I wish you could edit your own posts here ...
Harry Porter wrote:
People are bound to make a best-avoided association with Stanford
Wong.
I meant simply it was "best to avoid" confusion, not that Wong was
disreputable 
- H.
Using Double Down
Thanks! I like the discussion about these "alternate strategies",
follow them as best I can, and have learned a lot.
It is nice to get, every now and them, a real gem in a thread like
this. This, I think is one of them.
This seems to tell me, pure and simple, a "result".
Perhaps, similar information like this, using other games and other
strategies, summarized like this, would allow a lot of us dummies to
consider trying alternate strategies, based on numbers
like "stanfordwang" has given us below.
In response to "GO BIG RED!", dare I say, "HOOK 'EM HORNS!" ?
Thanks, again.
.....bl
--- In vpFREE@yahoogroups.com, "stanfordwang" <stanfordwang@y...>
wrote:
another data point to ponder:
game is 9/6 jacks or better with 1%
cashback/bounceback/comp/whatever
max ER strategy:
ER=100.54%, Variance=19.5, R(1)=0.999365501, 10%ror bankroll=3628max Bankroll Growth strategy (rf=628,sf=49):
ER=100.53%, Variance=17.6, R(1)=0.999316638, 10%ror bankroll=3369In English, what this means is that for a small drop in average
return of .01% the bankroll on a 5 coin quarter machine drops from
$4535 to $4211. Or, as a crude approximation (2SD), after 2000
hands,
max ER is $13.50 plus or minus $494 while max Bankroll Growth is
$13.25 plus or minus $469. Is it worth it? Are there other games
where the difference is greater or less? You will have to
investigate
···
and decide.
P.S. About my name: GO BIG RED!
bornloser1537 wrote:
Perhaps, similar information like this, using other games and other
strategies, summarized like this, would allow a lot of us dummies to
consider trying alternate strategies, based on numbers
like "stanfordwang" has given us below.
Forgive me if I'm beating a dead horse here. I strongly advise
against pursuit of alternate strategies until you've refined and honed
your "basic" max-EV strategy -- say to the extent that your vp
software practice consistently reflects no more than approx .05% ER
penalty (or less) due to mistakes.
Unless you've got the basic play down cold, an attempt to complicate
your play with pursuit of other strategies will certainly involve an
additional cost that outweighs ALL advantage to the alternate strategy.
- Harry
I can do nothing but agree with Harry Potter. I am a staunch
believer in "MAX-ER UEBERALLES!" for the masses. (Just a joke.)
But, we are all curious and, at least here within this group, a lot
of us are trying to learn. A clear-cut summary like I mentioned,
about what alternate strategies can do (probabilistically) would
help some of us dummies see, more completely, the reasons why these
discussions should continue, and, giving us something to hang our
hat on, so to speak, encourage us to follow them (the discussions,
that is) as best we can.
Thanks to one and all, allowing me, in some small way, to input some
of my thoughts.
.....bl
--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@v...>
wrote:
bornloser1537 wrote:
> Perhaps, similar information like this, using other games and
other
> strategies, summarized like this, would allow a lot of us
dummies to
> consider trying alternate strategies, based on numbers
> like "stanfordwang" has given us below.Forgive me if I'm beating a dead horse here. I strongly advise
against pursuit of alternate strategies until you've refined and
honed
your "basic" max-EV strategy -- say to the extent that your vp
software practice consistently reflects no more than approx .05% ER
penalty (or less) due to mistakes.Unless you've got the basic play down cold, an attempt to
complicate
your play with pursuit of other strategies will certainly involve
an
additional cost that outweighs ALL advantage to the alternate
strategy.
···
- Harry
Isn't the strategy that you call "max Bankroll Growth" the same as
the one that I call min-risk? In other words, isn't it "sorokin optimized"?
If so, it seems to me that it is misleading to call it "max Bankroll Growth"
when the example you give shows that the bankroll grows slower.
Or are you using "bankroll growth" in a way that doesn't mean _rate_
of growth? This strategy does give the highest probability of success
for growing the bankroll by a specified factor using a fixed unit size,
is that what you mean?
