Any Books Available on Short Term Play.

[Steve_Jacobs]

That is the key. The answer is "yes" but the trick is to figure out
how to state your objectives in terms that are mathematically
precise.

Finding the "best" way to do anything, whether it is playing VP or
driving your car, is really about trading something of value in
exchange for something else that has greater value to you. Optimal
tradeoffs are the name of the game. We want to get the most X in
exchange for the Y that we give up. When you want to drive your
car in the "best" way, you might try to maximize "miles per gallon"
or "miles per hour" but these are both tradeoffs, either trading gallons
of gasoline in exchange for miles advanced, or trading time for miles
advanced. Exchanging one resource or another. We seek to either
maximize what we receive for each resource unit that we give up, or
minimize what we give up in exchange for the resource we receive,
and any type of exchange can be expressed either as a minimization
problem or as an equivalent maximization problem.

In VP, the most well known exchange is "units returned per game
played," which is the basis for EV. Players who wish to use a different
basis for exchanging resources would be better served by tailoring
their playing strategies to the particular exchange that they prefer.

All of the alternate strategies that I've studied can be described as
"best X per Y" statements. Min-risk gives the best probability of
playing forever in exchange for each unit consumed through losing.
Best_Shot(royal) gives the highest probability of surviving to hit
a royal flush, in exchange for each unit (or bankroll) consumed by
losses. Min-cost(royal) loses the least amount, on average, while
waiting to hit a royal flush.

Try to describe what you want to achieve, in one of the following ways:

1) Most X per Y, or equivalently least Y per X. The X and Y can represent
any kind of resource, like dollars/units, time (in terms of games played),
or particular payoffs such as royal-flush, 4/kind. EV is most units returned
per game played. Some similar goals (but different enough to give slightly
different strategies) are min-cost [most units returned per unit consumed
by losses] or min-cost(flush) [minimum units lost, on average, between
flush payoffs].

2) Highest probability of doing X before going broke. For minimum
risk-of-ruin, this has the form "maximize probability of playing forever
without going broke." Some other objectives of this form are "best shot
at hitting a royal-flush before going broke" or "best shot at hitting a payoff
of 3/kind or better, before going broke". These can also describe finite
dollar goals like "best chance of starting with 25 units and reaching 300
units before going broke."

If you can express your objective in concrete terms, then there is a good
chance that an optimal strategy can be found that is tailored to your
specific goal, based on mathematics. There are two groups of "experts"
who you should ignore -- those who are rooted in snake oil rather than
mathematics, and those who claim that maximizing EV is the only solution.

···

On Friday 28 July 2006 12:36 pm, denflo60 wrote:

Can any of this be represented mathematically.

[nightoftheiguana2000]

i.e., maximize the Sharpe Ratio

Sharpe Ratio = (ER + Cashback -1) / sqrt(variance)

http://www.google.com/search?q=Sharpe+Ratio

···

--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...> wrote:

You make an allusion to an investing analogy in your post. There's no
escaping the fact that no prudent investor accepts greater risk
(translating into a more volatile investment) without a stronger
expected return. To do so is simply foolish in any sense (not to
suggest that there aren't more than a handful of fools out there).

[denflo60]

>
> Can any of this be represented mathematically.

That is the key. The answer is "yes" but the trick is to figure out
how to state your objectives in terms that are mathematically
precise.

Finding the "best" way to do anything, whether it is playing VP or
driving your car, is really about trading something of value in
exchange for something else that has greater value to you. Optimal
tradeoffs are the name of the game. We want to get the most X in
exchange for the Y that we give up. When you want to drive your
car in the "best" way, you might try to maximize "miles per gallon"
or "miles per hour" but these are both tradeoffs, either trading

gallons

of gasoline in exchange for miles advanced, or trading time for

miles

advanced. Exchanging one resource or another. We seek to either
maximize what we receive for each resource unit that we give up, or
minimize what we give up in exchange for the resource we receive,
and any type of exchange can be expressed either as a minimization
problem or as an equivalent maximization problem.

In VP, the most well known exchange is "units returned per game
played," which is the basis for EV. Players who wish to use a

different

basis for exchanging resources would be better served by tailoring
their playing strategies to the particular exchange that they

prefer.

