The point that the experts should be making is that the max-EV objective
is the only one that isn't stupid.<<
How do those who argue that max EV holds are, without exception, the only
correct holds explain the distinct shift of hold strategy in Multistrike?
And if a variation is acceptable in Multistrike in order to maximize the
chances of getting to the next level, why wouldn't the very same variations
be acceptable in some so-called short term strategy?
lb
Lawrence Boxer wrote:
How do those who argue that max EV holds are, without exception, the
only correct holds explain the distinct shift of hold strategy in
Multistrike?
And if a variation is acceptable in Multistrike in order to maximize
the chances of getting to the next level, why wouldn't the very same
variations be acceptable in some so-called short term strategy?
The strategies that have been published for Multi Strike play are max
EV strategies. It makes sense to sacrifice EV for play on one line if
the strategy provides greater opportunity for advancement to a higher
line offering greater EV. It's the overall EV that's being maximized,
not that of each individual line. Such a strategy is entirely
consistent with a "max EV" approach.
These strategies can also be deemed "long term" strategies, in the
manner that any "max EV" strategy can be called a long term strategy.
- Harry (who maintains that there are valid strategies other than
those which max EV, but also suggests that not all reasons for max-EV
deviation are rational.)
- Harry (who maintains that there are valid
strategies other than those which max EV, but
also suggests that not all reasons for max-EV
deviation are rational.)
Harry, I appreciate your always, non-judgemental, accepting yet
logical approach. It occurs to me -- a couple of times a year
visitor to LV -- that no one has yet mentioned my rationale for
playing. I play to have fun. I play VP because in general I get to
have fun longer than sitting at a slot machine and mindlessly
pressing a button. As I've read this thread I kept thinking about
what I'd do if I was playing my last hand before heading home and had
a choice of a couple to a royal or a high pair? I won't be back for
six months and don't play outside LV. It seems to me that so
many "serious" gamblers frequent this board, or at least post to it,
that the motivation for the vast majority of the playing public is
overlooked.
Scott K from Cincy
worldbefree wrote:
Harry, I appreciate your always, non-judgmental, accepting yet
logical approach.
Thanks, Scott. I'd have to say that I'm feeling decidedly more
judgmental and less accepting these days (although I trust that the
logic part hasn't suffered). That's sufficient to make me think I
really need to give it a rest around here.
It occurs to me -- a couple of times a year visitor to LV -- that no
one has yet mentioned my rationale for playing. I play to have fun.
That's the ultimate goal, Scott, irrespective of frequency of play.
The critical thing is to make sure that you can comfortably stay in
the game when the game turns sour for awhile.
Let me go on about this at length (which anyone, who finds it tedious
when I get a little long-winded, might best tune out).
------
I become concerned, probably unreasonably so, when I read of people
favoring higher volatility, inferior return play. My experience
suggests that such play is difficult to sustain short of a
considerable degree of luck. And the greater potential to rack up
larger, sizable losses is a short-term concept, not long-term.
When I travel to a casino, be it the 50+ miles to AC or cross country
to LV, I want to be able to comfortably (at least reasonably so) ride
out 6-8 hours of play a day. That brings me great satisfaction and to
find that I'm inclined to quit early because of heavier than
anticipated loss experience is very displeasing.
For myself, and perhaps I shouldn't extrapolate to others, my funds
are treated like water in the desert - I don't know when to expect
them to be replenished with wins. As a consequence, I'm
extraordinarily conservative in what I play and I do it with the
expectation that I may face rather severe results in the short term.
In other words, I go loaded for bear.
The games I select for play are largely lower volatility ones and I
strive to play at no less than a tiny fraction of a percent below
break even. (But I'm willing to allow for sub-100% play, which is why
I describe my own play as recreational - my purposes are just that. I
recognize the large hazard to my bankroll presented in this.)
When I read of those who intentionally seek out high volatile plays
with sub-optimal returns I become concerned. It makes me question if
they're likewise able to comfortably see out a day's play with
consistency - of course, that's not really my business. But I have no
question in my mind about the ultimate cost of such play and can't
rationalize it (again, not my business).
Scott, I don't expect that your goals in making your twice a year
pilgrimages are much different than mine. When you suggest a taking a
shot at a 2-cd RF rather than holding a high pair before leaving for
home, I don't have a problem with that. Hell, I'll throw a $20 or so
at a slot machine at some point each trip. I suppose a purist will
frown at both, but my concern is whether either is done with other
than an extremely limited frequency.
What I find troubling are those who make sub-optimal play a
significant contribution to their regular casino activity. I'm not
necessary suggesting max-EV play is optimal, but under standard
circumstances I'm hard pressed to accept that for a typical player
max-EV isn't the best option 95+% of the time. (And, Steve, you're
hardly the typical player here, and I expect your play is much more
frequently under non-standard circumstances.)
I think the large majority of players on this group (and I include
myself here) have sufficient challenges in reducing the cost of
inaccurate play and keeping play within the constraints of their
bankroll, that a non-standard approach to play is ill-advised.
It's my intent to be non-judgmental but I feel that discussions about
machine randomness and fairness, hot and cold machines, and the like,
while interesting, serve to distract this group from the basic
concepts of video poker that can serve us all in strengthening our
play and providing practical insight that bests directs our play efforts.
I'm not advocating censorship. But this group can pick and choose
where to concentrate it's efforts. This may well prove to be a
parting shot and I'm taking advantage of your post, Scott, to air it.
I'll try to stay off the soapbox, because I'm sure I've only managed
to demonstrate just how full of myself I am. I recognize I hardly own
the franchise on truth and wisdom here :).
