREE@yahoogroups.com, "rgmustain" <rgmustain@a...> wrote:

update my simulator.

Dick

#23

Not at this time. It would be easy to add. I'm not sure how meaningful
it is since any RF will meet the overall goal and end the session.

By the way, I am still working on some data gathering that analyzes
what subgoal would be optimal (if any).

Dick

···

--- In FREEvpFREE@yahoogroups.com, "rsing1111" <rsinger1111@c...> wrote:

Questions & comments:

1) Does your analysis tell you at which level(s) the RF's are hit?

#24

Right--It wouldn't change the number of winning sessions, but it
might be interesting to see how many lower level RF's there are
compared to upper level. Right now, in 252 sessions, I have one at
$25, two at $10, but more at $5 than $2 OR $1.

Back in 1996 I wasn't given any options for my 40-credit subgoal.
Just my overall session goal was recommended to be lowered from $3000
to $2500, which I did. So whatever you come up with would be
interesting.

Just as with your statement that you don't believe any progressive
system can end up positive, my position is that since I've had
exceptional success with my strategy and the fact that it is far more
interesting to play than straight-up expert strategy, I would never
go back.

···

--- In FREEvpFREE@yahoogroups.com, "rgmustain" <rgmustain@a...> wrote:

> 1) Does your analysis tell you at which level(s) the RF's are hit?

Not at this time. It would be easy to add. I'm not sure how
meaningful it is since any RF will meet the overall goal and end the
session.

#25

One more question. If you make a 40 credit subgoal I've been assuming
you only take out the 40 credits and any additional part of the win
would supplement your credits at the current level. If you take the
entire win (>= the subgoal) but less than a level reset then I need
to make some changes.

Dick

--- In FREEvpFREE@yahoogroups.com, "rsing1111" <rsinger1111@c...>
wrote:

--- In FREEvpFREE@yahoogroups.com, "rgmustain" <rgmustain@a...>

wrote:

> > 1) Does your analysis tell you at which level(s) the RF's are

hit?

>
> Not at this time. It would be easy to add. I'm not sure how
>meaningful it is since any RF will meet the overall goal and end

the

>session.

Right--It wouldn't change the number of winning sessions, but it
might be interesting to see how many lower level RF's there are
compared to upper level. Right now, in 252 sessions, I have one at
$25, two at $10, but more at $5 than $2 OR $1.

Back in 1996 I wasn't given any options for my 40-credit subgoal.
Just my overall session goal was recommended to be lowered from

$3000

to $2500, which I did. So whatever you come up with would be
interesting.

Just as with your statement that you don't believe any progressive
system can end up positive, my position is that since I've had
exceptional success with my strategy and the fact that it is far

more

···

interesting to play than straight-up expert strategy, I would never
go back.

#26

I'm not 100% sure I understand. I start with 100 credits at $1 BP. 50
credits into it I hit four fours for a 200 credits win and a 150 credit
profit. That 150 is now soft profit that will only go towards the
overall session win goal of $2500--unless I lose. Now I restart at
dollar BP and lose 100 credits with no cashouts, then lose 300 credits
with no cashouts. I go to $2, and lose 100 credits on BP with no
cashouts. On $2 DB I hit a 50-credit FH on my 1st hand. That's a 45
credit cashout. I now have $150 + $90 in soft profit. I restart on $2
DB. 100 credits in I hit four 6's, so I cash out, put another $100 into
soft pofit (now at $340), and begin again at $2 BP because I recovered
the 100 credits lost on $2 DB, the 100 credits lost on $2 BP, and along
with the first 45 credit cashout, I now have 95 credits profit at the
$2 level whereas I only require 40 whenever I reach a goal and restart
at a less volatile game (BP) within the same denomination. Note: Those
95 credits ($190) of 'soft profit' so far from the $2 level are to be
used as recovery of the dollar game losses in order to get back to
dollar BP if another 105 credits are cashed out on $2 along with at
least a 40-credit profit. So the $340 total in 'soft profit' above can
and does change whenever there is recovery. The entire purpose of the
strategy is to keep playing at the lowest level possible, and to wait
for the hits to come so the soft profit will eventually add up to at
least +$2500. That's why many sessions end at the $5 level, and quite a
few end at the $10 level.

···

--- In FREEvpFREE@yahoogroups.com, "rgmustain" <rgmustain@a...> wrote:

One more question. If you make a 40 credit subgoal I've been assuming
you only take out the 40 credits and any additional part of the win
would supplement your credits at the current level. If you take the
entire win (>= the subgoal) but less than a level reset then I need
to make some changes.

#27

--- In FREEvpFREE@yahoogroups.com, "rsing1111" <rsinger1111@c...>
wrote:

--- In FREEvpFREE@yahoogroups.com, "rgmustain" <rgmustain@a...>

wrote:

> One more question. If you make a 40 credit subgoal I've been

assuming

> you only take out the 40 credits and any additional part of the

win

> would supplement your credits at the current level. If you take

the

> entire win (>= the subgoal) but less than a level reset then I

need

> to make some changes.

I'm not 100% sure I understand. I start with 100 credits at $1 BP.

50

credits into it I hit four fours for a 200 credits win and a 150

credit

profit. That 150 is now soft profit that will only go towards the
overall session win goal of $2500--unless I lose. Now I restart at
dollar BP and lose 100 credits with no cashouts, then lose 300

credits

with no cashouts. I go to $2, and lose 100 credits on BP with no
cashouts. On $2 DB I hit a 50-credit FH on my 1st hand. That's a 45
credit cashout. I now have $150 + $90 in soft profit. I restart on

$2

DB. 100 credits in I hit four 6's, so I cash out, put another $100

into

soft pofit (now at $340), and begin again at $2 BP because I

recovered

the 100 credits lost on $2 DB, the 100 credits lost on $2 BP, and

along

with the first 45 credit cashout, I now have 95 credits profit at

the

$2 level whereas I only require 40 whenever I reach a goal and

restart

at a less volatile game (BP) within the same denomination. Note:

Those

95 credits ($190) of 'soft profit' so far from the $2 level are to

be

used as recovery of the dollar game losses in order to get back to
dollar BP if another 105 credits are cashed out on $2 along with at
least a 40-credit profit. So the $340 total in 'soft profit' above

can

and does change whenever there is recovery. The entire purpose of

the

strategy is to keep playing at the lowest level possible, and to

wait

for the hits to come so the soft profit will eventually add up to

at

least +$2500. That's why many sessions end at the $5 level, and

quite a

few end at the $10 level.

Looks like I will need to do some more work. I will look into this a
little further.

In the first example above I was pulling out $40 out of the $150 and
adding $110 to the current credits. In other words I put away only 40
credits worth of the win each time a win was at 40 credits. This 40
credit win would only go towards the overall goal of $2500 and never
be used to reset to a lower level. If the win was greater than 40
credits AND enough to recover both the current levels losses and the
previous levels losses, then I would reset.

I was never using the sum of the 40 credit wins for anything other
than the final goal. If any win plus the soft wins were greater than
$2500 then I would end the session with a net win. It looks like I
will need to use two soft win buckets, one for the previous levels
and one for the current level.

Let me know if this sounds right or if I'm still missing something.

By the way, I have some interesting results comparing my previous
understanding with using no subgoals. I ran several tests with a 40
credit subgoal and no subgoals. In every case the test with no
subgoal generated more overall wins. However, the payback was not
effected. Sometimes one way had a better overall payback and
sometimes it was the other.

The gain in wins was only around 2-4% so the difference was minimal.
On the 6 level game it went from an average of 80% to an average of
83%. Naturally the average win dropped by about the same amount as
the win rate increased.

Here's another little tidbit to consider. With the extra hands played
with no subgoal you end up with about 25% more coin-in per session.
In the example given below and a cashback rate of .2% you would get
around $202 with no subgoals and $166 with a 40 credit subgoal. Of
course, this difference is offset by the additional loss incurred by
playing more hands on negative machines. On positive machines this
would have a double benefit, however, you could simply run more
sessions to offset this difference.