All of the alternate strategies that I've studied can be described

as

"best X per Y" statements. Min-risk gives the best probability of
playing forever in exchange for each unit consumed through losing.
Best_Shot(royal) gives the highest probability of surviving to hit
a royal flush, in exchange for each unit (or bankroll) consumed by
losses. Min-cost(royal) loses the least amount, on average, while
waiting to hit a royal flush.

Try to describe what you want to achieve, in one of the following

ways:

1) Most X per Y, or equivalently least Y per X. The X and Y can

represent

any kind of resource, like dollars/units, time (in terms of games

played),

or particular payoffs such as royal-flush, 4/kind. EV is most

units returned

per game played. Some similar goals (but different enough to give

slightly

different strategies) are min-cost [most units returned per unit

consumed

by losses] or min-cost(flush) [minimum units lost, on average,

between

flush payoffs].

2) Highest probability of doing X before going broke. For minimum
risk-of-ruin, this has the form "maximize probability of playing

forever

without going broke." Some other objectives of this form are "best

shot

at hitting a royal-flush before going broke" or "best shot at

hitting a payoff

of 3/kind or better, before going broke". These can also describe

finite

dollar goals like "best chance of starting with 25 units and

reaching 300

units before going broke."

If you can express your objective in concrete terms, then there is

a good

chance that an optimal strategy can be found that is tailored to

your

specific goal, based on mathematics. There are two groups

of "experts"

who you should ignore -- those who are rooted in snake oil rather

than

mathematics, and those who claim that maximizing EV is the only

solution.

Steve: I thought I heard everything possible on the topic, but your
above statement I really find intriguing. Is there an article, paper
book, online reference etc. that describes how you go about doing
this? Denny

···

--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@...> wrote:

On Friday 28 July 2006 12:36 pm, denflo60 wrote:

[Skip_Hughes2]

Steve Jacobs wrote:

  Short term strategies do exist.

Not only do they exist, but a tournament is a perfect example of a situation that calls for a short-term strategy. And Bob has written about such strategies on a number of occasions. Should he be relegated to "Singerite" status? Hardly. Because he was using a short-term strategy to best accomplish his goal - winning a tournament.

I can think of much more likely scenarios than the kneecap or millionaire story, but in order to accept them one must at least acknowledge that real players are not "perfect". The may overplay their bankroll (something the expert would never, ever do, right?), but are much more likely to have a limit on how much they are willing to put at risk on a trip. In other words, they often have a set stake, not a bankroll and not only is that OK, it's very desirable for most players. One must also accept that not everyone has the same goals as the expert.

So given those concessions to reality over perfection, here are some circumstances we can postulate and test:

A player is down to his last $500. The casino he's staying at has four 99%+ games, but if one plays at the dollar level one can achieve an extra 1.18% in cashback and and other added EV. He can play up to 8 hours if his stake lasts. He may or may not play video poker for another year. The games available are Bonus Poker, Jacks or Better, White Hot Aces and Triple Double Bonus. The "always play the max EV" rule says TDB is the game to play. But it depends on your goals. Here are results of analysis with Dunbar:
Game return ROR end BR end BR w/o Ruins
TDB 100.76% 89% 530 4934
WHA 100.75% 82% 574 3262
JB 100.72% 65% 645 1836
Bonus 100.35% 73% 535 1959

(I'm not sure how that will turn out. If it doesn't come out OK I'll post the results in plain text.

Obviously, the only way the TDB player survives is to hit one or more major jackpots (as the last column clearly shows). Same thing for the WHA player. So if the player's goal is to come home with $4,000 or more, the max EV strategy is the best in this case. For a guy who wants to take a shot on the day, hoping to play as long as possible and have the best chance to keep some or all of his $500, JB is the choice, followed by Bonus Poker which is still much better than TDB or WHA in spite of a .35% lower EV. (I ran 10,000 trials of each of these). The Bonus example is important since the top three are all very close together in EV.