- Harry
Harry,
I sense in your words some discomfort on your part about some topics.
Since I started this topic, I feel a little guilty. It is not my
intention to create uneasiness.
Certainly your approach to gambling is the same one I have. I don't
like to risk too much money, and I like to play long hours. I often
achieve my goal, and often do not.
It has been said that skilled Video Poker players have to have
patience, but sometimes the patience must be that of Job. I just made
in Frugal a Pick'em simulation of 500,000 games. The end result was a
payback of 99.18%, which is a loss of about 20,000 units. This can
happen to a real player. A real player will have to content with
another 500,000 games that might not prove to be much better. It's
not that the mathematics does not work, it's that the predictions
mathematics makes in VP are statistic. An individual could actually
experience something on the wrong tail of the curves.
I do view video poker as a game, and I am constantly looking for
different ways to win. Maybe my impatience to hit a jackpot is
greater than my patience at reaping long term rewards. I assure you I
hate to lose as much as you.
I find it amusing to try to find situations in which maximizing EV is
not the proper thing to do. Here is another that even you might
encounter one day: tournaments. Suppose you go to a Video Poker
tournament, and they have normal DB machines in it. Assume these
rules: each gambler can play for an hour, just an hour, and at the
end the person with the highest score wins. What is the proper
strategy here? It is not obvious right away that maximizing EV is the
answer. Maybe the answer is some sort of strategy like the one you
would use in level 1 of Multi Strike. Certainly the problem needs
examining if you accept to participate in that tournament. Certainly
the idea of one such tournament is not out of the question as a
possibility of something one day a casino might offer.
Let us pick another problem closer to your stated play. Suppose you
go to a casino that has comped you, and you want to play 8 hours
there. Suppose it does not have fabulous machines, but you still want
to play there because you like the comps. Suppose also you have $500
for an 8 hour session, and you want to do nothing more than play. The
best machines in each denomination in this casino are these: 8/5
Bonus in dollars, 9/7 DB in quarters, 8/5 JB in nickels. What machine
in what denomination will you play? It might be the answer to this
problem is the one that maximazes EV, but it is not a priori obvious
that is the answer, given the stated problem of a certain bankroll
and a goal of playing with it a certain number of hours. There are
volatility and risk of ruin considerations that might rule out
maximizing EV as the best solution to this particular problem.
Your knowledge of Video Poker is great enough to consider these
problems and find solutions. I remember a message of yours in which
you stated you had chosen to play 9/6 Jacks or Better instead of 10/7
DB, and you gave your reasons. There it is, a given set of
circumstances presented you with a personal Video Poker problem, and
your solution to it was not to maximize long term EV since you chose
to play a machine with a payback 0.6% inferior than the one you could
play.
I apologize if I had unintentionally rubbed you the wrong way, it was
not intentional. I don't agree 100% of the time with what you say,
but I always read your messages since very often they are
educational, valuable and informative and, besides, they are always
interesting and well written.
Regards,
E
--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@v...>
wrote:
What I find troubling are those who make sub-optimal play a
significant contribution to their regular casino activity. I'm not
necessary suggesting max-EV play is optimal, but under standard
circumstances I'm hard pressed to accept that for a typical player
max-EV isn't the best option 95+% of the time. (And, Steve, you're
hardly the typical player here, and I expect your play is much more
frequently under non-standard circumstances.)I think the large majority of players on this group (and I include
myself here) have sufficient challenges in reducing the cost of
inaccurate play and keeping play within the constraints of their
bankroll, that a non-standard approach to play is ill-advised.It's my intent to be non-judgmental but I feel that discussions
about
machine randomness and fairness, hot and cold machines, and the
like,
while interesting, serve to distract this group from the basic
concepts of video poker that can serve us all in strengthening our
play and providing practical insight that bests directs our play
efforts.
I'm not advocating censorship. But this group can pick and choose
where to concentrate it's efforts. This may well prove to be a
parting shot and I'm taking advantage of your post, Scott, to air
it.
I'll try to stay off the soapbox, because I'm sure I've only managed
to demonstrate just how full of myself I am. I recognize I hardly
own
the franchise on truth and wisdom here :).
- Harry
I just made
in Frugal a Pick'em simulation of 500,000 games. The end result was
a
payback of 99.18%, which is a loss of about 20,000 units. This can
happen to a real player. A real player will have to content with
another 500,000 games that might not prove to be much better. It's
not that the mathematics does not work, it's that the predictions
mathematics makes in VP are statistic. An individual could actually
experience something on the wrong tail of the curves.
I also ran some 1 million hand simulations in winpoker against a 40+
variance game that pays right around 100%. I found results of +/-
1.5% from the EV. Most recreation players will never play 1 million
hands, so it's easy to see why some people are considered lucky, and
other unlucky.
Here is another that even you might
encounter one day: tournaments. Suppose you go to a Video Poker
tournament, and they have normal DB machines in it. Assume these
rules: each gambler can play for an hour, just an hour, and at the
end the person with the highest score wins. What is the proper
strategy here? It is not obvious right away that maximizing EV is
the answer.
I just played in a similar tournament last month. Each player got a
total of 30 minutes playing FP JOB. Based on the number of entries
and my assumption for average number of hands I calculated the number
of RFs to be around 3-4 (turned out to be 3). In addition, there were
only 10 paying spots (it was free to enter). With this in mind I
adopted a stragegy of going for RFs. Although I failed to get one, I
still think this was the right strategy (and somewhat verifies what
Steve Jacobs has been promting). Had I gotten one early, then I would
have changed to my normal strategy (which is speed first, accuracy
second ... I don't correct most mistakes that I notice after pressing
the hold keys).