Also, you can check out the total RFs below (I did not average these
per session because of the low number of RFs). The average number of
hands per session decreases level by level. This is more evident when
subgoals are not used. Level 2 has about 40% of the hands as level 1,
level 3 has about 40% of the hands as level 2, and so on. When a 40
credit subgoal is used the drop in hands is much less. The lower
level plays around 60% of the next higher level. I should also note
that using a 40 credit subgoal reduces the number of hands played per
session significantly (4200 vs. 6600) and with the higher percentage
played at a higher denom this has the effect of increasing the
volatility as well.

In either case your RFs should follow the same pattern. Given this
ratio you have clearly been fortunate to hit as many as you have at
the $5 level.

···

----------------------------------------------------------------------
-------------------

Run 1) with 40 credit subgoals over 1000 sessions

seed = 2345
8-5BP 0.99166 10-7DB 1.001725 8-5BP 0.99166 10-7DB 1.001725 8-5BP
0.99166 10-6DDB 1.00067 8-5BP 0.99166 9-5TB+ 0.998033 8-5BP 0.99166 9-
5TB+ 0.998033
Average hands at level 1 = 1147 with 38 royals
Average hands at level 2 = 729 with 12 royals
Average hands at level 3 = 505 with 15 royals
Average hands at level 4 = 538 with 9 royals
Average hands at level 5 = 296 with 5 royals
Average hands at level 6 = 313 with 7 royals
Average hands at level 7 = 210 with 8 royals
Average hands at level 8 = 186 with 4 royals
Average hands at level 9 = 108 with 2 royals
Average hands at level 10 = 115 with 4 royals
Number of wins = 682 averaging 6341.612903
Number of losses = 318 averaging 14725.974843
Subgoal hits = 11.468 Level resets = 5.869 Level losses = 12.275
Average wagered = 82981.84 for payback of 99.568725 (-357.88/session)
Expected payback = 99.543586 Total hands per session = 4153.834
Average bet = 3.995434

Run 2) with no subgoals over 1000 sessions

seed = 2345
8-5BP 0.99166 10-7DB 1.001725 8-5BP 0.99166 10-7DB 1.001725 8-5BP
0.99166 10-6DDB 1.00067 8-5BP 0.99166 9-5TB+ 0.998033 8-5BP 0.99166 9-
5TB+ 0.998033
Average hands at level 1 = 2776 with 78 royals
Average hands at level 2 = 1047 with 19 royals
Average hands at level 3 = 742 with 19 royals
Average hands at level 4 = 699 with 12 royals
Average hands at level 5 = 367 with 10 royals
Average hands at level 6 = 355 with 12 royals
Average hands at level 7 = 233 with 6 royals
Average hands at level 8 = 197 with 1 royals
Average hands at level 9 = 116 with 5 royals
Average hands at level 10 = 105 with 1 royals
Number of wins = 694 averaging 6353.854467
Number of losses = 306 averaging 15594.754902
Subgoal hits = 0 Level resets = 10.839 Level losses = 16.561001
Average wagered = 100957.475 for payback of 99.641017 (-
362.42/session)
Expected payback = 99.513194 Total hands per session = 6643.276
Average bet = 3.039388

#28

In the first example above I was pulling out $40 out of the $150
and adding $110 to the current credits. In other words I put away
only 40 credits worth of the win each time a win was at 40 credits.
This 40 credit win would only go towards the overall goal of $2500
and never be used to reset to a lower level. If the win was greater
than 40 credits AND enough to recover both the current levels losses
and the previous levels losses, then I would reset. I was never
using the sum of the 40 credit wins for anything other than the
final goal. If any win plus the soft wins were greater than
$2500 then I would end the session with a net win. It looks like I
will need to use two soft win buckets, one for the previous levels
and one for the current level. Let me know if this sounds right or

if I'm still missing something.

The only procedure you didn't have down now seems clearly understood.
Soft profits ARE used towards the overall session win goal, but their
first purpose is to keep the player at the lowest level possible.
That's why there's always a requirement to have made at least a 40-
credit profit when covering losses and reverting back to BP at any
level. These particular 'profits' are never risked, and serve to
reduce the overall loss if the session ends up a loser as well as
alternately serve to total up to a winning session.

By the way, I have some interesting results comparing my previous
understanding with using no subgoals. I ran several tests with a 40
credit subgoal and no subgoals. In every case the test with no
subgoal generated more overall wins. However, the payback was not
effected. Sometimes one way had a better overall payback and
sometimes it was the other. The gain in wins was only around 2-4%
so the difference was minimal. On the 6 level game it went from an
average of 80% to an average of 83%. Naturally the average win
dropped by about the same amount as the win rate increased.

I think that will change once your program is changed. The method in
which you utilized the subgoals seems like it would support your
analyses with no subgoals. I would have thought it would be a more
radical difference though.

Here's another little tidbit to consider. With the extra hands
played with no subgoal you end up with about 25% more coin-in per
session. In the example given below and a cashback rate of .2% you
would get around $202 with no subgoals and $166 with a 40 credit
subgoal. Of course, this difference is offset by the additional loss
incurred by playing more hands on negative machines. On positive
machines this would have a double benefit, however, you could simply
run more sessions to offset this difference.

That appears to fall into place as being reasonable. In the
strategy's original development I did not include slot club benefits
because I did not want to rely upon using the card for overall profit-
taking. As I found after about 150 sessions, this type of play with a
card attracts eyes, and I don't want to be tracked. Eventually, as I
figured, Harrah's & Bellagio caught on and banned me for over a year.
I stopped using my card at that time with this strategy only, and
although this style play attracts eyes at many casinos even without a
card (because they're always coming over and asking if I'd like
to "join" their player's clubs, especially when they see me at $5 and
above machines) when issued W2G's the small talk usually evolves
into "I'll probably lose it all anyway when I come back" which of
course takes their minds off of the effects of any large win. I 're-
entered' Harrah's system on my own through playing my other
strategies with a card at the Rio. Ironically, I went back to
Bellagio and played a few sessions without a card, and that's where I
also then hit the $25 RF. Not a word was said.

Also, you can check out the total RFs below (I did not average
these per session because of the low number of RFs). The average
number of hands per session decreases level by level. This is more
evident when subgoals are not used. Level 2 has about 40% of the
hands as level 1, level 3 has about 40% of the hands as level 2, and
so on. When a 40 credit subgoal is used the drop in hands is much
less. The lower level plays around 60% of the next higher level. I
should also note that using a 40 credit subgoal reduces the number
of hands played per session significantly (4200 vs. 6600) and with
the higher percentage played at a higher denom this has the effect
of increasing the volatility as well. In either case your RFs should
follow the same pattern. Given this ratio you have clearly been
fortunate to hit as many as you have at the $5 level.

Interesting. And I've always known I have had better RF luck at the
$5 machines. There was one stretch in I think 2001 that I hit $5
royals 3 sessions in a row.

Regarding the special plays: I remember these were analyzed on their
own merit, that is, as a function of their true value in relationship
to either a final smaller winning hand or the opportunity of
improving somewhat on a dealt small winning hand (i.e., dealt 2-pr.
in DB and going for the FH). EV-wise, a hand's value is a hand's
value. The intangible is in using these plays to attain a goal, or
(and much less prevalent) in NOT using these plays because the hand's
possibility of obtaining the goal (usually subgoal) with the small
winner makes it more reasonable to make the optimal play. What was
looked at was the frequency of hitting the big winners by 'going for
them' when the opportunity existed. Many times we're dealt two 3's
for instance - and nothing else - so we naturally go for the quad.
How many more times are "two 3's" and two other cards (not Aces)
dealt that expert play says never to go for the 3's, but we would
have hit them if we did? Over millions of hands, it should be the
optimal play that prevails. But in the short-term and with goals in
mind, my plays have the advantage. I'm trying to look through old
records to quantify how/why that is, but having just moving it may
take a little while.