Obviously there could be a myriad of examples of this with a infinite number of bankroll, game and other factors, without resorting to extreme circumstances. One may draw their own conclusions from them. But people who wish to consider these kinds of questions, deserve better than to be relegated to the back alley of serious video poker discussion. Those who are willing to explore these situational problems are better equipped to make informed decisions than those who don't.
Thanks,
Skip
www.vpinsider.com
www.vpplayer.com
VPFREE DISCOUNT: http://www.vpplayer.com/GROUP/vpfree.html
(use vpfree/vpfree)

···

On Friday 28 July 2006 11:40 am, Adams Myth wrote:

[Harry_Porter]

Skip Hughes wrote:

Obviously there could be a myriad of examples of this with a
infinite number of bankroll, game and other factors, without
resorting to extreme circumstances. One may draw their own
conclusions from them. But people who wish to consider these kinds of
questions, deserve better than to be relegated to the back alley of
serious video poker discussion. Those who are willing to explore
these situational problems are better equipped to make informed
decisions than those who don't.

With the exception of tail-chasing bankroll management discussions,
I've never sensed there is anyone who desires to totally sideline any
serious consideration of alternative (non max-EV) vp strategy. And
I'll go as far as to say that a grasp of the concepts behind
alternative goal strategies gives one a better understanding of play
fundamentals.

That said, those who inquire after alternative strategies for their
day-to-day play (vs. for a tournament or specialized situations such
as chasing a progressive that poses a bankroll stretch) typically are
coping with challenges that an alternative strategy is unlikely to
adequately address. For example, someone who is uncomfortable with
the bankroll risk of a given play using max-EV strategy is likely to
be only marginally mollified by the realities achieved using a
min-risk strategy (the numbers that play out in the vpFREE FAQ on the
topic:
http://members.cox.net/vpfree/FAQ_S.htm
points to as much).

My take on the alternative strategy topic is that someone who's
investigating it out of some motive other than curiosity or an
academic interest is likely seeking an elixir that isn't to be found.
Such a person might well be served by striving for a better grasp of
core max-EV concepts and come to terms with why these don't seem a
satisfactory precept for play.

- Harry

[Skip_Hughes2]

Harry Porter wrote:

I've never sensed there is anyone who desires to totally sideline any
serious consideration of alternative (non max-EV) vp strategy.

Oh, I thought there was someone who fit that description. Sorry.

Thanks,
Skip
www.vpinsider.com
www.vpplayer.com
VPFREE DISCOUNT: http://www.vpplayer.com/GROUP/vpfree.html
(use vpfree/vpfree)

[Harry_Porter]

I wrote:

I've never sensed there is anyone who desires to totally sideline any
serious consideration of alternative (non max-EV) vp strategy.

Skip Hughes replied:

> Oh, I thought there was someone who fit that description. Sorry.

No prob, Skip ... of course, my sensibilities aren't what they once
were

- H.

[Adams_Myth]

It looks as though there is more to this than the usual CW.

I perhaps said more than I care to, more than I should have. I'll shut
up and listen to whoever posts on this topic for a while.

The Tournament Strategy is a special situation. In a way, Bob Dancer
touched on a Tournament Strategy heavily weighted towards chasing the
Royal Flush, in his column on the Four-to-a-Royal promotion. But here
you are playing against all the others in the tournament, whereas
usually in Video Poker you are playing against no one in particular.

A Myth

···

--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@...> wrote:

Short term strategies do exist. That goes against the mainstream view
of VP experts, but I'm used to that by now. The problem with the
mainstream is that it is so focused on EV that it can't think outside
the EV box.

[Adams_Myth]

Some other objectives of this form are "best shot
at hitting a royal-flush before going broke" or "best shot at

hitting a payoff

of 3/kind or better, before going broke". These can also describe

finite

dollar goals like "best chance of starting with 25 units and

reaching 300

units before going broke."

I too find this intriguing. Suppose the "objective" is
"Min-cost(royal)", that of losing the least amount, on average, while
waiting to hit a royal flush.

What would be the strategy, for a VP player to follow? Would it be
expressable at the so-called Readers Digest level? (I don't intend
this to be a rhetorical question. I am genuinely interested; not
necessarily in hitting the Royal Flush, but in general understanding
of strategies.