···
On Wednesday 25 February 2004 01:56 am, stanfordwang wrote:
another data point to ponder:
game is 9/6 jacks or better with 1% cashback/bounceback/comp/whatevermax ER strategy:
ER=100.54%, Variance=19.5, R(1)=0.999365501, 10%ror bankroll=3628max Bankroll Growth strategy (rf=628,sf=49):
ER=100.53%, Variance=17.6, R(1)=0.999316638, 10%ror bankroll=3369In English, what this means is that for a small drop in average
return of .01% the bankroll on a 5 coin quarter machine drops from
$4535 to $4211. Or, as a crude approximation (2SD), after 2000 hands,
max ER is $13.50 plus or minus $494 while max Bankroll Growth is
$13.25 plus or minus $469. Is it worth it? Are there other games
where the difference is greater or less? You will have to investigate
and decide.
another data point to ponder:
...
P.S. About my name: GO BIG RED!
You went to Indiana University???
···
--- In vpFREE@yahoogroups.com, "stanfordwang" <stanfordwang@y...> wrote:
--
Pat O'Connell
Who went to Purdue and UNM
--- In vpFREE@yahoogroups.com, "stanfordwang" <stanfordwang@y...>
wrote:
Are there other games
where the difference is greater or less? You will have to
investigate
and decide.
Teach us how in a manner that we can understand
DWK
> another data point to ponder:
> game is 9/6 jacks or better with 1%
cashback/bounceback/comp/whatever
>
> max ER strategy:
> ER=100.54%, Variance=19.5, R(1)=0.999365501, 10%ror bankroll=3628
>
> max Bankroll Growth strategy (rf=628,sf=49):
> ER=100.53%, Variance=17.6, R(1)=0.999316638, 10%ror bankroll=3369
>
> In English, what this means is that for a small drop in average
> return of .01% the bankroll on a 5 coin quarter machine drops from
> $4535 to $4211. Or, as a crude approximation (2SD), after 2000
hands,
> max ER is $13.50 plus or minus $494 while max Bankroll Growth is
> $13.25 plus or minus $469. Is it worth it? Are there other games
> where the difference is greater or less? You will have to
investigate
> and decide.
Isn't the strategy that you call "max Bankroll Growth" the same as
the one that I call min-risk? In other words, isn't it "sorokin
optimized"?
If so, it seems to me that it is misleading to call it "max
Bankroll Growth"
when the example you give shows that the bankroll grows slower.
Or are you using "bankroll growth" in a way that doesn't mean _rate_
of growth? This strategy does give the highest probability of
success
for growing the bankroll by a specified factor using a fixed unit
size,
is that what you mean?
Yes, the strategy is Sorokin optimized, generated by setting the
royal to 628 instead of 800 and the straight flush to 49 instead of
50. But this is also the Max Bankroll Growth strategy.
Using the example above, after 2,000 hands:
Max ER strategy: bankroll growth = $13.50/$4535 = 0.298%
Max Bankroll Growth strategy: bankroll growth = $13.25/$4211 = 0.315%
Bankroll defined as money at risk, as it should be, because there is
always a finite chance (in the example, 10% risk of ruin) that you
could lose your entire bankroll. A riskier game requires a larger
bankroll, the question to ask is does the return justify the larger
bankroll. Bankroll growth is a good way to answer that question.
Seems to me, in this example, Max ER strategy does not justify the
larger bankroll (money at risk) required when compared to the results
returned by Max Bankroll Growth (Sorokin optimized) strategy.
···
--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x> wrote:
On Wednesday 25 February 2004 01:56 am, stanfordwang wrote:
Sorry, second request...where do I find the "min-risk" strategy for
9/6 JoB.
Thanks in advance,
Dave
--- "deuceswild1000" <deuceswild1000@y...> wrote:
--- "stanfordwang" <stanfordwang@y...> wrote:
> Are there other games
> where the difference is greater or less? You will have to
> investigate and decide.
Teach us how in a manner that we can understand
You can generate Sorokin optimized strategies using the data in:
http://groups.yahoo.com/group/vpFREE/message/26615
For example, for full pay deuces wild, substitute 623 for 800 for the
royal flush and 188 for 200 for quad deuces, and you will get the
Sorokin strategy. (I'm assuming you have a software package that
generates strategy for a given paytable, like vpsm or frugal)
To figure out the results of Sorokin strategy, unless there is some
software package that does it for you, you will have to do it by hand
like I do, as in:
http://groups.yahoo.com/group/vpFREE/message/26582
Harry Porter wrote:
I wish you could edit your own posts here ...
Harry Porter wrote:
> People are bound to make a best-avoided association with Stanford
> Wong.I meant simply it was "best to avoid" confusion, not that Wong was
disreputable
Oh, that's just GREAT. _NOW_ you tell us, ... but it's too late. I have already sent a scathing email to Mr. Wong, telling him to never write to me again. I hope he will accept my apologies.