···

--- In FREEvpFREE@yahoogroups.com, "rgmustain" <rgmustain@a...> wrote:

#29

I'm still not sure I have it EXACTLY right. However, I'm not sure it
matters. What I have found by varying the subgoals and the mechanisms
is a definite pattern. I don't think these should be too surprising.

The more money taken out as you play reduces the total number of
hands played. Here's an example with all money won used to reset a
previous level. A subgoal value of 0 was used:

seed = 34567
8-5BP 0.99166 10-7DB 1.001725 8-5BP 0.99166 10-7DB 1.001725 8-5BP
0.99166 10-6DDB 1.00067 8-5BP 0.99166 9-5TB+ 0.998033 8-5BP 0.99166 9-
5TB+ 0.998033
Average hands at level 1 = 6570 with 165 royals
Average hands at level 2 = 3830 with 75 royals
Average hands at level 3 = 1011 with 21 royals
Average hands at level 4 = 871 with 12 royals
Average hands at level 5 = 338 with 8 royals
Average hands at level 6 = 356 with 8 royals
Average hands at level 7 = 207 with 8 royals
Average hands at level 8 = 199 with 3 royals
Average hands at level 9 = 84 with 3 royals
Average hands at level 10 = 94 with 2 royals
Number of wins = 704 averaging 6262.663352
Number of losses = 296 averaging 15627.804054
Subgoal hits = 344.962006 Level resets = 70.797997 Level losses =
75.555
Average wagered = 130856.88 for payback of 99.834235 (-
216.915/session)
Expected payback = 99.547592 Total hands per session = 13563.417
Average bet = 1.929556, CB per session at .2% = 261.71376

The more often you use wins to revert back to lower levels the more
hands you will play in a session with the majority of the hands at
the lower denominations.

On the other hand, if all credits are played at the level they are
won (subgoal > win goal) then the total hands played will be the
lowest. This generally increases the average bet which increases the
average win, however, you will always lose the maximum in your
losses.

seed = 34567
8-5BP 0.99166 10-7DB 1.001725 8-5BP 0.99166 10-7DB 1.001725 8-5BP
0.99166 10-6DDB 1.00067 8-5BP 0.99166 9-5TB+ 0.998033 8-5BP 0.99166 9-
5TB+ 0.998033
Average hands at level 1 = 697 with 9 royals
Average hands at level 2 = 1786 with 30 royals
Average hands at level 3 = 518 with 10 royals
Average hands at level 4 = 1091 with 20 royals
Average hands at level 5 = 325 with 8 royals
Average hands at level 6 = 383 with 11 royals
Average hands at level 7 = 230 with 4 royals
Average hands at level 8 = 214 with 3 royals
Average hands at level 9 = 120 with 3 royals
Average hands at level 10 = 122 with 3 royals
Number of wins = 705 averaging 6235.794326
Number of losses = 295 averaging 17200
Subgoal hits = 0 Level resets = 0 Level losses = 6.578
Average wagered = 98914.475 for payback of 99.314797 (-
677.765/session)
Expected payback = 99.623211 Total hands per session = 5491.722
Average bet = 3.602312, CB per session at .2% = 197.82895

The final example uses a 40 credit subgoal (Robs' strategy). As you
can see this method finds its' way in the middle of the two extremes.
Setting higher subgoals would approach the second example. Note that
the average bet and the number of hands played are between the other
two examples.

seed = 34567
8-5BP 0.99166 10-7DB 1.001725 8-5BP 0.99166 10-7DB 1.001725 8-5BP
0.99166 10-6DDB 1.00067 8-5BP 0.99166 9-5TB+ 0.998033 8-5BP 0.99166 9-
5TB+ 0.998033
Average hands at level 1 = 3045 with 71 royals
Average hands at level 2 = 3165 with 71 royals
Average hands at level 3 = 889 with 19 royals
Average hands at level 4 = 930 with 11 royals
Average hands at level 5 = 290 with 7 royals
Average hands at level 6 = 336 with 6 royals
Average hands at level 7 = 152 with 3 royals
Average hands at level 8 = 174 with 3 royals
Average hands at level 9 = 78 with 2 royals
Average hands at level 10 = 99 with 0 royals
Number of wins = 692 averaging 5482.348266
Number of losses = 308 averaging 15157.711039
Subgoal hits = 43.215 Level resets = 34.179001 Level losses =
39.299999
Average wagered = 103395.855 for payback of 99.153941 (-
874.79/session)
Expected payback = 99.613997 Total hands per session = 9161.318
Average bet = 2.257227, CB per session at .2% = 206.79171

You should ignore the payback of these various example. By selecting
another seed I can make any approach return the best. No method
changes the overall payback of the game. However, good luck at the
highest levels dominates everything else in determining long term
success. Almost every time the best payback will be determined by
whatever simulation has the most RFs at the higher levels.

The next thing I am going to try is to vary the probabilities of the
lower levels. I will do this by reduces the probability of two pair
and 3 of a kind and increasing the 4 of kinds. The idea is to
simulate the special plays. I realize this will never simulate them
exactly, however, I want to see to what degree they influence a given
simulation.

I will also be looking at positive plays. I think the current sims
are somewhat influenced by the number of hands played using BP. This
is the lowest return game of the bunch. By replacing this game with a
higher payback game, even make it a reasonable progressive, and it
may make a big difference.

Dick

#30

One statement you made below "On the other hand, if all credits are
played at the level they are won (subgoal > win goal) then the total
hands played will be the lowest. This generally increases the average
bet which increases the average win, however, you will always lose
the maximum in your losses."

I don't understand how my losses will always be 'the maximum'. Does
that mean (using just 5 levels) it's $17,200? I know you've run
thousands of sims, but in 252 sessions that has not happened. I must
be misunderstanding.

I agree with your approach trying to incorporate the special plays.
Also, is it possible to run 10% of the sessions at 6 levels?

I'm still not sure I have it EXACTLY right. However, I'm not sure

it

matters. What I have found by varying the subgoals and the

mechanisms

is a definite pattern. I don't think these should be too surprising.

The more money taken out as you play reduces the total number of
hands played. Here's an example with all money won used to reset a
previous level. A subgoal value of 0 was used:

seed = 34567
8-5BP 0.99166 10-7DB 1.001725 8-5BP 0.99166 10-7DB 1.001725 8-5BP
0.99166 10-6DDB 1.00067 8-5BP 0.99166 9-5TB+ 0.998033 8-5BP 0.99166

9-

5TB+ 0.998033
Average hands at level 1 = 6570 with 165 royals
Average hands at level 2 = 3830 with 75 royals
Average hands at level 3 = 1011 with 21 royals
Average hands at level 4 = 871 with 12 royals
Average hands at level 5 = 338 with 8 royals
Average hands at level 6 = 356 with 8 royals
Average hands at level 7 = 207 with 8 royals
Average hands at level 8 = 199 with 3 royals
Average hands at level 9 = 84 with 3 royals
Average hands at level 10 = 94 with 2 royals
Number of wins = 704 averaging 6262.663352
Number of losses = 296 averaging 15627.804054
Subgoal hits = 344.962006 Level resets = 70.797997 Level losses =
75.555
Average wagered = 130856.88 for payback of 99.834235 (-
216.915/session)
Expected payback = 99.547592 Total hands per session = 13563.417
Average bet = 1.929556, CB per session at .2% = 261.71376

The more often you use wins to revert back to lower levels the more
hands you will play in a session with the majority of the hands at
the lower denominations.