···

--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@...> wrote:

[Steve_Jacobs]

Check out the FAQ_S link that others have posted. There are also
a couple dozen post over the last couple of years, in which I try
to describe how me method works. Do a search using the phrase
"virtual payoff" to find most of those posts.

Another key idea that works for some types of goals is to think about
how you would determince when a session has been a "success" and
when it has been a "failure". If you can clearly define conditions that mark
the end of a session and count as "success" and "failure", then that is enough
to form the basis for an optimal strategy by maximizing the probability of
success. For example, there was a recent discussion where someone said
(paraphrasing) "I count it as a success if I meet a coin-in requirement." I've
been working on a strategy for that goal, and twice I thought I had it solved
but later realized my approach was flawed. I have a new approach that I
believe is correct, but haven't had time to adapt my programs yet.

You need to have a way to determine when you have reached your goal, or
a way to measure progress toward the goal, in a way that allows numbers
to be attached to the strategy. Otherwise, there is no mathematical basis
for measuring the "goodness" of the playing strategy.

···

On Saturday 29 July 2006 1:13 pm, denflo60 wrote:

--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@...> wrote:
> On Friday 28 July 2006 12:36 pm, denflo60 wrote:
> > Can any of this be represented mathematically.
>
> That is the key. The answer is "yes" but the trick is to figure out
> how to state your objectives in terms that are mathematically
> precise.
>
> Finding the "best" way to do anything, whether it is playing VP or
> driving your car, is really about trading something of value in
> exchange for something else that has greater value to you.

Steve: I thought I heard everything possible on the topic, but your
above statement I really find intriguing. Is there an article, paper
book, online reference etc. that describes how you go about doing
this? Denny

[Harry_Porter]

Adams Myth wrote:

I too find this intriguing. Suppose the "objective" is
"Min-cost(royal)", that of losing the least amount, on average, while
waiting to hit a royal flush.

What would be the strategy, for a VP player to follow? Would it be
expressable at the so-called Readers Digest level?

This is described, among other alternate strategies, in the vpFREE FAQ
entry of the subject authored by Steve Jacobs. It can be found at:
http://members.cox.net/vpfree/FAQ_S.htm#MCR

The min-cost(royal) strategy is among the simplest of alternate
strategies to devise. You simply set the RF payoff equal to a value
that yields an ER of 100% for the game in question. For example, for
9/6 Jacks, the RF should be set at 4880 credits.

The resulting strategy yields a minimum expected loss between royals
and thus the greatest expected profit over the course of a royal
cycle. However, it will necessarily reduce your EV/ER for play over
any given number of hands.

That statement may seem a little paradoxical. Because the length of a
royal cycle is affected it will turn out that, even though the
expected profit is maximized, the average profit per hand is reduced.

This strategy is worthy of consideration when tackling a progressive
play at a denomination or variance that is significantly greater than
the play you're usually comfortable with since it cushions the
downside of failing to hit the progressive. I don't find it advisable
for typical day-to-day play.

- Harry

[Steve_Jacobs]

Rather than list the strategy itself, I'll describe how you can compute
it using any VP analyzer. This is a trial-and-error approach, but it
doesn't take too long.

The trick is to pretend that the payoff for a royal flush is just large
enough to make the game have a return of exactly 100%. If the
real game is unfavorable (return less than 100%), then a slightly
larger payoff for royals would turn the game into a breakeven game.
If the real game is favorable, then a slightly lower payoff for royals
will give a breakeven game. For example, 9/6 JoB return 99.54%
when playing max-EV strategy. If you increase the royal payoff
to 976 units and run a VP analyser, the return will be a tiny bit
larger than 100%. The playing strategy produced by the VP
program will be the min-cost(royal) strategy. In addition, the
976 units is the average cost of playing until you hit a royal,
using the new strategy. In comparison, the max-EV strategy
will lose an average of 984.22 units between royals.

This works because breakeven games have a special property.
For a breakeven game, each hand payoff occurs exactly often
enough to pay off the losses incurred while waiting for that hand.
So, in a 9/6 JoB game with a 976 unit payoff for royals, the cost
of straights will be exactly 4 units, while the cost of flushes will
be exactly 6 units and the cost of 4/kind will be exactly 25 units.