Bill
Bill Velek wrote:
snipped some additional description/explanation of virtual payoffs
Virtual payoffs
are determined by scaling the actual payoffs according to a
scaling policy that is consistent with your objective. Max-EV
uses no scaling at all, just the actual payoffs. Min-cost uses
a linear scaling policy, but excludes one unit of each payoff
from the scaling process.
Do you mean that you are adjusting each hand to account for the fact
that one betting unit for each hand is merely a return of your bet?
Correct.
I.e., Jacks+ is really a push, so you make it '0', and with two-pair,
we're really only 'winning' one betting unit, so you change it from '2'
to '1'?
Sort of. You subtract one from each payoff, as you describe, then you
scale all the payoffs up or down until you find an "exchange rate" that
would make the game breakeven. The amount of scaling required
determines the cost.
If you take the max-EV 9/6 JoB strategy and do this, you will find
the cost is 1.00843257. This mean you end up losing an average
of 1.0084... units to the machine for each unit that comes out. A
net push counts neither as a unit lost nor a unit won, it is a
non-event.
I assume that the reason why you are not having to include a
line for a negative one (-1) for losing hands is because it would just
reproduce the identical max-ER strategy;
Mostly. In addition, doing that would be require counting a push as
both a win and a loss that occur simultaneously.
this is why we don't need to
include any per-line adjustments for coin-in cash-back, although
whatever difference that factor might make would probably be so slight
as to still never make any discernable difference in choices anyway.
Cash-back would change the computation, and I haven't included
that in any of the min-cost strategies that I've compute. But, this
raises an important point -- for "nonstandard" strategies, coin-in
cash-back and coin-out cash-back will not necessarily be
equivalent. This probably won't impact min-cost, but it would
definitely impact min-risk. I don't know if Sorokin made any
distinction between the two, but if not then the Sorokin formula
may only work correctly for one case (the formula I've seen
with Sorokin's name attached is correct for coin-out cash-back).
> Min-risk uses a non-linear scaling
> policy, scaling a payoff of N units to a value of (1-R^N)/(1-R),
> for a risk parameter of R.Are you saying that you use the above formula to compute a necessarily
different factor for each different hand in a paytable?
Correct.
... and could
you give an example -- at least of a value for R and what that
represents?
For 9/6 JoB with max-EV strategy, R is 1.000424895337. This implies
that the royal payoff is scaled up to a virtual payoff of 952.54 units,
and STFL scales up to 50.524 units. The other payoffs scale by
smaller values, down to two pair at 2.000424895377 units, equal
in value to (1+R).
I'm having a little difficulty here because I thought I
understood the min-risk (and I assume that is just a shortened name for
min-RoR, right?) ...
The strategies that I call min-risk do correspond to min-RoR strategies
for favorable games. However, I also apply the equivalent concept to
unfavorable games, where risk-of-ruin has no meaning.
to be completely independent of either
bankroll/stake and goals, as well as duration of play (number of games),
but rather that it just generated the absolutely optimal strategy for
playing as long as possible, and that there is not really a particular
risk level that has anything to do with the strategy (other than just an
incidental result).
That all sounds kind of nebulous. Risk is a very concrete concept,
and can be interpreted in a straightforward manner. For a specified
goal and bankroll, risk is simply the probability of going broke before
reaching the goal. High risk means a high probability of going broke,
low risk means a low probability of going broke. This should not be
confused with the value R, which is not necessarily a probability.
For any initial bankroll B and goal bankroll G, the probability of
reaching the goal is given by:
p(success) = (1 - R^B) / (1 - R^G)
This formula works for both favorable and unfavorable games. For
games that are exactly breakeven, the formula gets replaced by:
p(success) = B / G
For favorable games, the parameter R is less than one and is
numerically equal to the probability of going broke if you
start with a single unit bankroll and make the goal bankroll
infinite.
For unfavorable games, the parameter R is equal to your
opponent's risk of ruin. Minimizing risk is the same as making
R as small as possible. So, for unfavorable games minimizing
risk is equivalent to playing in such a way that your opponent's
risk of ruin is maximized.
In trying to grasp this, I keep leaning toward
imagining that the risk parameter is some sort of acceptable risk level,
such as 10% risk of ruin, for which the R value would be .1 -- but I
can't seem to substitute any values into your formula to produce
anything that resembles the values in your table, below.
For VP games, R is always only a tiny bit larger or smaller than 1.
A 9/6 JoB game with a royal jackpot of 1300 units gives R=0.9995826.