Dick
--- In vpFREE@yahoogroups.com, "mubowor" <erchalb@c...> wrote:
<<Here is another that even you might
encounter one day: tournaments. Suppose you go to a Video Poker
tournament, and they have normal DB machines in it. Assume these
rules: each gambler can play for an hour, just an hour, and at the
end the person with the highest score wins. What is the proper
strategy here? It is not obvious right away that maximizing EV is the answer.>>
I think you are not using the phrase "maximizing EV" in the way that most of us do and that is why some of your discussion is generating opposing views. It is not the same as "using basic strategy." For example, in Multi-Strike, you DO vary from regular basic strategy, but only in order to maximize the EV of that type of game. In tournament play, you DO vary from regular play basic strategy in order to maximize your EV to get in the money.
To put it another way, if you play all 4 lines of MS with the basic strategy you would use on a single line of the same pay schedule, you will not even achieve the EV of the single-line game, much less get the higher return that is possible by altering your strategy. Therefore in that game, you must alter your strategy to maximize EV.
This is much different than someone who departs from basic strategy because they have a different goal, i.e. hoping to hit it big before they go home rather than looking at the long-term consequences.
Everyone has the right to play any way they want to - and depart from basic strategy anytime they feel like it - and the right to not be judged. It is fine for people to have different goals. However, I have said many times that I don't need to encourage people to play by the seat of their pants - they do a good job on that without my help. My goal in writing about gambling is to show people the mathematical facts so they are aware of how different goals can impact their long-term results. If you know the facts, and then chose to depart from basic strategy - that is fine. However, so many people don't even realize that there is a way that might improve their gambling results - I like helping to "turn on the light bulb."
____________________
Jean $cott - "The Frugal Gambler"
MORE FRUGAL GAMBLING can NOW
be ordered, autographed, at a pre-pub
discount, at http://www.FrugalGambler.biz
[Non-text portions of this message have been removed]
I find it amusing to try to find situations in which maximizing EV is
not the proper thing to do.
It is refreshing to find another TOTB person ("Think Outside The Box").
There seem to be only a handful of us here.
Here is another that even you might
encounter one day: tournaments. Suppose you go to a Video Poker
tournament, and they have normal DB machines in it. Assume these
rules: each gambler can play for an hour, just an hour, and at the
end the person with the highest score wins. What is the proper
strategy here? It is not obvious right away that maximizing EV is the
answer.
I'll make a stronger statement -- it isn't hard to see that maximizing EV
is wrong. Example: you're at the last hand of the hour of play, and
you know your total isn't big enough to win a prize. The EV of that
particular hand is totally meaningless. If your only hope to get paid
is to hit a royal flush, then you should draw five cards to a dealt
34567 Straight Flush. You'd also break up 4-kind, full house, 3-kind
and every other hand in order to make the draw which maximizes
your probability of hitting a royal. Any other play, in this specific
context, would be suboptimal assuming your objective is to maximize
the expected value of your tournament winnings.
Assuming you are "playing blind" in that you aren't allowed to know
if others are ahead of you, one approach for tournaments is to set a
target for final bankroll that you believe will be large enought to win.
Then, play to maximize the probability of hitting that target within the
time allowed. The optimal strategy for this goal is extremely complex
and thus difficult to compute, and has very little to do with maximizing
the EV and any particular play.
Maybe the answer is some sort of strategy like the one you
would use in level 1 of Multi Strike. Certainly the problem needs
examining if you accept to participate in that tournament. Certainly
the idea of one such tournament is not out of the question as a
possibility of something one day a casino might offer.
I've played in such VP tournaments, but they were set up for BARGE
and not available to the general public.
Let us pick another problem closer to your stated play. Suppose you
go to a casino that has comped you, and you want to play 8 hours
there. Suppose it does not have fabulous machines, but you still want
to play there because you like the comps. Suppose also you have $500
for an 8 hour session, and you want to do nothing more than play. The
best machines in each denomination in this casino are these: 8/5
Bonus in dollars, 9/7 DB in quarters, 8/5 JB in nickels. What machine
in what denomination will you play? It might be the answer to this
problem is the one that maximazes EV, but it is not a priori obvious
that is the answer, given the stated problem of a certain bankroll
and a goal of playing with it a certain number of hours.
Once again, we can find "correct" plays for this situation that go
against max-EV. If you've been playing 4 hours and you're down
to your last bet, and your objective is truly to play another 4 hours,
then max-EV strategy is not correct. What you want for this situation
is a minimum ROR strategy, which is slightly different than max-EV.
There are
volatility and risk of ruin considerations that might rule out
maximizing EV as the best solution to this particular problem.
Right. That is precisely the kind of thing that I've been talking about
in recent posts. The "best" strategy is relative to your objective, and
max-EV ignores all other considerations, such as risk of ruin or time
constraints.
Expectation isn't everything. Never was, never will be.
On Thursday 02 October 2003 10:30 am, mubowor wrote:
Thanks for your reply to this thread that has gotten away from TDB.
I know your advice is sound and if I lived in Las Vegas and played
every day, I would be too busy perfecting my strategy of difficult
positive games available such as AA or even 10/7 DB and playing them
for profit, rather than indulging in counter examples to perfect
strategy.
Away from Las Vegas and the VP machines, one amuses oneself with all
sorts of situations. One where one does not maximize ER would be the
following. I ask indulgence on your part for the exaggerated example;
its purpose is not to be disrespectful, but dramatic. Suppose you
were a modern day Queen Marie Antoinette instead of Queen of Comps,
and you were carried off to your execution just for being Queen. On
the way to the guillotine there is a Jacks or Better machine and the
executioner tells you he has instructions to pardon your life if you
play one single game of Video Poker and you do not lose. In go the
five coins. The hand that appears is four to a Royal, Js Qs Ks As,
and another ace. Would you hold the four to a Royal following perfect
strategy? Or would you hold the pair of aces saving your life?