I hope that explanation was clear enough. The min-cost(royal)
strategy was actually the first alternate strategy that I studied
for video poker, and discovering the connection with breakeven
games had a profound effect on my thought process (at the
time, it blew my mind).

···

On Saturday 29 July 2006 10:30 pm, Adams Myth wrote:

--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@...> wrote:
> Some other objectives of this form are "best shot
> at hitting a royal-flush before going broke" or "best shot at

hitting a payoff

> of 3/kind or better, before going broke". These can also describe

finite

> dollar goals like "best chance of starting with 25 units and

reaching 300

> units before going broke."

I too find this intriguing. Suppose the "objective" is
"Min-cost(royal)", that of losing the least amount, on average, while
waiting to hit a royal flush.

What would be the strategy, for a VP player to follow? Would it be
expressable at the so-called Readers Digest level? (I don't intend
this to be a rhetorical question. I am genuinely interested; not
necessarily in hitting the Royal Flush, but in general understanding
of strategies.

[Harry_Porter]

Steve Jacobs wrote:

For example, 9/6 JoB return 99.54% when playing max-EV strategy. If
you increase the royal payoff to 976 units and run a VP analyser, the
return will be a tiny bit larger than 100%. The playing strategy
produced by the VP program will be the min-cost(royal) strategy.

In addition, the 976 units is the average cost of playing until you
hit a royal, using the new strategy. In comparison, the max-EV
strategy will lose an average of 984.22 units between royals.

Steve, the additional info I'm providing here isn't intended to be
adversarial -- I just want to round out the statistics for consideration:

As you note, min-cost(royal) <MCR> strategy will yield a cost between
royals that is 8.2 bets smaller than max-EV <MEV> strategy -- 41
credits (on a 5 credit wager).

And it does so with a relatively nominal sacrifice to ER -- 99.51% vs.
99.54%, an impairment of .03%.

As I noted last night, this lower cost is a consequence (in part) of a
shorter MCR royal cycle (MCR = 35939 hands; MEV = 40390). By pushing
harder for a MCR royal, you play fewer hands between royals during
which you expect a drain on play.

However, the exp. loss per hand between royals for MCR is larger than
for MEV. Over the course of a number of hands equal to the MCR royal
cycle, if you fail to hit a royal, your expected MCR loss is 977.5
bets; your expected M6EV loss during that time is 912.9 bets -- a
greater MCR loss of 323 credits (again, 5 cr bet).

The greater loss per period of play, yet smaller loss in absence of a
royal over the course of a royal cycle is why I'm prompted to say that
its applicability is to minimize downside risk while chasing a
progressive.

Even then, I'm hard pressed to believe that a loss reduction of 41
credits (out of an expected loss for MEV strategy of 4921 bets) puts
MCR alternate strategy in the position of making a progressive shot
any more comfortable. Personally, I'm inclined to stick with max-EV.

But, admittedly, each person's goals and risk sensitivity differs.

- Harry

[Steve_Jacobs]

Steve Jacobs wrote:
> For example, 9/6 JoB return 99.54% when playing max-EV strategy. If
> you increase the royal payoff to 976 units and run a VP analyser, the
> return will be a tiny bit larger than 100%. The playing strategy
> produced by the VP program will be the min-cost(royal) strategy.
>
> In addition, the 976 units is the average cost of playing until you
> hit a royal, using the new strategy. In comparison, the max-EV
> strategy will lose an average of 984.22 units between royals.

Steve, the additional info I'm providing here isn't intended to be
adversarial -- I just want to round out the statistics for consideration:

As you note, min-cost(royal) <MCR> strategy will yield a cost between
royals that is 8.2 bets smaller than max-EV <MEV> strategy -- 41
credits (on a 5 credit wager).

And it does so with a relatively nominal sacrifice to ER -- 99.51% vs.
99.54%, an impairment of .03%.

As I noted last night, this lower cost is a consequence (in part) of a
shorter MCR royal cycle (MCR = 35939 hands; MEV = 40390). By pushing
harder for a MCR royal, you play fewer hands between royals during
which you expect a drain on play.