This means that if you start with a bankroll of one unit and try to
grow an infinite bankroll, you will have a 99.95826% probability
of going broke.
If you start with a 100 unit bankroll, your probability of eventually
busting out is R^100, for this game that equals a 95.9% chance
of busting instead of getting filthy rich.
To reduce the risk to 50%, we need a bankroll that satisfies:
R^B = 0.5
So, the required bankroll is:
B = ln(0.5) / ln(R)
For this game, a 1660 unit bankroll gives a 50% RoR.
Each time we add 1660 units to the bankroll, the risk is
cut in half. So, 3320 units gives a 25% RoR and 4980
units gives a 12.5% RoR.
For a 10% risk level, we need B = ln(0.1) / ln(R) = 5516.
Each additional 5516 units reduces RoR by another
factor of 10, so a 1% RoR comes from 11032 units and
0.1% RoR comes from 16548 units.
The RoR values all come from using an infinite bankroll
as the "final" goal. When the target bankroll is finite, it
is easier to compute probability of success rather than
risk of failure.
p(success) = (1 - R^B) / (1 - R^G)
p(failure) = 1 - p(success) = (R^B - R^G) / (1 - R^G)
Using this formula and the R value above, we find that
the probability of turning a 100 unit bankroll into 500
units is given by:
p(success) = (1 - R^100) / (1 - R^500) = 0.217
so we have a 21.7% chance of reaching this goal,
assuming that we start with 100 units and keep playing
until we either go broke or reach the 500 unit target.
So, computing risk of ruin is only a small fraction of the
problems that can be solved using the risk parameter
for a given strategy.
Finally, I'll repeat one caveat that I've mentioned in
previous posts. These formulae are only exact when the
underlying game is a simple coin flip. For games like VP
that have multiple possible payoff values, computing the
exact probability of hitting a goal is more complicated, so
using the formula above gives an approximation. The
larger the target bankroll, the better the approximation.
It is possible to get a feel for how good the approximation
is, by modeling the VP game as an endless series of
coin flips using a risk-equivalent coin which has the
same R value as to real game. But for now, I'd suggest
that you play with the formula for a while to get a good
feel for how it works. Once you understand that risk
boils down to the probability of failure, it all makes
a lot more sense.
In a nutshell, the min-risk strategy gives the best
probability of success for a broad range of goals,
when the player continues playing until the goal
is reached or the bankroll is lost. RoR is only a
small part of the overall story.
No, that's not quite the case.
The problem is those random fluctuations. All a strategy can give us is a distribution of what our result will be after a fairly large number of hands.
Different strategies will produce different distributions.
Of all the distributions, the "standard" strategy, the MaxER strategy, has the highest mean.
Steve has pointed out that there are other strategies, with lower variance. For a positive-ER game, that means less risk. By playing one of the lower-variance strategies, one could in theory play more hands, and get a higher return that way, while still having less risk.
One measure of risk is Risk-of-Ruin, which is the chance that one's accumulated losses reach a point at which one must stop playing. "Ruin" in the real world generally doesn't mean ruin; it means the player has to do something else before resuming play. Steve's example was going to the ATM and withdrawing more money.
An occasional LV visitor might stop play until the next trip. A pro might have to work at a wage-earning job for a while.
By using a lower-risk strategy, a player can average fewer "ruins" -- trips to the ATM -- per unit of profit. But, that also means playing more hands per unit of profit.
The strategy which minimizes ruins per unit of profit, is the one we've been calling MinRisk. It's not straightforward to find in general, but it can be found for any particular set of payoffs.
···
--- In vpFREE@yahoogroups.com, "bornloser1537" <bornloser1537@y...> wrote:
But, with the MAX ER strategy, it will always be the most it
can be, aside from random fluctuations about which we are helpless > to do anything.
http://groups.yahoo.com/group/vpFREE/message/26440
<a href="http://groups.yahoo.com/group/vpFREE/message/26440">
http://groups.yahoo.com/group/vpFREE/message/26440</a>
"Jacks or Better 8/5" is a typo and should be "Jacks
or Better 9/6".
vpFREE Administrator
···
On 25 Feb 2004 at 20:02, Dave wrote:
Sorry, second request...where do I find the "min-risk"
strategy for 9/6 JoB.
<<bornloser1537 wrote:
Perhaps, similar information like this, using other games and other
strategies, summarized like this, would allow a lot of us dummies to
consider trying alternate strategies, based on numbers
like "stanfordwang" has given us below.