On the other hand, if all credits are played at the level they are
won (subgoal > win goal) then the total hands played will be the
lowest. This generally increases the average bet which increases

the

average win, however, you will always lose the maximum in your
losses.

seed = 34567
8-5BP 0.99166 10-7DB 1.001725 8-5BP 0.99166 10-7DB 1.001725 8-5BP
0.99166 10-6DDB 1.00067 8-5BP 0.99166 9-5TB+ 0.998033 8-5BP 0.99166

9-

5TB+ 0.998033
Average hands at level 1 = 697 with 9 royals
Average hands at level 2 = 1786 with 30 royals
Average hands at level 3 = 518 with 10 royals
Average hands at level 4 = 1091 with 20 royals
Average hands at level 5 = 325 with 8 royals
Average hands at level 6 = 383 with 11 royals
Average hands at level 7 = 230 with 4 royals
Average hands at level 8 = 214 with 3 royals
Average hands at level 9 = 120 with 3 royals
Average hands at level 10 = 122 with 3 royals
Number of wins = 705 averaging 6235.794326
Number of losses = 295 averaging 17200
Subgoal hits = 0 Level resets = 0 Level losses = 6.578
Average wagered = 98914.475 for payback of 99.314797 (-
677.765/session)
Expected payback = 99.623211 Total hands per session = 5491.722
Average bet = 3.602312, CB per session at .2% = 197.82895

The final example uses a 40 credit subgoal (Robs' strategy). As you
can see this method finds its' way in the middle of the two

extremes.

Setting higher subgoals would approach the second example. Note

that

the average bet and the number of hands played are between the

other

two examples.

seed = 34567
8-5BP 0.99166 10-7DB 1.001725 8-5BP 0.99166 10-7DB 1.001725 8-5BP
0.99166 10-6DDB 1.00067 8-5BP 0.99166 9-5TB+ 0.998033 8-5BP 0.99166

9-

5TB+ 0.998033
Average hands at level 1 = 3045 with 71 royals
Average hands at level 2 = 3165 with 71 royals
Average hands at level 3 = 889 with 19 royals
Average hands at level 4 = 930 with 11 royals
Average hands at level 5 = 290 with 7 royals
Average hands at level 6 = 336 with 6 royals
Average hands at level 7 = 152 with 3 royals
Average hands at level 8 = 174 with 3 royals
Average hands at level 9 = 78 with 2 royals
Average hands at level 10 = 99 with 0 royals
Number of wins = 692 averaging 5482.348266
Number of losses = 308 averaging 15157.711039
Subgoal hits = 43.215 Level resets = 34.179001 Level losses =
39.299999
Average wagered = 103395.855 for payback of 99.153941 (-
874.79/session)
Expected payback = 99.613997 Total hands per session = 9161.318
Average bet = 2.257227, CB per session at .2% = 206.79171

You should ignore the payback of these various example. By

selecting

another seed I can make any approach return the best. No method
changes the overall payback of the game. However, good luck at the
highest levels dominates everything else in determining long term
success. Almost every time the best payback will be determined by
whatever simulation has the most RFs at the higher levels.

The next thing I am going to try is to vary the probabilities of

the

lower levels. I will do this by reduces the probability of two pair
and 3 of a kind and increasing the 4 of kinds. The idea is to
simulate the special plays. I realize this will never simulate them
exactly, however, I want to see to what degree they influence a

given

simulation.

I will also be looking at positive plays. I think the current sims
are somewhat influenced by the number of hands played using BP.

This

is the lowest return game of the bunch. By replacing this game with

a

···

--- In FREEvpFREE@yahoogroups.com, "rgmustain" <rgmustain@a...> wrote:

higher payback game, even make it a reasonable progressive, and it
may make a big difference.

Dick

#31

--- In FREEvpFREE@yahoogroups.com, "rsing1111" <rsinger1111@c...>
wrote:

One statement you made below "On the other hand, if all credits are
played at the level they are won (subgoal > win goal) then the

total

hands played will be the lowest. This generally increases the

average

bet which increases the average win, however, you will always lose
the maximum in your losses."

I don't understand how my losses will always be 'the maximum'. Does
that mean (using just 5 levels) it's $17,200? I know you've run
thousands of sims, but in 252 sessions that has not happened. I

must

be misunderstanding.

This statement was not intended to evaluate your strategy. It is
intended to evaluate a strategy that never uses subgoals. Since a
strategy of this kind would never generate any small wins you would
always lose the maximum if you don't reach the primary goal. This is
the opposite of a strategy that uses ALL money won to reset to lower
levels. You strategy falls somewhere inbetween.

If you go back and look at the results you will see I showed the 3
different types of strategies. I did this to show how subgoals impact
the way the progression runs. I thought this was an interesting
result in the degree to which the sims changed. Maybe I need to
describe this in more detail.

I agree with your approach trying to incorporate the special plays.
Also, is it possible to run 10% of the sessions at 6 levels?

Yes. I will look into this.

#32

I've re-read it and I now understand.

--- In FREEvpFREE@yahoogroups.com, "rsing1111" <rsinger1111@c...>
wrote:
>
> One statement you made below "On the other hand, if all credits

are

> played at the level they are won (subgoal > win goal) then the
total
> hands played will be the lowest. This generally increases the
average
> bet which increases the average win, however, you will always

lose

> the maximum in your losses."
>
> I don't understand how my losses will always be 'the maximum'.

Does

> that mean (using just 5 levels) it's $17,200? I know you've run
> thousands of sims, but in 252 sessions that has not happened. I
must
> be misunderstanding.

This statement was not intended to evaluate your strategy. It is
intended to evaluate a strategy that never uses subgoals. Since a
strategy of this kind would never generate any small wins you would
always lose the maximum if you don't reach the primary goal. This

is

the opposite of a strategy that uses ALL money won to reset to

lower

levels. You strategy falls somewhere inbetween.

If you go back and look at the results you will see I showed the 3
different types of strategies. I did this to show how subgoals

impact

the way the progression runs. I thought this was an interesting
result in the degree to which the sims changed. Maybe I need to
describe this in more detail.

>
> I agree with your approach trying to incorporate the special

plays.

···

--- In FREEvpFREE@yahoogroups.com, "rgmustain" <rgmustain@a...> wrote:

> Also, is it possible to run 10% of the sessions at 6 levels?

Yes. I will look into this.

#33

--- In FREEvpFREE@yahoogroups.com, "rsing1111" <rsinger1111@c...>
wrote:

I agree with your approach trying to incorporate the special plays.
Also, is it possible to run 10% of the sessions at 6 levels?

Here is a 1000 session run with 10% at level 6. You'll need to
multiply result levels 11 and 12 by 10 to get the average number of
hands since the program still divides the all the levels by the total
sessions. I also replaced BP with Aces and Eights to show how the
better payback (99.8) increases the number of hands. I also made a
change to TBP to reduce the two pairs and increase the quads. This
netted a lower payback for this game. This is my first attempt at
this combination. I plan on looking at it in more detail to better
assess the impact to the play.

seed = 11653
Aand8 0.997818 10-7DB 1.001725 Aand8 0.997818 10-7DB 1.001725 Aand8
0.997818 10-6DDB 1.00067 Aand8 0.997818 9-5TB+ 0.995467 Aand8
0.997818 9-5TB+ 0.995467 Aand8 0.997818 8-5SA 0.998371
Average hands at level 1 = 2717 with 52 royals
Average hands at level 2 = 2844 with 58 royals
Average hands at level 3 = 785 with 18 royals
Average hands at level 4 = 842 with 15 royals
Average hands at level 5 = 284 with 11 royals
Average hands at level 6 = 320 with 11 royals
Average hands at level 7 = 148 with 5 royals
Average hands at level 8 = 164 with 6 royals
Average hands at level 9 = 75 with 4 royals
Average hands at level 10 = 87 with 3 royals
Average hands at level 11 = 4 with 0 royals
Average hands at level 12 = 4 with 0 royals
Number of wins = 738 averaging 6366.863144
Number of losses = 262 averaging 17765.19084
Subgoal hits = 38.683998 Level resets = 30.587999 Level losses =
35.438
Average wagered = 99925.74 for payback of 100.044298 (44.265/session)
Expected payback = 99.849518 Total hands per session = 8280.154
Average bet = 2.41362, CB per session at .2% = 199.85148

#34

Questions: When you eliminate the 2-pr. to go for a quad, is there a
determinant that only does it at certain times when a special quad
can occur? For instance, 2's, 3's, & 4's on all the Advanced Bonus
games; plus J's, Q's, & K's on SDBP. Also, except in BP on $25 &
$100. I always keep a pair of Aces over two pair, regardless if the
FH will get me to a goal.