That's correct, but only if the original game is unfavorable. For favorable
games, MCR pushes harder for other payoffs at the expense of the
royal, playing more hands between royal payoffs.

However, the exp. loss per hand between royals for MCR is larger than
for MEV. Over the course of a number of hands equal to the MCR royal
cycle, if you fail to hit a royal, your expected MCR loss is 977.5
bets; your expected M6EV loss during that time is 912.9 bets -- a
greater MCR loss of 323 credits (again, 5 cr bet).

Actually, your expected MCR loss is 976 bets, exactly equal to the
"virtual payoff" that gives a breakeven game. Your number above
is probably due to roundoff error. The MCR strategy has a loss rate
of 2.7157% between royals. The MEV loss rate between royals is
(984.22 units / 40390.55) = 2.4368%, so the expected MEV loss
during the MCR cycle of 35939 is 875.76 units, so the difference
is more like 501 credits at 5cr/bet.

The greater loss per period of play, yet smaller loss in absence of a
royal over the course of a royal cycle is why I'm prompted to say that
its applicability is to minimize downside risk while chasing a
progressive.

It's applicability is to lose the least number of units, on average, between
royal flushes. This maximizes net dollars per royal rather than net dollars
per hand played. With MCR you pay 976 units and get back 800 units from
the royal, for a net cost of 176 units per royal. With MEV strategy you pay
984.22 units and get back 800, for a net cost of 184.22 units per royal. Of
course, this works the same way whether there is a progressive or not.

Even then, I'm hard pressed to believe that a loss reduction of 41
credits (out of an expected loss for MEV strategy of 4921 bets) puts
MCR alternate strategy in the position of making a progressive shot
any more comfortable. Personally, I'm inclined to stick with max-EV.

Harry, I think you're always inclined to stick with max-EV, and your
analysis here is to rationalize that choice. But really, there isn't a
need to rationalize. If you prefer to maximize net dollars per hand
played, then max-EV is the correct choice FOR YOU. If a player
decides they would rather maximize net dollars per royal flush, then
min-cost(royal) is a better strategy FOR THEM.

But, admittedly, each person's goals and risk sensitivity differs.

Exactly. If someone else chooses differently than you, it is not
a reflection on either player. It simply reflects a different choice
in how to trade resources. $$$/hand vs. $$$/royal is the difference
here.

Risk sensitivity is really a different matter than cost sensitivity.
If you have a limited bankroll and you want the highest probability
of having that bankroll survive until you hit a royal, then best-shot(royal)
is the appropriate strategy. The BSR strategy requires a bankroll
of 720 units to gives a 50% chance of hitting a royal before going
broke. The MEV strategy requires a bankroll of 730.6 units to give
the same 50% chance of surviving to hit a royal. The BSR values
the royal at 1038.7 units, so it tries harder for a royal than either
MEV or MCR, with a royal cycle of 35136.3. The BSR strategy has
an EV of 99.497% and royals cost 976.66 units when playing the
BSR strategy.

The BSR strategy is a good choice for people who want to play each
unit as if it were their last, and get the best shot at parlaying that
unit (and any downstream winnings from that unit) into a royal. Such
a player might approach the game by bringing a rack of dollars to
the machine, then put a single unit into play and keep playing credits
until they either hit a royal (counting that unit as a "win") or lose all
the credits (counting that unit as a "loss"). This risks a single unit
at a time from the initial bankroll, so it gives the maximum number
of royals per "initial unit" consumed. The success rate for BSR strategy
is one royal per 1038.7 attempts. In comparison, MEV strategy yields
one royal in 1054.5 attempts while MCR strategy yields one royal in
1039.4 attempts.

···

On Sunday 30 July 2006 6:40 am, Harry Porter wrote:

[Harry_Porter]

Steve Jacobs wrote:

Harry, I think you're always inclined to stick with max-EV, and your
analysis here is to rationalize that choice. But really, there isn't
a need to rationalize. If you prefer to maximize net dollars per
hand played, then max-EV is the correct choice FOR YOU. If a player
decides they would rather maximize net dollars per royal flush, then
min-cost(royal) is a better strategy FOR THEM.

Steve, first, thanks for correcting some of my math. I resorted to a
little back of the envelope calculation that didn't serve me well,
although the general relationships held true.