I'm sure in this play, no matter how mathematically correct it is
considered, you would not play the perfect strategy hold of four to a
Royal, thus, essentially, possibly ending all future play. You would
play the incorrect pair of aces, thus ensuring a long term.
I hope that is what you would do. Further, I hope there is no one
that has such blind faith in perfect strategy that in a similar
situation they would play the four to a Royal because it
is "mathematically correct".
I repeat, your advise is useful, and for those who live in Las Vegas
or frequent that city often and have access to the good machines and
the good situations, their efforts are best spent learning perfect
strategies and playing those machines long term. On the other hand,
you have put on people's hands that toy, the Frugal software, that
people will use in different ways searching for alternatives that
might not be optimal, but could help satisfy some secondary goal.
Thanks to all your contributions the hobby of Video Poker is more fun
to all of us players. Regards.
E
Everyone has the right to play any way they want to - and depart
from basic strategy anytime they feel like it - and the right to not
be judged. It is fine for people to have different goals. However,
I have said many times that I don't need to encourage people to play
by the seat of their pants - they do a good job on that without my
help. My goal in writing about gambling is to show people the
mathematical facts so they are aware of how different goals can
impact their long-term results. If you know the facts, and then
chose to depart from basic strategy - that is fine. However, so many
people don't even realize that there is a way that might improve
their gambling results - I like helping to "turn on the light
bulb."
--- In vpFREE@yahoogroups.com, "Jean Scott" <QueenofComps@f...> wrote:
____________________
Jean $cott - "The Frugal Gambler"
MORE FRUGAL GAMBLING can NOW
be ordered, autographed, at a pre-pub
discount, at http://www.FrugalGambler.biz[Non-text portions of this message have been removed]
mubowor wrote:
One where one does not maximize ER would be the following ...
< snip >
Would you hold the four to a Royal following perfect
strategy? Or would you hold the pair of aces saving your life?
Ed, ER is a bit awkward to use in your example, but EV fits -- yes,
you would follow "perfect" strategy in this case and, yes, you would
hold the Aces. These are consistent with each other.
The credits earned from the hand played are irrelevent in determining
EV. The only "payoff" here is saving your ass and so it's the only
variable relevent to determining EV. And a 100% "save your ass"
expectation from holding the pair is better than the 49% expectation
from holding 4 to the Royal.
It's a problem somewhat akin to the tournament question you posed
earlier. There the only relevent payoffs are the cash rewards to
successful finishers.
As Jean has suggested, you've got some confusion in how you're looking
at the "perfect strategy" and ER/EV question.
- Harry
Harry,
Yes, the problem here is an all or nothing problem, purposely so. I
think, though, it could show that even if most cases are black and
white, there are sometimes shades of greys.
By the way, I must agree with you that I am confused by the
definitions of ER and EV. I think I know what EV is, but I'm not sure
all the definitions I have read of it coincide. I confess often I
can't tell what's semantics and what's math when language is used
loosely. When I wrote my preceding post, I looked up quickly the
Strategy Chart in Frugal to see what the numbers there were labeled,
and they were labeled ER, 93.52 for four to a Royal, and 7.68 for the
high pair. I decided that was enough for my purposes.
I have read the FAQs we are encouraged to read, and one part I do not
understand is that relating to ER and EV. This is the definition
there:
"42. What does Expected Return (ER) mean? - ER is a percentage
return figure and it equals [EV divided by Coin-in]. In video poker
circles, EV is sometimes used incorrectly as being interchangeable
with ER.
43. What does Expected Value (EV) mean? - EV = [ER] X [Coin-
in]. EV is the sum of [all possible outcomes times the probability of
the outcomes occurring]. The EV of a video poker hand is the average
value of all the wins attainable, after retaining the optimum cards
and redrawing."
I am embarrassed to admit I do get lost in the above two paragraphs,
even if I do understand the underlying philosophy and could reproduce
the numbers in strategy charts with due patience.
In any case, isn't it true that the ER of hand A is larger than the
ER of hand B if and only if the EV of hand A is larger than the EV of
hand B? If so, then I don't think I have a confusion in using perfect
strategy for all practical purposes. I do grant you that points 42
and 43 of FAQ have me mystified.
E
--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@v...>
wrote:
mubowor wrote:
> One where one does not maximize ER would be the following ...
< snip >
> Would you hold the four to a Royal following perfect
> strategy? Or would you hold the pair of aces saving your life?Ed, ER is a bit awkward to use in your example, but EV fits -- yes,
you would follow "perfect" strategy in this case and, yes, you would
hold the Aces. These are consistent with each other.The credits earned from the hand played are irrelevent in
determining
EV. The only "payoff" here is saving your ass and so it's the only
variable relevent to determining EV. And a 100% "save your ass"
expectation from holding the pair is better than the 49% expectation
from holding 4 to the Royal.It's a problem somewhat akin to the tournament question you posed
earlier. There the only relevent payoffs are the cash rewards to
successful finishers.As Jean has suggested, you've got some confusion in how you're
looking
at the "perfect strategy" and ER/EV question.
- Harry
<<Suppose you
were a modern day Queen Marie Antoinette instead of Queen of Comps,
and you were carried off to your execution just for being Queen.>>
I dub you my knight-of-getting-in-the-last-word!!!!!! 