Then Harry Porter continued:
<<Forgive me if I'm beating a dead horse here. I strongly advise
against pursuit of alternate strategies until you've refined and honed
your "basic" max-EV strategy -- say to the extent that your vp
software practice consistently reflects no more than approx .05% ER
penalty (or less) due to mistakes.>>
In the example they were talking about, the difference between the two strategies was the difference between $4535 and $4211 - a $324 difference.
This is totally foreign to most gamblers. Most gamblers, including most skilled VP players, who are praying for a different strategy are those with MUCH SMALLER bankrolls. Actually they want a strategy for full-pay DW so their $300-500 bankroll will let them play just as long as if they have the $8000+ that Tomski gives for a very small ROR (risk of ruin). These alternative strategies are useful for pros who play A LOT or for teams with a lot of players - but they really only give significant results at big-bankroll levels - they are used especially for team and/or progressive play.
Perhaps I am wrong - I am still struggling to follow this thread - but I don't see any of these alternate strategies increasing the playing time or profit SIGNIFICANTLY for someone with a bankroll under $1000 - even less for someone with one under $500. I still say that the biggest problem for most skilled advantage VP players is being under-bankrolled. If you don't have a big enough bankroll, you will have to face the fact that you will have many many short session before you go broke.
So - I will once again, in another e-mail, repeat the article I wrote in Strictly Slots a long time ago - and tell you some concrete ways that you can make your bankroll go further and reduce your odds of going broke.
Unless you've got the basic play down cold, an attempt to complicate
your play with pursuit of other strategies will certainly involve an
additional cost that outweighs ALL advantage to the alternate strategy.
···
________________________________________
Jean $¢ott - Go to http://www.FrugalGambler.biz
for VP software and strategy cards; "frugal" books;
and the NEW "Tax Help for the Frugal Gambler."
[Non-text portions of this message have been removed]
<<Does Frugal Video Poker allow you to change the strategy and
calculate the resulting average return and variance?>>
I know it does let you calculate the new EV. Maybe Harry or someone else more math oriented than I can answer whether it will show the variance.
···
________________________________________
Jean $¢ott - Go to http://www.FrugalGambler.biz
for VP software and strategy cards; "frugal" books;
and the NEW "Tax Help for the Frugal Gambler."
[Non-text portions of this message have been removed]
Jean Scott wrote:
In the example they were talking about, the difference between the
two strategies was the difference between $4535 and $4211 - a $324
difference.This is totally foreign to most gamblers. Most gamblers, including
most skilled VP players, who are praying for a different strategy
are those with MUCH SMALLER bankrolls. Actually they want a
strategy for full-pay DW so their $300-500 bankroll will let them
play just as long as if they have the $8000+ that Tomski gives for a
very small ROR (risk of ruin).
Jean,
I just want to clarify something. The $4K+ values were discussing
what I think you've referred to as "lifetime" bankrolls (or something
to that effect), with a 10% risk of ruin. As in, "exhaust this amount
and you walk from the game forever". This goes for Tomski's MUCH more
conservative bankrolle estimate.
Are you suggesting that the $300-500 player bankroll you've noted is
on the same basis? Or is this a "trip" bankroll, in which case we're
talking apples and oranges.
Someone who is playing on a $300-500 trip bankroll is likely to be
working out of a lifetime bankroll that's in the ballpark of these
numbers. If the $300+ IS a lifetime bankroll, they should stick to
nickle and dime poker.
- Harry
(I wish the applicable terminology was "trip stake" and "bankroll",
but that WOULD be beating a dead horse
<<bornloser1537 wrote:
Perhaps, similar information like this, using other games and other
strategies, summarized like this, would allow a lot of us dummies to
consider trying alternate strategies, based on numbers
like "stanfordwang" has given us below.
Then Harry Porter continued:
<<Forgive me if I'm beating a dead horse here. I strongly advise
against pursuit of alternate strategies until you've refined and honed
your "basic" max-EV strategy -- say to the extent that your vp
software practice consistently reflects no more than approx .05% ER
penalty (or less) due to mistakes.>>
Then Jean Scott pointed out:
In the example they were talking about, the difference between the two
strategies was the difference between $4535 and $4211 - a $324 difference.
These numbers represent the required bankroll needed to achieve a
certain risk or ruin.
Jean continues:
This is totally foreign to most gamblers. Most gamblers, including most
skilled VP players, who are praying for a different strategy are those with
MUCH SMALLER bankrolls.