Concerning the preference alternatives above, it's notable that most
players will find both desirable. I expect that no player seeks one
goal at the absolute expense of all others. The inquiring player who
is considering an alternative strategy likely looks to evaluate the
tradeoffs involved. That was the focus of my post, which identified
those for the case of min-cost(royal) vs. max-EV.

I don't think the situation is best expressed as a strict preference
for one vs. the other. A discerning player will make a decision,
balancing the tradeoffs.

- Harry

[Dunbar]

Denny, you asked some questions that can easily be answered using
Dunbar's Risk Analyzer for Video Poker. I've embedded the answers
below:

Now as a $25 machine player what would be my likelihood of wins
versus losses for 5 day plays at 4-5 hours per day with for example
double double bonus versus JOB where only a Royal will give you a
positive score.

If you start with the $62.5K bankroll that you propose below, then
you would win 37% of the "sessions" playing Double Double Bonus
compared to 28% of the sessions playing JOB. That assumes you play
22 hours at 300 plays/hr.

Is $62.5K enough for a 5 day session or do I require $100K or more.

Starting with $62.5, you would go broke 2% of the time playing JOB.
You would go broke 33% of the time playing DDB.

Starting with $100K, you would go broke less than 0.5% of the time
playing JOB; you would go broke 7% of the time playing DDB.

Interesting, huh? Even though you go broke WAY more often playing
DDB, you also finish ahead significantly more often playing DDB.

What happens to these numbers if I pay double bonus which gives me

a

headache because my old brain has difficulty remembers the fine
points of penalty cards etc.

With Double Bonus, a $62.5K bankroll will have a 14% RoR. The chance
of having a winning session is 44%.

A $100K bankroll will have just a 1% RoR. The chance of having a
winning session is still 44%. That's right, reducing the RoR from
14% to 1% has almost no effect on the chance of finishing ahead!

You can answer questions like this for almost any single-line video
poker game with DRA-VP. Analyzing the bankroll requirements for
Short-Term play was the main reason I created the program. (I wanted
to know how much money to bring on MY trips!)

The results I presented ignore the effects of cashback, tips, play
errors, and state tax withholdings. However, each of these factors
can easily be incorporated into the session calculations by DRA-VP.

--Dunbar

···

--- In vpFREE@yahoogroups.com, "denflo60" <dennis.florence@...> wrote:

[Tom_Robertson1]

Steve Jacobs wrote:

Harry, I think you're always inclined to stick with max-EV, and your
analysis here is to rationalize that choice. But really, there isn't
a need to rationalize. If you prefer to maximize net dollars per
hand played, then max-EV is the correct choice FOR YOU. If a player
decides they would rather maximize net dollars per royal flush, then
min-cost(royal) is a better strategy FOR THEM.

I have a philosophical nit to pick with this, Steve. It still doesn't
address what strategy is best for them, but only what strategy they
perceive as being best for them. You could just as easily say that
playing to minimize EV would be the correct choice for those who
prefer to lose as much money as they can. Goals aren't always clear
or even known. I've never had a definite goal in mind. "Win as much
money as I can over the next 20 years as safely as possible"
approximates my approach, but definite goals have some arbitrariness
to them, anyway, and aren't necessarily completely correlated with
what's best for the player. I don't expect a mathematical analysis to
ever solve these problems. It's entirely possible to play for 20
years and then realize that one hardly went about accomplishing what
one really wanted to in the best way, even if one strictly followed
the mathematical approach that was optimal for one's explicitly
defined goal. I have yet to come up with a way to strictly quantify
how much to adjust my strategy to balance risk and EV, and, 10 years
from now, I may decide that I adjusted it way too much or too little
the whole time.

Steve, first, thanks for correcting some of my math. I resorted to a
little back of the envelope calculation that didn't serve me well,
although the general relationships held true.

Concerning the preference alternatives above, it's notable that most
players will find both desirable. I expect that no player seeks one
goal at the absolute expense of all others. The inquiring player who
is considering an alternative strategy likely looks to evaluate the
tradeoffs involved. That was the focus of my post, which identified
those for the case of min-cost(royal) vs. max-EV.