I didn't see any RF's at level 6. How about letting me have one or
two?

--- In FREEvpFREE@yahoogroups.com, "rsing1111" <rsinger1111@c...>
wrote:

> I agree with your approach trying to incorporate the special

plays.

> Also, is it possible to run 10% of the sessions at 6 levels?

Here is a 1000 session run with 10% at level 6. You'll need to
multiply result levels 11 and 12 by 10 to get the average number of
hands since the program still divides the all the levels by the

total

sessions. I also replaced BP with Aces and Eights to show how the
better payback (99.8) increases the number of hands. I also made a
change to TBP to reduce the two pairs and increase the quads. This
netted a lower payback for this game. This is my first attempt at
this combination. I plan on looking at it in more detail to better
assess the impact to the play.

seed = 11653
Aand8 0.997818 10-7DB 1.001725 Aand8 0.997818 10-7DB 1.001725 Aand8
0.997818 10-6DDB 1.00067 Aand8 0.997818 9-5TB+ 0.995467 Aand8
0.997818 9-5TB+ 0.995467 Aand8 0.997818 8-5SA 0.998371
Average hands at level 1 = 2717 with 52 royals
Average hands at level 2 = 2844 with 58 royals
Average hands at level 3 = 785 with 18 royals
Average hands at level 4 = 842 with 15 royals
Average hands at level 5 = 284 with 11 royals
Average hands at level 6 = 320 with 11 royals
Average hands at level 7 = 148 with 5 royals
Average hands at level 8 = 164 with 6 royals
Average hands at level 9 = 75 with 4 royals
Average hands at level 10 = 87 with 3 royals
Average hands at level 11 = 4 with 0 royals
Average hands at level 12 = 4 with 0 royals
Number of wins = 738 averaging 6366.863144
Number of losses = 262 averaging 17765.19084
Subgoal hits = 38.683998 Level resets = 30.587999 Level losses =
35.438
Average wagered = 99925.74 for payback of 100.044298

(44.265/session)

···

--- In FREEvpFREE@yahoogroups.com, "rgmustain" <rgmustain@a...> wrote:

Expected payback = 99.849518 Total hands per session = 8280.154
Average bet = 2.41362, CB per session at .2% = 199.85148

#35

--- In FREEvpFREE@yahoogroups.com, "rsing1111" <rsinger1111@c...>
wrote:

Questions: When you eliminate the 2-pr. to go for a quad, is there

a

determinant that only does it at certain times when a special quad
can occur? For instance, 2's, 3's, & 4's on all the Advanced Bonus
games; plus J's, Q's, & K's on SDBP. Also, except in BP on $25 &
$100. I always keep a pair of Aces over two pair, regardless if the
FH will get me to a goal.

I didn't see any RF's at level 6. How about letting me have one or
two?

OK, here's one.

seed = 59994
Aand8 0.997818 10-7DB 1.001725 Aand8 0.997818 10-7DB 1.001725 Aand8
0.997818 10-6DDB 1.00067 Aand8 0.997818 9-5TB+ 0.995467 Aand8
0.997818 9-5TB+ 0.995467 Aand8 0.997818 8-5SA 0.998371
Average hands at level 1 = 2753 with 69 royals
Average hands at level 2 = 2839 with 73 royals
Average hands at level 3 = 781 with 16 royals
Average hands at level 4 = 835 with 17 royals
Average hands at level 5 = 277 with 5 royals
Average hands at level 6 = 319 with 4 royals
Average hands at level 7 = 152 with 4 royals
Average hands at level 8 = 169 with 5 royals
Average hands at level 9 = 77 with 2 royals
Average hands at level 10 = 82 with 2 royals
Average hands at level 11 = 4 with 0 royals
Average hands at level 12 = 5 with 1 royals
Number of wins = 760 averaging 6299.144737
Number of losses = 240 averaging 17502.333333
Subgoal hits = 38.831001 Level resets = 30.724001 Level losses =
35.313
Average wagered = 99795.645 for payback of 100.587992 (586.79/session)
Expected payback = 99.850042 Total hands per session = 8298.276
Average bet = 2.405214, CB per session at .2% = 199.59129

#36

I don't have the ability to discern specific cards on any hand. My
simulator only looks at hand results. This is done by examining how
often a hand occurs and using that to determine the probability of that
hand occurring. TO simulate these plays I increased the probability of
hitting the bonus quads and lowered the probability of hitting two pair
by simply changing how often they occur. This reduced the overall
payback (as expected). When applied to the simulations it does not
change the expected results. The overall results always approach the
expected results over time. With a progression it justs takes a little
longer.

I even tried running a progression using all positive games. I ran a
250 session sim 100 times to see how often the results exceeded
expectation. Here's a list of the results. The first column is the
actual results while the second column is the expected results. The
final number (49) is the number of times the expected results were
exceeded out of the total of 100. I changed the initial RNG seed on
each run. The wide range of results is very illuminating. It shows that
even for a positive set of games that the results can vary widely. The
49-51 ratio will be satisfying to those who think that's exactly what
should happen. I expect I would see the same thing with any set of
games (positive or negative).

starting seed = 4665564
99.980085 100.357508
101.756359 100.368806
99.141989 100.350262
98.907961 100.366304
98.321967 100.362153
100.215396 100.377546
105.71472 100.384406
100.667939 100.367886
101.845098 100.353123
100.052629 100.361836
98.449705 100.363018
99.003131 100.364958
98.115734 100.370781
100.239854 100.351
98.030315 100.369134
101.115029 100.361825
100.08179 100.361619
99.827441 100.369295
99.820034 100.367762
98.66508 100.34444
102.129609 100.382079
99.846044 100.354477
99.162209 100.357118
105.207271 100.367776
101.454015 100.366538
102.469237 100.366721
103.304821 100.370744
101.004198 100.369163
101.325167 100.389192
100.266225 100.379644
101.725596 100.385187
99.987202 100.363152
102.718679 100.367062
102.931626 100.36908
98.477857 100.354135
103.319487 100.373544
99.734407 100.368135
99.949089 100.361633
102.208048 100.372214
100.736569 100.375857
99.464818 100.355183
101.725052 100.376352
100.868766 100.385715
100.620338 100.362676
99.837715 100.359776
101.296141 100.368449
103.024831 100.363375
97.459764 100.371201
100.274734 100.36329
101.349243 100.362649
100.682489 100.353607
101.498906 100.36854
101.265777 100.357269
101.141265 100.377461
101.799235 100.359962
100.453099 100.359311
100.383038 100.349135
100.972312 100.367276
98.605494 100.373545
98.436663 100.364468
102.791472 100.373973
100.194031 100.357015
100.371692 100.373491
98.559464 100.352239
100.361331 100.355103
98.772599 100.36398
100.224813 100.353317
100.313037 100.366084
100.422492 100.360574
100.626853 100.364549
99.26369 100.364142
103.439155 100.359859
101.551 100.360675
101.143107 100.359624
100.8123 100.362828
100.144569 100.366244
99.342481 100.374173
101.300745 100.373595
101.698171 100.373001
98.17152 100.341307
101.203162 100.347445
98.900331 100.342244
98.234795 100.364119
101.392741 100.367235
99.33634 100.367587
97.51755 100.369766
100.888699 100.358792
101.275315 100.358759
100.412353 100.362328
99.725917 100.352509
98.6699 100.35576
100.039965 100.368425
99.085646 100.373547
99.746595 100.362146
97.670293 100.356196
101.608649 100.362645
102.566112 100.376652
98.420368 100.351049
100.228531 100.368028
49

···

--- In FREEvpFREE@yahoogroups.com, "rsing1111" <rsinger1111@c...> wrote:

Questions: When you eliminate the 2-pr. to go for a quad, is there a
determinant that only does it at certain times when a special quad
can occur? For instance, 2's, 3's, & 4's on all the Advanced Bonus
games; plus J's, Q's, & K's on SDBP. Also, except in BP on $25 &
$100. I always keep a pair of Aces over two pair, regardless if the
FH will get me to a goal.