If the risk of ruin is relaxed, then the required bankrolls will be reduced
by equal factors. This means that the $4535 and $4211 figures would
scale down to $435.5 and $421.1 with a much larger risk of ruin. When
comparing the max-ER strategy to the min-risk strategy, the bankroll
requirement for the min-risk strategy will always be lower than the
bankroll requirement for the max-ER strategy. More importantly, no
matter what level of risk is deemed "acceptable" by the player, the
min-risk strategy will lower the bankroll requirement by the same
percentage.
So, the min-risk strategy has the same power to reduce bankroll
requirements whether you have large session bankrolls or small
session bankrolls.
Actually they want a strategy for full-pay DW so
their $300-500 bankroll will let them play just as long as if they have the
$8000+ that Tomski gives for a very small ROR (risk of ruin).
Yes, and we all want VP games with 125% returns too, but that
is dreaming. The risk is a tied to the size of bankroll _and_ to
the strategy.
These
alternative strategies are useful for pros who play A LOT or for teams with
a lot of players - but they really only give significant results at
big-bankroll levels - they are used especially for team and/or progressive
play.
Not true, as described above. If the min-risk strategy reduces the required
bankroll by 5% when applied at a 1% risk of ruin, then it will also reduce
the required bankroll by 5% when applied at a 50% risk of ruin. Players
with small bankroll are simply playing at a higher level of risk than players
with large bankrolls.
Perhaps I am wrong - I am still struggling to follow this thread - but I
don't see any of these alternate strategies increasing the playing time or
profit SIGNIFICANTLY for someone with a bankroll under $1000 - even less
for someone with one under $500. I still say that the biggest problem for
most skilled advantage VP players is being under-bankrolled. If you don't
have a big enough bankroll, you will have to face the fact that you will
have many many short session before you go broke.So - I will once again, in another e-mail, repeat the article I wrote in
Strictly Slots a long time ago - and tell you some concrete ways that you
can make your bankroll go further and reduce your odds of going broke.
Using a min-risk strategy _is_ a concrete way of minimizing how often
one must go to the ATM, and it isn't just for "well bankrolled" players.
Unless you've got the basic play down cold, an attempt to complicate
your play with pursuit of other strategies will certainly involve an
additional cost that outweighs ALL advantage to the alternate strategy.
I'm sorry, but that is pure myth. The min-risk strategy is no more
complicated than the max-ER strategy, it simply has a different
ordering of plays in the priority list.
Steve Jacobs wrote: <<If the risk of ruin is relaxed, then the required bankrolls will be reduced
by equal factors. This means that the $4535 and $4211 figures would
scale down to $435.5 and $421.1 with a much larger risk of ruin.>>
This is exactly the point I was trying to make. Someone with a bankroll or trip stake of less than $500 wants to come to Vegas for four days and make this amount last the whole time even if they don't win. I'm saying that the $14 they will "save" by using some reduced-risk strategy will not give them significantly more playing time or significantly reduce their trips to the ATM.
<<Players
with small bankroll are simply playing at a higher level of risk than players
with large bankrolls.>>
I agree with this 123% (I choose that # to show off I do know a little math :). Therefore, in my practical opinion, there are much better ways to reduce risk than alternate strategies. First, you have to be honest with yourself: what is your goal - to always play at the highest 100%+ EV you can so you are headed toward a point of profit in the long term - or, do you want to play longer and enjoy more "casino entertainment." With a small bankroll you can't have it both ways. If you are determined to make a long-term profit, you play a good math-based strategy (max EV or min-risk or whatever) on 100%+ plays as long as your bankroll holds out - and then you quit playing until your bankroll is replenished . If you want more "time on device," as the casino calls it, then you have to sacrifice the profit-making goal and stick with the entertainment goal (which I do not think is a bad idea). Then the #1 best way to stretch out your time is to drop down in denomination, even if that means playing under 100% schedules. Or, play short coin. Or switch to penny or nickel slots. Or use the literally 1000's of small money-saving hints I write about.
God, I don't have time to post as much as I am doing. Everybody just go out to a casino and HAVE FUN.
···
________________________________________
Jean $¢ott - Go to http://www.FrugalGambler.biz
for VPsoftware and strategy cards; "frugal" books;
and the NEW "Tax Help for the Frugal Gambler."
[Non-text portions of this message have been removed]
Tom, thanks for the link to Steve's strategy. Looking at this
strategy, the first notable change is holding several 3RFs over a
high pair. Now, I'm not a math major, but how exactly does throwing
away a sure win for the possibility of a longshot royal lower risk???
Maybe there's something I'm not seeing here....
Dave