____________________
Jean $cott - "The Frugal Gambler"
MORE FRUGAL GAMBLING can NOW
be ordered, autographed, at a pre-pub
discount, at http://www.FrugalGambler.biz
[Non-text portions of this message have been removed]
mubowor wrote:
> One where one does not maximize ER would be the following ...< snip >
> Would you hold the four to a Royal following perfect
> strategy? Or would you hold the pair of aces saving your life?Ed, ER is a bit awkward to use in your example, but EV fits -- yes,
you would follow "perfect" strategy in this case and, yes, you would
hold the Aces. These are consistent with each other.
ER and EV are different forms of the same basic concept. I don't
see how one can be "awkward" while the other is clear.
The credits earned from the hand played are irrelevent in determining
EV. The only "payoff" here is saving your ass and so it's the only
variable relevent to determining EV. And a 100% "save your ass"
expectation from holding the pair is better than the 49% expectation
from holding 4 to the Royal.
Mathematically, this is changing to a different random variable for
which we maximize expected value. The max-EV strategies for VP
are based on maximizing "mean bankroll after one play". The random
variable in this case is "player is alive (value =1 if true, 0 if false)".
It's a problem somewhat akin to the tournament question you posed
earlier. There the only relevent payoffs are the cash rewards to
successful finishers.
Yes, and the random variable is "value of prize".
As Jean has suggested, you've got some confusion in how you're looking
at the "perfect strategy" and ER/EV question.
Personally, I don't think Ed is particularly confused. He has discerned a
subtle point -- optimal strategies don't exist in a vacuum, they depend
on your choice of which random variable is used as the basis for solving
the optimization problem. The "usual" definition of EV is based on one
specific random variable, but there are often (if not always) alternatives
which are worth considering.
On Friday 03 October 2003 04:01 pm, Harry Porter wrote:
Yes, this is true. They are two different forms of the same mathematical
concept. ER uses "total bankroll" as the random variable, while EV uses
"change in bankroll" as the random variable.
On Friday 03 October 2003 04:47 pm, mubowor wrote:
In any case, isn't it true that the ER of hand A is larger than the
ER of hand B if and only if the EV of hand A is larger than the EV of
hand B?
Steve Jacobs wrote:
ER and EV are different forms of the same basic concept. I don't
see how one can be "awkward" while the other is clear.
Perhaps I'm mistaken then. However, my take is that EV is an absolute
value. For example, if a possible outcome of an event is a reward of
100 credits and there's a 60% likelihood of that outcome (and 40% of a
0 credit outcome) the EV is 60. In Ed's "Save the Queen" example, in
holding 4 to the Royal the EV is a 49% chance of saving your ass.
ER is, as the administrator defines it, EV/coin-in. If there is no
coin-in, as in this example or a tournament (where EV is based upon
the tournament prizes), I find application of the term ER "awkward".
Mathematically, this is changing to a different random variable for
which we maximize expected value. The max-EV strategies for VP
are based on maximizing "mean bankroll after one play". The random
variable in this case is "player is alive (value =1 if true, 0 if
false)".
I'm not sure what you mean by "changing" since there isn't any other
economic variable to maximize in this instance.
> It's a problem somewhat akin to the tournament question you posed
> earlier. There the only relevent payoffs are the cash rewards to
> successful finishers.Yes, and the random variable is "value of prize".
And, so, is there any disagreement here?
> As Jean has suggested, you've got some confusion in how you're
> looking at the "perfect strategy" and ER/EV question.Personally, I don't think Ed is particularly confused. He has
discerned a subtle point -- optimal strategies don't exist in a
vacuum, they depend on your choice of which random variable is used
as the basis for solving the optimization problem. The "usual"
definition of EV is based on one specific random variable, but there
are often (if not always) alternatives which are worth considering.
Perhaps, however Ed's post suggested that someone might approach the
"Save the Queen" example by desiring to optimize the credits on the
machine meter, which in themselves have no economic value. I don't
think Jean, or anyone else for that matter, suggested that's what
"perfect strategy" is about. It's about optimizing the economic value
at hand, at those credits have no economic value.
------
But Steve, I hope that I haven't suggested that there aren't alternate
variables in a given case that might be chosen for optimization.
Take a variation on "Save the Queen". Let's assume that what's at
risk are the lives of 10 members of the royal family (all of whom are
equally valued). The choices are a default that 6 are killed, or they
may opt to spin a wheel with 11 equally weighted outcomes (0 to 10
deaths) - EV number of deaths = 5. Spinning the wheel is "optimal" in
reducing the expected number of deaths, however, the family may choose
to fix the deaths at 6 rather than risk that a much greater portion of
the family may be wiped out.
Actually, this is a risk preference problem that's akin to why someone
might opt for a lower risk (variance), lower return VP game over one
with higher values of each.
But once one has selected a game to play, there are extraordinarily
few circumstances under which EV/ER aren't the variables to maximize.
Again, I don't deny that some don't exist. But in a vp group such as
this, while it's important to acknowledge that such circumstances
exist, it's critical to suggest that they're few and far between for
the typical player and that EV/ER is the thing to stress.
Otherwise, you get the suggestion that it may be reasonable to
sacrifice considerable EV/ER to assure a greater likelihood of a RF.
That's simply unsound strategy if you're going to play the game
rationally. You might very well use comparable reasoning to suggest a
player hold any and all red cards because they get very excited when
the final hand is entirely red.
There simply are other games they should play if that's how they get
their kicks, not one in which they have money at risk.
- Harry
Steve Jacobs wrote:
> ER and EV are different forms of the same basic concept. I don't
> see how one can be "awkward" while the other is clear.Perhaps I'm mistaken then. However, my take is that EV is an absolute
value.