#37

I guess you've gone as far as you could go. It all seems to lead down
the same path in one way or another. When I worked this I only looked
at 500 sessions because I didn't think I'd ever topple that, and a
number of the calculations were incorporated manually. True,
the 'science' was reduced the more my special plays that deviate from
optimal play were incorporated, but that's where short-term
expectation was involved and how it affected the per session results.
Some were big losses and there were more big winners than I've
experienced.

Variance is a big question when analyzing the strategy. For instance,
this weekend at Mandalay Bay I met my family (sister/brother/others)
who have never bought in to what I do, how I do it, or my results.
Fact is they're not into gambling. So I played a session for all to
see--only I started at 25c and went up to $10 (24c/$1/$5/$10). The
reason--they aren't used to seeing thousands of dollars from someone
they know being thrown around in a casino, and I tried to keep the
shock factor at a minimum. Most BP games were either 6/5 or 7/5, and
the DDB was 8/4. Terrible pay tables, but I truthfully don't rely on
them to win. I did rather lousy at the lower end, but all the big
quads--Aces several times, etc. - came at the top end and I left
+$2900. This is rather typical of what I've experienced in 250
previous sessions. Did negative games matter? Sure, I lost the
opportunity to play with the extra credits because of short-pay FH's
& Flushes, and I might have hit a Royal with those that were never
there. But I hit the Aces and other quads with what I DID have, and
without the progression I'd be crying in my beer even right now. The
longer the session on the same denomination the poorer I'd do--most
of the time. How I play it's just the opposite.

--- In FREEvpFREE@yahoogroups.com, "rsing1111" <rsinger1111@c...>

wrote:

>
> Questions: When you eliminate the 2-pr. to go for a quad, is

there a

> determinant that only does it at certain times when a special

quad

> can occur? For instance, 2's, 3's, & 4's on all the Advanced

Bonus

> games; plus J's, Q's, & K's on SDBP. Also, except in BP on $25 &
> $100. I always keep a pair of Aces over two pair, regardless if

the

> FH will get me to a goal.

I don't have the ability to discern specific cards on any hand. My
simulator only looks at hand results. This is done by examining how
often a hand occurs and using that to determine the probability of

that

hand occurring. TO simulate these plays I increased the probability

of

hitting the bonus quads and lowered the probability of hitting two

pair

by simply changing how often they occur. This reduced the overall
payback (as expected). When applied to the simulations it does not
change the expected results. The overall results always approach

the

expected results over time. With a progression it justs takes a

little

longer.

I even tried running a progression using all positive games. I ran

a

250 session sim 100 times to see how often the results exceeded
expectation. Here's a list of the results. The first column is the
actual results while the second column is the expected results. The
final number (49) is the number of times the expected results were
exceeded out of the total of 100. I changed the initial RNG seed on
each run. The wide range of results is very illuminating. It shows

that

even for a positive set of games that the results can vary widely.

The

49-51 ratio will be satisfying to those who think that's exactly

what

···

--- In FREEvpFREE@yahoogroups.com, "rgmustain" <rgmustain@a...> wrote:

should happen. I expect I would see the same thing with any set of
games (positive or negative).

starting seed = 4665564
99.980085 100.357508
101.756359 100.368806
99.141989 100.350262
98.907961 100.366304
98.321967 100.362153
100.215396 100.377546
105.71472 100.384406
100.667939 100.367886
101.845098 100.353123
100.052629 100.361836
98.449705 100.363018
99.003131 100.364958
98.115734 100.370781
100.239854 100.351
98.030315 100.369134
101.115029 100.361825
100.08179 100.361619
99.827441 100.369295
99.820034 100.367762
98.66508 100.34444
102.129609 100.382079
99.846044 100.354477
99.162209 100.357118
105.207271 100.367776
101.454015 100.366538
102.469237 100.366721
103.304821 100.370744
101.004198 100.369163
101.325167 100.389192
100.266225 100.379644
101.725596 100.385187
99.987202 100.363152
102.718679 100.367062
102.931626 100.36908
98.477857 100.354135
103.319487 100.373544
99.734407 100.368135
99.949089 100.361633
102.208048 100.372214
100.736569 100.375857
99.464818 100.355183
101.725052 100.376352
100.868766 100.385715
100.620338 100.362676
99.837715 100.359776
101.296141 100.368449
103.024831 100.363375
97.459764 100.371201
100.274734 100.36329
101.349243 100.362649
100.682489 100.353607
101.498906 100.36854
101.265777 100.357269
101.141265 100.377461
101.799235 100.359962
100.453099 100.359311
100.383038 100.349135
100.972312 100.367276
98.605494 100.373545
98.436663 100.364468
102.791472 100.373973
100.194031 100.357015
100.371692 100.373491
98.559464 100.352239
100.361331 100.355103
98.772599 100.36398
100.224813 100.353317
100.313037 100.366084
100.422492 100.360574
100.626853 100.364549
99.26369 100.364142
103.439155 100.359859
101.551 100.360675
101.143107 100.359624
100.8123 100.362828
100.144569 100.366244
99.342481 100.374173
101.300745 100.373595
101.698171 100.373001
98.17152 100.341307
101.203162 100.347445
98.900331 100.342244
98.234795 100.364119
101.392741 100.367235
99.33634 100.367587
97.51755 100.369766
100.888699 100.358792
101.275315 100.358759
100.412353 100.362328
99.725917 100.352509
98.6699 100.35576
100.039965 100.368425
99.085646 100.373547
99.746595 100.362146
97.670293 100.356196
101.608649 100.362645
102.566112 100.376652
98.420368 100.351049
100.228531 100.368028
49

#38

Rob,
      You've always made it a point to do what you say you're going to do....I can appreciate....but I noticed that you made a decision not to play anything above dollars throughout 2005. Did you play anything above dollars here and when you went on the session after the exchange with Cogno Scienti a few months back?

···

----- Original Message -----
  From: rsing1111
  To: FREEvpFREE@yahoogroups.com
  Sent: Monday, December 19, 2005 3:25 AM
  Subject: [FREEvpFREE] Re: Strategy

  I guess you've gone as far as you could go. It all seems to lead down
  the same path in one way or another. When I worked this I only looked
  at 500 sessions because I didn't think I'd ever topple that, and a
  number of the calculations were incorporated manually. True,
  the 'science' was reduced the more my special plays that deviate from
  optimal play were incorporated, but that's where short-term
  expectation was involved and how it affected the per session results.
  Some were big losses and there were more big winners than I've
  experienced.

  Variance is a big question when analyzing the strategy. For instance,
  this weekend at Mandalay Bay I met my family (sister/brother/others)
  who have never bought in to what I do, how I do it, or my results.
  Fact is they're not into gambling. So I played a session for all to
  see--only I started at 25c and went up to $10 (24c/$1/$5/$10). The
  reason--they aren't used to seeing thousands of dollars from someone
  they know being thrown around in a casino, and I tried to keep the
  shock factor at a minimum. Most BP games were either 6/5 or 7/5, and
  the DDB was 8/4. Terrible pay tables, but I truthfully don't rely on
  them to win. I did rather lousy at the lower end, but all the big
  quads--Aces several times, etc. - came at the top end and I left
  +$2900. This is rather typical of what I've experienced in 250
  previous sessions. Did negative games matter? Sure, I lost the
  opportunity to play with the extra credits because of short-pay FH's
  & Flushes, and I might have hit a Royal with those that were never
  there. But I hit the Aces and other quads with what I DID have, and
  without the progression I'd be crying in my beer even right now. The
  longer the session on the same denomination the poorer I'd do--most
  of the time. How I play it's just the opposite.