I don't think the situation is best expressed as a strict preference
for one vs. the other. A discerning player will make a decision,
balancing the tradeoffs.

- Harry

Exactly, Harry. Where to draw the line is a guessing game, which
implies that there is an unknowable ideal that is being guessed at.
Establishing definite goals and applying strictly mathematically
correct approaches for those goals hardly solves the problem. Maybe
the best way to look at what approaches mathematical analyses come up
with is as limits. Maybe max-EV shows the limit that there should be
to one's aggression and min-cost(royal) shows the limit to how
conservatively one should play, in between which it's anybody's guess.

[denflo60]

--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...>
wrote:

Adams Myth wrote:
> I too find this intriguing. Suppose the "objective" is
> "Min-cost(royal)", that of losing the least amount, on average,

while

> waiting to hit a royal flush.
>
> What would be the strategy, for a VP player to follow? Would it be
> expressable at the so-called Readers Digest level?

This is described, among other alternate strategies, in the vpFREE

FAQ

entry of the subject authored by Steve Jacobs. It can be found at:
http://members.cox.net/vpfree/FAQ_S.htm#MCR

Steve and Harry: Thanks for the hinters and the address at which I
can finjd same. Denny

The min-cost(royal) strategy is among the simplest of alternate
strategies to devise. You simply set the RF payoff equal to a value
that yields an ER of 100% for the game in question. For example,

for

9/6 Jacks, the RF should be set at 4880 credits.

The resulting strategy yields a minimum expected loss between royals
and thus the greatest expected profit over the course of a royal
cycle. However, it will necessarily reduce your EV/ER for play over
any given number of hands.

That statement may seem a little paradoxical. Because the length

of a

royal cycle is affected it will turn out that, even though the
expected profit is maximized, the average profit per hand is

reduced.

This strategy is worthy of consideration when tackling a progressive
play at a denomination or variance that is significantly greater

than

the play you're usually comfortable with since it cushions the
downside of failing to hit the progressive. I don't find it

advisable

···

for typical day-to-day play.

- Harry

[Harry_Porter]

Tom Robertson wrote:

Maybe the best way to look at what approaches mathematical analyses
come up with is as limits. Maybe max-EV shows the limit that there
should be to one's aggression and min-cost(royal) shows the limit to
how conservatively one should play, in between which it's anybody's
guess.

I get the appeal of that thought. But, as I would expect Steve to
point out, their are other "reasonable" goal oriented strategies also
on that same spectrum that may lie between these two in
aggressiveness, or lie outside. I don't expect that there's an
absolute boundary to how "one should play" and still play within some
rationality.

Steve suggested earlier today that I have a bias toward max-ER in my
approach to vp. He's inaccurate in that.

Of all active players I know, I find no one that's more averse when it
comes to risk (I use the term loosely -- think of it in terms of
session loss exposure, long term bankroll exposure, etc). That's
gives rise to a considerable leaning toward something other than a
max-ER strategy.

However, when I review the limitations to what alternative strategies
can achieve in mitigating my risk concerns, I find the benefit to be
of an insufficient magnitude to divert from a max-EV strategy.

That said, I welcome the window that Steve (and others) opened in
airing alternate strategies here. My comprehension of them has added
dimension to my overall grasp of vp mechanics.

- Harry

[nightoftheiguana2000]

Do you use min risk strategy for double bonus?

5SF>4RF>PAT>4SF>2P>HP>4FL>3RF>4STo>MP>JT9s>QJ9s>LP>AKQJ>3SF0>4STi3H>QJs>3FS1>3FL2H>2RF2H>4STi2H>KQJ>QJT>4STi1H>QJ>JTs>3SF2>3FL1H>2H>QTs>1H>4STi>3FL

FVP says 100.14% return, variance = 27.03

Seems to me it's sufficiently different from max-EV strategy.

Also, since so many double-double players seem to crave quads or
better, maybe a min-cost quad or better strategy is called for.

···

--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@...> wrote:

However, when I review the limitations to what alternative strategies
can achieve in mitigating my risk concerns, I find the benefit to be
of an insufficient magnitude to divert from a max-EV strategy.