If that were the case, we would never talk about "negative EV," but that
phrase pops up all the time. A favorable game has an ER greater than 100%
and a positive EV. An unfavorable game has an ER less than 100% and
and negative EV.
For example, if a possible outcome of an event is a reward of
100 credits and there's a 60% likelihood of that outcome (and 40% of a
0 credit outcome) the EV is 60.
Strictly speaking, this represents an ER of 6,000%. This is a "no lose"
scenario, and those are rare in gambling situations. No-lose scenarios
always have non-negative EV.
In Ed's "Save the Queen" example, in
holding 4 to the Royal the EV is a 49% chance of saving your ass.
This should probably be ER instead of EV. Of those players exposed
to the game, 49% are returned alive. That is an EV of -51%.
ER is, as the administrator defines it, EV/coin-in. If there is no
coin-in, as in this example or a tournament (where EV is based upon
the tournament prizes), I find application of the term ER "awkward".
For a tournament, the "coin-in" is the entry fee. For the life/death
situation, the "coin-in" is a live body. But, I think the definitions in
the FAQ are misleading at best, and should be updated.
l'll use E[expr] to represent the expected value of some mathematical
expression that is represented as "expr". When the initial bet is treated
as a single unit, it is represented by a value of 1. ER (expected return)
is then:
ER = E[1+X*p(X)] where the "1" is the initial bet, X is a particular outcome
like +10 bets or -1 bet, and p(X) is the probability of that outcome. Summing
over permitted values of X gives the exptected value of the expression.
ER can be expressed as a pure number like 1.0123, meaning that the
game returns an average of 1.0123 units for every unit played, or it
can be expressed as a percentage of 101.23%. Either way expresses
the total amount returned to the player.
EV simply removes the original bet from the equation, and expresses
the CHANGE in bankroll as a result of the wager. So, we have:
EV = E[X*p(X)]. This can be positive or negative, depending on
whether the average outcome represents a gain or a loss for the
player. EV can also be expressed either as a pure number or as
a percentage. For the case described above with ER, the outcome
here has an EV of +0.0123 units or +1.23%. It might be more
mathematically precies to call this EG for "expected gain," but it
doesn't matter much since terms like EV/EG/ER and not used
consistently, so you have to read carefully to figure out the
author's meaning from the context.
So, we have at least 4 ways to decribe the same concept. We can talk
in terms of EV or ER, and we can talk in terms of units or percentages,
but they all boil down to the same thing after the dust settles.
> Mathematically, this is changing to a different random variable for
> which we maximize expected value. The max-EV strategies for VP
> are based on maximizing "mean bankroll after one play". The random
> variable in this case is "player is alive (value =1 if true, 0 if
> false)".I'm not sure what you mean by "changing" since there isn't any other
economic variable to maximize in this instance.
Not true. The player can still choose to maximize the EV of the bet
itself. That wouldn't be my choice, but maybe the player is suicidal
Using death as an outcome makes the situation too extreme, so let's
reduce the penalty for losing. Also, let's assume that you be faced
with such a situation one week from today, so that you will have time
to prepare an appropriate strategy for any situation that might turn up
on the VP machine. Consider the following possibilities:
Result of Losing:
1) Certain Death
2) Mostly Dead (a la "The Princess Bride")
3) Loss of a pinky finger
4) Public humiliation (perhaps dropped off naked in Central Park)
5) Forced to endure a bad hair cut (perhaps a shaved head)
6) Forced to listen to a one hour lecture on "The Evils of Gambling"
7) Laughed at and verbally abused by your captors.
8) No extra penalty whatsoever.
For case 1), rational people would likely to be interested in learning
the playing strategy which absolutely minimizes the probability of
losing.
What about case 5)? How much monetary EV are you willing to
sacrifice do keep your hair intact? For those who already sport
a cue-ball, this reverts to case 8, but some this would be almost
like case 1). So, faced with this situation, the "optimal" strategy
will be different for different players. That doesn't make one player's
choice "better" than anothers, only different. What is best for you
and your hair implies nothing about what is best for me and my hair.
I put forth that this is true in general, and not just for this kind of
special situation. The CHOICE to maximize EV is not inherently
the "best" choice for every person, and alternate strategies exist
that are every bit as mathematically justifiable as maximizing EV.
The problem with max-EV is that is gives no weight to considerations
of overall risk, is only considers reward.
For case 8), the "experts" would mostly say "play max-EV strategy".
Case 8 is the one where I claim there are other "mathematically
correct" alternatives that should be considered, but which the
"classical" VP experts never mention. Factors of risk, time constraints,
or other considerations are left out of the max-EV equation. Including
these factors leads to different strategies that are just as valid as
max-EV. Those who believe that max-EV is the only "correct"
approach are mistaken.
> Personally, I don't think Ed is particularly confused. He has
> discerned a subtle point -- optimal strategies don't exist in a
> vacuum, they depend on your choice of which random variable is used
> as the basis for solving the optimization problem. The "usual"
> definition of EV is based on one specific random variable, but there
> are often (if not always) alternatives which are worth considering.Perhaps, however Ed's post suggested that someone might approach the
"Save the Queen" example by desiring to optimize the credits on the
machine meter, which in themselves have no economic value. I don't
think Jean, or anyone else for that matter, suggested that's what
"perfect strategy" is about. It's about optimizing the economic value
at hand, at those credits have no economic value.
You're assuming the player won't receive those credits if they survive.
If the conditions are "you lose, you die, but if you win, you get the
payoff" then they credits have economic value. If the payoff is big
enough and the probability of losing small enough, the I'd submit
there is a point where it is worth risking your life in order to win
a sufficient reward. Example: you get a 99.99999% chance of winning
$10 million, but if you lose you die. Give a legitimate offer from people
who I absolutely trusted, I'd accept such a proposition, because it
amounts to a virtual certain win. My risk of keeling over from a
heart attack in my sleep tonight are much higher than my risk of
death from such an unlikely event.