  --- In FREEvpFREE@yahoogroups.com, "rgmustain" <rgmustain@a...> wrote:
  >
  > --- In FREEvpFREE@yahoogroups.com, "rsing1111" <rsinger1111@c...>
  wrote:
  > >
  > > Questions: When you eliminate the 2-pr. to go for a quad, is
  there a
  > > determinant that only does it at certain times when a special
  quad
  > > can occur? For instance, 2's, 3's, & 4's on all the Advanced
  Bonus
  > > games; plus J's, Q's, & K's on SDBP. Also, except in BP on $25 &
  > > $100. I always keep a pair of Aces over two pair, regardless if
  the
  > > FH will get me to a goal.
  >
  > I don't have the ability to discern specific cards on any hand. My
  > simulator only looks at hand results. This is done by examining how
  > often a hand occurs and using that to determine the probability of
  that
  > hand occurring. TO simulate these plays I increased the probability
  of
  > hitting the bonus quads and lowered the probability of hitting two
  pair
  > by simply changing how often they occur. This reduced the overall
  > payback (as expected). When applied to the simulations it does not
  > change the expected results. The overall results always approach
  the
  > expected results over time. With a progression it justs takes a
  little
  > longer.
  >
  > I even tried running a progression using all positive games. I ran
  a
  > 250 session sim 100 times to see how often the results exceeded
  > expectation. Here's a list of the results. The first column is the
  > actual results while the second column is the expected results. The
  > final number (49) is the number of times the expected results were
  > exceeded out of the total of 100. I changed the initial RNG seed on
  > each run. The wide range of results is very illuminating. It shows
  that
  > even for a positive set of games that the results can vary widely.
  The
  > 49-51 ratio will be satisfying to those who think that's exactly
  what
  > should happen. I expect I would see the same thing with any set of
  > games (positive or negative).
  >
  > starting seed = 4665564
  > 99.980085 100.357508
  > 101.756359 100.368806
  > 99.141989 100.350262
  > 98.907961 100.366304
  > 98.321967 100.362153
  > 100.215396 100.377546
  > 105.71472 100.384406
  > 100.667939 100.367886
  > 101.845098 100.353123
  > 100.052629 100.361836
  > 98.449705 100.363018
  > 99.003131 100.364958
  > 98.115734 100.370781
  > 100.239854 100.351
  > 98.030315 100.369134
  > 101.115029 100.361825
  > 100.08179 100.361619
  > 99.827441 100.369295
  > 99.820034 100.367762
  > 98.66508 100.34444
  > 102.129609 100.382079
  > 99.846044 100.354477
  > 99.162209 100.357118
  > 105.207271 100.367776
  > 101.454015 100.366538
  > 102.469237 100.366721
  > 103.304821 100.370744
  > 101.004198 100.369163
  > 101.325167 100.389192
  > 100.266225 100.379644
  > 101.725596 100.385187
  > 99.987202 100.363152
  > 102.718679 100.367062
  > 102.931626 100.36908
  > 98.477857 100.354135
  > 103.319487 100.373544
  > 99.734407 100.368135
  > 99.949089 100.361633
  > 102.208048 100.372214
  > 100.736569 100.375857
  > 99.464818 100.355183
  > 101.725052 100.376352
  > 100.868766 100.385715
  > 100.620338 100.362676
  > 99.837715 100.359776
  > 101.296141 100.368449
  > 103.024831 100.363375
  > 97.459764 100.371201
  > 100.274734 100.36329
  > 101.349243 100.362649
  > 100.682489 100.353607
  > 101.498906 100.36854
  > 101.265777 100.357269
  > 101.141265 100.377461
  > 101.799235 100.359962
  > 100.453099 100.359311
  > 100.383038 100.349135
  > 100.972312 100.367276
  > 98.605494 100.373545
  > 98.436663 100.364468
  > 102.791472 100.373973
  > 100.194031 100.357015
  > 100.371692 100.373491
  > 98.559464 100.352239
  > 100.361331 100.355103
  > 98.772599 100.36398
  > 100.224813 100.353317
  > 100.313037 100.366084
  > 100.422492 100.360574
  > 100.626853 100.364549
  > 99.26369 100.364142
  > 103.439155 100.359859
  > 101.551 100.360675
  > 101.143107 100.359624
  > 100.8123 100.362828
  > 100.144569 100.366244
  > 99.342481 100.374173
  > 101.300745 100.373595
  > 101.698171 100.373001
  > 98.17152 100.341307
  > 101.203162 100.347445
  > 98.900331 100.342244
  > 98.234795 100.364119
  > 101.392741 100.367235
  > 99.33634 100.367587
  > 97.51755 100.369766
  > 100.888699 100.358792
  > 101.275315 100.358759
  > 100.412353 100.362328
  > 99.725917 100.352509
  > 98.6699 100.35576
  > 100.039965 100.368425
  > 99.085646 100.373547
  > 99.746595 100.362146
  > 97.670293 100.356196
  > 101.608649 100.362645
  > 102.566112 100.376652
  > 98.420368 100.351049
  > 100.228531 100.368028
  > 49
  >

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[Non-text portions of this message have been removed]

#39

Yes, but when my family's involved exceptions are always more
important than anything else. In this case, they've never been out to
understand what I do and how I do it, and in fact believed I should
have stayed working my 'corporate America' job instead of becoming
involved in such a 'degenerate activity'. I played a Romp Thru Town
type strategy, and they now have a more favorable view of how I make
my living. It still freaked them out to see me pull out $10,000 and
put in a thousand at a time. If you can remember back before you
gambled, carrying around that kind of cash certainly wasn't normal,
and in that scenario money was far better used to fix the car or add
a room.

I'm not recalling which session that was after the exchange with
Congo.

--- In FREEvpFREE@yahoogroups.com, "James Burtnett" <jimb777@w...>
wrote:

Rob,
You've always made it a point to do what you say you're going to

do....I can appreciate....but I noticed that you made a decision not
to play anything above dollars throughout 2005. Did you play
anything above dollars here and when you went on the session after
the exchange with Cogno Scienti a few months back?

                                     
  From: rsing1111
  To: FREEvpFREE@yahoogroups.com
  Sent: Monday, December 19, 2005 3:25 AM
  Subject: [FREEvpFREE] Re: Strategy

  I guess you've gone as far as you could go. It all seems to lead

down

  the same path in one way or another. When I worked this I only

looked

  at 500 sessions because I didn't think I'd ever topple that, and

a

  number of the calculations were incorporated manually. True,
  the 'science' was reduced the more my special plays that deviate

from

  optimal play were incorporated, but that's where short-term
  expectation was involved and how it affected the per session

results.

  Some were big losses and there were more big winners than I've
  experienced.

  Variance is a big question when analyzing the strategy. For

instance,

  this weekend at Mandalay Bay I met my family

(sister/brother/others)

  who have never bought in to what I do, how I do it, or my

results.

  Fact is they're not into gambling. So I played a session for all

to

  see--only I started at 25c and went up to $10 (24c/$1/$5/$10).

The

  reason--they aren't used to seeing thousands of dollars from

someone

  they know being thrown around in a casino, and I tried to keep

the

  shock factor at a minimum. Most BP games were either 6/5 or 7/5,

and

  the DDB was 8/4. Terrible pay tables, but I truthfully don't rely

on

  them to win. I did rather lousy at the lower end, but all the big
  quads--Aces several times, etc. - came at the top end and I left
  +$2900. This is rather typical of what I've experienced in 250
  previous sessions. Did negative games matter? Sure, I lost the
  opportunity to play with the extra credits because of short-pay

FH's

  & Flushes, and I might have hit a Royal with those that were

never

  there. But I hit the Aces and other quads with what I DID have,

and

  without the progression I'd be crying in my beer even right now.

The

  longer the session on the same denomination the poorer I'd do--

most

  of the time. How I play it's just the opposite.

  --- In FREEvpFREE@yahoogroups.com, "rgmustain" <rgmustain@a...>

wrote:

  >
  > --- In FREEvpFREE@yahoogroups.com, "rsing1111"

<rsinger1111@c...>

  wrote:
  > >
  > > Questions: When you eliminate the 2-pr. to go for a quad, is
  there a
  > > determinant that only does it at certain times when a special
  quad
  > > can occur? For instance, 2's, 3's, & 4's on all the Advanced
  Bonus
  > > games; plus J's, Q's, & K's on SDBP. Also, except in BP on

$25 &

  > > $100. I always keep a pair of Aces over two pair, regardless

if

  the
  > > FH will get me to a goal.
  >
  > I don't have the ability to discern specific cards on any hand.