But Steve, I hope that I haven't suggested that there aren't alternate
variables in a given case that might be chosen for optimization.Take a variation on "Save the Queen". Let's assume that what's at
risk are the lives of 10 members of the royal family (all of whom are
equally valued). The choices are a default that 6 are killed, or they
may opt to spin a wheel with 11 equally weighted outcomes (0 to 10
deaths) - EV number of deaths = 5. Spinning the wheel is "optimal" in
reducing the expected number of deaths, however, the family may choose
to fix the deaths at 6 rather than risk that a much greater portion of
the family may be wiped out.Actually, this is a risk preference problem that's akin to why someone
might opt for a lower risk (variance), lower return VP game over one
with higher values of each.
Agreed.
But once one has selected a game to play, there are extraordinarily
few circumstances under which EV/ER aren't the variables to maximize.
Again, I don't deny that some don't exist. But in a vp group such as
this, while it's important to acknowledge that such circumstances
exist, it's critical to suggest that they're few and far between for
the typical player and that EV/ER is the thing to stress.
I used to believe this, but I no longer do. There has been too much
emphasis on EV for too long. Those who take gambling seriuosly hear
so much thumping on the max-EV drum, that the more subtle parts of
the melody are competely lost (if they are "played" at all by the authors).
Readers are left with the mistaken impression that anyone who doesn't
maximize EV is simply wrong and that max-EV is the only "intelligent"
way to play. I constantly see posting on this forum that echo that very
sentiment.
My message: Free Your Mind. If you believe that max-EV is the one
true way, and no others can possibly exist, then you have either
misunderstood or been led astray by "experts" who don't fully comprehend
all of the mathematics that comes into play when finding optimal strategies.
(I don't mean that to be directed at Harry, who has one of the freest minds
around).
Otherwise, you get the suggestion that it may be reasonable to
sacrifice considerable EV/ER to assure a greater likelihood of a RF.
Let me turn that around. The problem with the prevailing max-EV
mentality is that it precludes almost any consideration of the possibility
that sacrificing EV/ER may be correct. "Just maximize EV period" is
the wrong answer, but it is pretty much what the experts tell people
to do.
The problem with the status quo is that we have rampant opinions in
the opposite extreme -- too many people don't understand that there
are very meaningful considerations other than max-EV. People have
become max-EV zombies who have been so totally ingrained with
the max-EV message that they no longer give ANY consideration to
other options. To some extent, this can be traced back to experts
who themselves believe too much in max-EV, and who have forgotten
(or perhaps never knew) that EV isn't everything.
That's simply unsound strategy if you're going to play the game
rationally. You might very well use comparable reasoning to suggest a
player hold any and all red cards because they get very excited when
the final hand is entirely red.
As you know, I'm not advocating irrational play, and the things I'm talking
about can all be reduced to mathematics. Also, I'm not claiming that
it isn't rational to maximize EV, I'm only trying to point out that max-EV
isn't the ONLY rational way to play. Also, in this context I would
define "rational" as "mathematically justifiable in order to meet a
stated objective."
There simply are other games they should play if that's how they get
their kicks, not one in which they have money at risk.
Well, it is their money to risk, and if they TRULY enjoy getting a final
hand that is all red, and that brings them sufficient happiness in
exchange for the monetary cost, then I won't claim that they got poor
value for their entertainment dollar. However, that isn't something that
can be easily reduced to mathematical terms, so it isn't really the kind
of thing that I'm talking about.
On Saturday 04 October 2003 08:37 am, Harry Porter wrote:
Steve Jacobs wrote: <<My message: Free Your Mind. If you believe that max-EV is the one true way, and no others can possibly exist, then you have either misunderstood or been led astray by "experts" who don't fully comprehend
all of the mathematics that comes into play when finding optimal strategies.>>
I must say I have gotten lost in this thread. Help me out, Steve - how does your "belief" (which is respected) differ from Rob Singer's (which is not so respected). I am always willing to try to process new ideas.
Actually, Steve, can you explain your belief in plain words (perhaps with examples without so much math) so we non-math people can understand it. Is it this: there are other goals that people have that might have them (mathematically correct) choose a different hold on a hand than perfect strategy. If that goal is to go for a win in the short term, then that seems to be the same thing Rob Singer is saying. For that person with this goal who varies his strategy for the short term by holding sub-optimal plays, what happens in the LONG run? If these sub-optimal plays in the short term (and they make the game under 100%) are used over a long period of play, will not the result be a lot of mostly-smaller winning sessions, but the fewer losing sessions will be more severe and that person's long-term ER (expected results) will very likely be a total loss figure very near the max-EV percentage?
I do understand (a little) the concept when you are playing a one-machine progressive. (If it is a whole bank of machines with one progressive, I realize that there are many factors to consider.) If you don't have a large enough bankroll statistically to have a very high confidence level of hitting the progressive jackpot in the time you have to spend on this progressive long-term (either at this time or every time it goes positive), you can use the perfect strategy for the base game with the normal non-progressive jackpot instead of a different (computer-derived mathematically correct) strategy that "goes for" the royal more often. With an adjusted royal strategy you will lose more on your way to that royal. However, you will hit the royal more often and sooner (if everything averages out, which it nearly always doesn't in the short term) and your long term ER will be a win probably very near the max-EV percentage. On the other hand, if you use the basic game strategy on a negative base game, you might conserve your bankroll but in the long term, you will have a losing ER very close to what you would have if you were playing the same schedule without a progressive jackpot. In other words, you have to depend on "luck" to hit the jackpot early and pull out a win - but luck plays a decreasing role the longer you play - so in the long run (ultimately) skill (the math) is the only factor that matters.