My

  > simulator only looks at hand results. This is done by examining

how

  > often a hand occurs and using that to determine the probability

of

  that
  > hand occurring. TO simulate these plays I increased the

probability

  of
  > hitting the bonus quads and lowered the probability of hitting

two

  pair
  > by simply changing how often they occur. This reduced the

overall

  > payback (as expected). When applied to the simulations it does

not

  > change the expected results. The overall results always

approach

  the
  > expected results over time. With a progression it justs takes a
  little
  > longer.
  >
  > I even tried running a progression using all positive games. I

ran

  a
  > 250 session sim 100 times to see how often the results exceeded
  > expectation. Here's a list of the results. The first column is

the

  > actual results while the second column is the expected results.

The

  > final number (49) is the number of times the expected results

were

  > exceeded out of the total of 100. I changed the initial RNG

seed on

  > each run. The wide range of results is very illuminating. It

shows

  that
  > even for a positive set of games that the results can vary

widely.

  The
  > 49-51 ratio will be satisfying to those who think that's

exactly

  what
  > should happen. I expect I would see the same thing with any set

of

···

  ----- Original Message -----
  > games (positive or negative).
  >
  > starting seed = 4665564
  > 99.980085 100.357508
  > 101.756359 100.368806
  > 99.141989 100.350262
  > 98.907961 100.366304
  > 98.321967 100.362153
  > 100.215396 100.377546
  > 105.71472 100.384406
  > 100.667939 100.367886
  > 101.845098 100.353123
  > 100.052629 100.361836
  > 98.449705 100.363018
  > 99.003131 100.364958
  > 98.115734 100.370781
  > 100.239854 100.351
  > 98.030315 100.369134
  > 101.115029 100.361825
  > 100.08179 100.361619
  > 99.827441 100.369295
  > 99.820034 100.367762
  > 98.66508 100.34444
  > 102.129609 100.382079
  > 99.846044 100.354477
  > 99.162209 100.357118
  > 105.207271 100.367776
  > 101.454015 100.366538
  > 102.469237 100.366721
  > 103.304821 100.370744
  > 101.004198 100.369163
  > 101.325167 100.389192
  > 100.266225 100.379644
  > 101.725596 100.385187
  > 99.987202 100.363152
  > 102.718679 100.367062
  > 102.931626 100.36908
  > 98.477857 100.354135
  > 103.319487 100.373544
  > 99.734407 100.368135
  > 99.949089 100.361633
  > 102.208048 100.372214
  > 100.736569 100.375857
  > 99.464818 100.355183
  > 101.725052 100.376352
  > 100.868766 100.385715
  > 100.620338 100.362676
  > 99.837715 100.359776
  > 101.296141 100.368449
  > 103.024831 100.363375
  > 97.459764 100.371201
  > 100.274734 100.36329
  > 101.349243 100.362649
  > 100.682489 100.353607
  > 101.498906 100.36854
  > 101.265777 100.357269
  > 101.141265 100.377461
  > 101.799235 100.359962
  > 100.453099 100.359311
  > 100.383038 100.349135
  > 100.972312 100.367276
  > 98.605494 100.373545
  > 98.436663 100.364468
  > 102.791472 100.373973
  > 100.194031 100.357015
  > 100.371692 100.373491
  > 98.559464 100.352239
  > 100.361331 100.355103
  > 98.772599 100.36398
  > 100.224813 100.353317
  > 100.313037 100.366084
  > 100.422492 100.360574
  > 100.626853 100.364549
  > 99.26369 100.364142
  > 103.439155 100.359859
  > 101.551 100.360675
  > 101.143107 100.359624
  > 100.8123 100.362828
  > 100.144569 100.366244
  > 99.342481 100.374173
  > 101.300745 100.373595
  > 101.698171 100.373001
  > 98.17152 100.341307
  > 101.203162 100.347445
  > 98.900331 100.342244
  > 98.234795 100.364119
  > 101.392741 100.367235
  > 99.33634 100.367587
  > 97.51755 100.369766
  > 100.888699 100.358792
  > 101.275315 100.358759
  > 100.412353 100.362328
  > 99.725917 100.352509
  > 98.6699 100.35576
  > 100.039965 100.368425
  > 99.085646 100.373547
  > 99.746595 100.362146
  > 97.670293 100.356196
  > 101.608649 100.362645
  > 102.566112 100.376652
  > 98.420368 100.351049
  > 100.228531 100.368028
  > 49
  >

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[Non-text portions of this message have been removed]

#40

--- In FREEvpFREE@yahoogroups.com, "rsing1111" <rsinger1111@c...>
wrote:

I guess you've gone as far as you could go. It all seems to lead

down

the same path in one way or another. When I worked this I only

looked

at 500 sessions because I didn't think I'd ever topple that, and a
number of the calculations were incorporated manually. True,
the 'science' was reduced the more my special plays that deviate

from

optimal play were incorporated, but that's where short-term
expectation was involved and how it affected the per session

results.

Some were big losses and there were more big winners than I've
experienced.

The way to think about it for my approach is that the number of two
pairs are slightly reduced and the bonus quads hit more often. It
seems like this is exactly what you would see by applying your
special plays. What can never be simulated is whether you have some
instinct on when to make such plays. However, the simulations
demonstrate that it is certainly possible to be successful with or
without the special plays. They also show it is possible to have
disastrous results. The question no one will never be able to answer
is whether you would have been more or less successful by simply
using expert play on positive plays at an intermediate level ($5) and
sticking to your overall goal ($2500).

Variance is a big question when analyzing the strategy. For

instance,

this weekend at Mandalay Bay I met my family

(sister/brother/others)

who have never bought in to what I do, how I do it, or my results.
Fact is they're not into gambling. So I played a session for all to
see--only I started at 25c and went up to $10 (24c/$1/$5/$10). The
reason--they aren't used to seeing thousands of dollars from

someone

they know being thrown around in a casino, and I tried to keep the
shock factor at a minimum. Most BP games were either 6/5 or 7/5,

and

the DDB was 8/4. Terrible pay tables, but I truthfully don't rely

on

them to win. I did rather lousy at the lower end, but all the big
quads--Aces several times, etc. - came at the top end and I left
+$2900. This is rather typical of what I've experienced in 250
previous sessions.

Natually, this is what you'd expect from "hitting" on the higher
denom games. However, until you can show where this can be
accomplished on a regular basis (over expectation) then I think it is
dangerous to promote this kind of approach. I would suggest you
provide some of the information (now available through this
simulation) on your website. I have no problem with you pointing out
that all of these results require perfect play of the games used.

Did negative games matter? Sure, I lost the
opportunity to play with the extra credits because of short-pay

FH's

& Flushes, and I might have hit a Royal with those that were never
there. But I hit the Aces and other quads with what I DID have, and
without the progression I'd be crying in my beer even right now.

The

longer the session on the same denomination the poorer I'd do--most
of the time. How I play it's just the opposite.

Not sure if this is completely true. If you had played only at the $1
or $2 denom and hit just as many sets of aces you surely would have
had some success. In fact, if you look at the average bet I provide
in my output, it shows that you could have had pretty much the same
overall results as the progression if you played only at this
particular denomination. Fewer session wins to be sure, but smaller
losses when you did lose.

I've thought about using a progression for positive games. However,
the trade-offs don't work for me. It depends so much on your luck at
the high denominations which means the long term is even longer.
While this is clearly a good thing for negative plays, it doesn't
really make much sense for positive plays. It also gets down to
enjoyment. I doubt you really enjoyed your play at the .25 level and
I really wouldn't enjoy playing at denoms below my current level. You
could have had a $1000 RF and still missed your $2500 goal. I just
would not enjoy this prospect.

Dick