Am I wrong in saying: If you have the statistically proper bankroll for a play and you expect to play long term (which is a very long time, but we never know the exact figure), it is always better LONG-TERM to ALWAYS use the optimal strategy and never vary from it???
I think this thread is important - and I wish I understood the math better - but it seems that most people are varying from basic strategy because:
1. They are impatient and want to win so bad RIGHT NOW.
2. Their bankroll is limited so they want to maximize the time they can spend playing. (However, many of the choice of games and deviations from basic strategy show that they are really #1 and that these decisions do not maximize their playing time at all).
3. They play so occasionally that they feel they will never get to the long run. (This feeling is not always mathematically based. Most people play longer than they think they do - and they use this as an excuse to validate #1!!!!)
Steve, I respect your mathematical expertise. Can you give me an example of a goal where choice of game or varying from basic strategy is the mathematically correct thing to do if you have the necessary bankroll and if you played forever, you would win more than you would lose, that is, you would be a long-term winner. I just can't think of one - but maybe my weakness in math is clouding my mind here.
A note: I have said many times that no one has the right to judge or condemn another person for his gambling goals. However, I think we need to make a big difference between psychological goals (like #1 above) and mathematical facts. You have every right to play however you want and I won't criticize you. However, if you have "short-term" goals, I don't think you should justify them by criticizing people who look at the long-term math. We all on this list NEED badly to clear up the difference here - because the longer this thread goes on, the more newbies (and many who are not newbies but who are sincerely trying to do the best thing mathematically) are going to be confused - and perhaps throw away valid math considerations. And it can lead to "throwing the baby out with the bath water."
Here is what I wrote in More Frugal Gambling - is it accurate mathematically, I wonder?
"Expected Value (EV)-For comparison purposes, I put a percentage figure beside each game. This is commonly called the "expected value," or "EV" for short, of the game, although it would be more accurate to call it the "theoretical payback" or "average payback" of the game, when you use a computer-derived perfect strategy for an infinite number of hands. We will discuss this more fully in the chapter called "What to Expect," so you'll understand what this EV figure really means when you actually get into a casino. For now, however, simply look at it as one way to compare games. (I have rounded down to two decimal places in most cases.)
And in another place:
Earlier in the section, where I talked about choosing the right game, I listed an EV for each game, expressed as a percentage, i.e. Jacks or Better (99.5%). EV is an abbreviation for "expected value" and it was originally used to talk about any one VP hand. The strategy charts were made up so that you could choose the best hold for any group of five cards depending on the EV of the held cards as determined by computer simulations using millions and millions of trials.
However, sometime in the past, people started talking about the EV of a whole game, rather than just a hand. "Expected value" is not a good description for a VP game when we're talking about the "results" of a computer programmed to play the game perfectly indefinitely, which is indeed how we get those percentages I put in parentheses. Often, more precise phrases have been used, like "expected return" or "expected payback" or "predicted return," but their abbreviations have never caught hold."
____________________
Jean $cott - "The Frugal Gambler"
MORE FRUGAL GAMBLING can NOW
be ordered, autographed, at a pre-pub
discount, at http://www.FrugalGambler.biz
[Non-text portions of this message have been removed]
Thanks for clarifying.
Lenny Frome in 'America's National Game of Chance - Video Poker' uses
EV all the time, and there is a definition and calculations, so it is
clear what it means. Frugal uses ER all the time, but is is amply and
clearly discussed in the Help. Different authors will use different
terms, equivalent but not exactly equal. Sometimes one can discover
what they are talking about.
Say you encounter someone in Las Vegas of a foreign natinality and on
speaking of Video Poker this person talks about "the gathered
moonshine extracted in the hand" and after a while you realize it is
sort of a variation of ER he is talking about, you can then discuss
strategy, knowing how this person deals with the conceps.
Thanks again for clarifying. It makes me feel I'm not really in the
Twilight Zone, as I sometimes feel. LOL.
E
> In any case, isn't it true that the ER of hand A is larger than
the
> ER of hand B if and only if the EV of hand A is larger than the
EV of
> hand B?
Yes, this is true. They are two different forms of the same
mathematical
concept. ER uses "total bankroll" as the random variable, while EV
uses
--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x> wrote:
On Friday 03 October 2003 04:47 pm, mubowor wrote:
"change in bankroll" as the random variable.
Steve Jacobs wrote:
(I don't mean that to be directed at Harry, who has one of the freest
minds around).
Hmmm, I'd like to take that as a compliment, Steve. But you have to
admit that it does smack of suggesting I'm indiscriminate ... Somewhat
akin to describing someone as "easy"
- H.
I'm sorry, I didn't intend to "smack" 
Let me clarify: A free mind is not a weak mind, but a free mind is also
not overly rigid in its thinking. A free mind knows that doubt is not a
weakness, but an important part of the learning process, and so a free
mind is able to question and update its own beliefs as new information
becomes available. A free mind is rarely, perhaps never, absolutely
certain about anything.
Certainly there is a great difference between an "open/free mind"
and an "airhead"
On Saturday 04 October 2003 03:36 pm, Harry Porter wrote:
Steve Jacobs wrote:
> (I don't mean that to be directed at Harry, who has one of the freest
> minds around).Hmmm, I'd like to take that as a compliment, Steve. But you have to
admit that it does smack of suggesting I'm indiscriminate ... Somewhat
akin to describing someone as "easy"