Hi Steve Jacobs,
I came out of my cave for some fresh air, and read your post. I'm not
sure I understand all the details. Read your post again and you'll
see there are some typos, and there are some numerical conclusions
that are not obvious; but I grant you I might be a bit lost due to
not being too smart. I think maybe I do understand what you mean in
general. You are saying that the max EV mathematical model works
perfectly for someone with unlimited funds and unlimited time. You
are saying if I understand you correctly, that this is generally not
the case. On an evening in town people have some bucks to blow and
they want to make some cash; in other words, for example, they are
willing to risk, say, $100, and are willing to be satisfied if they
win $1,000 (goal). You give a more extreme example, a risk of a
dollar and a win goal of 35 dollars. Since this is a VP group, a lot
of people were unhappy that you chose craps and roulette and
suggested working out examples in VP. I could try to work out the
analogous example on VP, but, as I said, I did not understand
completely your post so I can't do that. Stumbling in the dark it
occurs to me that perhaps you could change your example to risk a
hundred, and try to get a thousand in an evening. Then you walk to a
casino that only has quarter Jacks or Better and quarter Atlantic
City Joker Poker. The first machine has a payback of 99.54% (97.56%
without a royal), a royal cycle of 40,390 and a variance of 19.51.
The second machine has a payback of 97.19% (90% with no quintet,
ouch!), a quintet cycle of 10,994, and a variance of 70.41. Surely if
you have a lot of money and time, as I said, you will want to play
the first machine if the comps and cash back are good enough. But if
you have $100 to blow and some good fellow is after you and might
terminate you by midnight if you don't come up with a thousand, would
the mathematics tell you it is smarter to play the second machine?
Here are some choices:
1. - Bankroll preservation. You stay home and keep the $100. You face
the fellow at midnight and tell him you only have $100, but will
definitely produce the rest. He might spare your life to collect more
dough.
2. - You play the JB machine, and have a few free drinks to relax
your nerves. You might or might not make money depending.
3. - You play the Joker machine and have a few free drinks too. You
might or might not make money. Your chances of a thousand in that
short time are better here than in 2, and your chances of a straight
flush that pays 500, and thus gives you back the hundred are better
here too. But, of course, if you don't hit those combinations you
might lose more than on point 2.
How does one make a mathematical model of your evening's predicament?
Can one relate this imaginary problem with your roulette and craps
example, the AC machine being the roulette, the JB machine being
craps?
I tell you, me, I like being lots of standard deviations away from
the expected return, in the right direction Lawrence Boxer likes. How
can that happen? Well, give me a bunch of consecutive royals. There
is nothing in the mathematics to rule that out. Unfortunately, there
is also nothing in the mathematics to lead me to get those honey
bunches of royals. Some gamblers have lucky stars, others are star
crossed, most grind away.
I can see your examples try to introduce into the mathematical
modeling of gambling other factors pertinent to the gambling
situation. You seem to have something that is clear in your mind
since you have insisted on these topics repeatedly, but a lot of the
statements you make are hypothetical, tentative, inconclusive a few
signs of this are your frequent uses of quotation marks, question
marks and parentheses-, which leads me to suspect you have not worked
out completely, even for yourself, your dogmas. I wish you luck in
that, as well as in gambling.
E
"There are two kinds of charlatan: the man who is called a charlatan,
and the man who really is one. The first is the quack who cures you;
the second is the highly qualified person who doesn't." Chesterton.
> vpFREE Dogma
>
> Although we continue to see new video poker games and analytical
> software, mathematically based video poker principles and playing
> strategies are pretty cut and dried.
I'm forced to disagree. To borrow a phrase, "... the truth is not
only
stranger than you imagine, it is stranger than you CAN imagine..."
OK, I hope that is a bit of an exaggeration, but part of the message
that I'm trying (in vain?) to convey in this forum is that EV
doesn't
quite work the way most people think that it "should" work.
> Playing Strategy
>
> In routine, everyday play anyone trying to maximize their profits
will
> always use optimal EV strategy when playing a hand.
You're not going to like this, but that statement is false and
misleading.
I know you won't agree, but that is part of what I've been trying to
say in my posts. Max-EV does NOT necessarily maximize profits!
> Players with different
> goals may choose other strategies, but in doing so they lower
their profit
> expectations.
That simply isn't true. There are at least three factors that
interact to
determine the player's expected outcome. EV is only one of those
factors,
in addition there is a nebulous factor that I'll just call "risk"
and there
is the player's chosen objective -- what they are striving to
accomplish
in terms of shaping their bankroll.
The max-EV strategy is designed to optimize the outcome of one
isolated wager, in terms of average number of dollars returned to
the player by making that wager. This is very much like saying
"if I want the most money back RIGHT NOW, what is the best
play." This is misguided. That's right, it is misguided, and I'll
give
an example below to illustrate. The truly optimal play can only
be determined when also taking into consideration the risk and
the overall objective.
Here's an example (I may have posted this here previously, but
I'm not sure). Suppose you want to parlay a one-unit bankroll
into N units, where you pick N in advance, and then go play until
you either reach the goal of N units, or lose. The average return
will be N*p(winning N) - 1*[1 - p(winning N)] or just (p*N - (1-p))
or (p*(N-1) - 1). For now let's pick some number for N, say 36.
So, the stated objective is "parlay one dollar into 36 dollars, or
go bust trying".
We can try to reach this objective in a single bet, or we can use
a series of bets in varying amounts. This choices made here define
our betting strategy, and the game(s) played may or may not involve
playing decisions. VP allows the player to make meaningful
playing decisions, while games like Baccarat and Roulette allow
no choice other than size and type of wager.
Now suppose that you only have two games to choose from. You
can play at a craps table which allows no odds bets, or you can
play roulette. You are free to switch back and forth and make any
wagers that you want. These are unfavorable games, so to give
the "intelligent" gambler some motivation for playing, we'll say
that
the casino has agreed, as a special promotion, to double the final
bankoll to 72 dollars for those players lucky enough to reach the
goal of 36 units. This does not change the objective -- it is still
best to maximize the overall probability of ending up with a 36 unit
bankroll.
In terms of EV, the two best bets at the craps table are the "pass"
and the "don't pass" which both have a house edge of 1.4%. The
"don't pass" is slightly better, so we'll assume that when craps is
selected, the player will wager on "don't pass" (with no odds
allowed).
The roulette game is a standard American double-zero game where
any wager has a house edge of 5.26%.
Conventional wisdom is that the craps wager is "much better" because
is has a much lower house edge. But that doesn't tell the whole
story.
If we bet our $1 bankroll on a single number at the roulette table,
we
get a 1/38 chance of winning a 35:1 payoff, which takes us directly
to our goal of $36. If we play craps instead, the "don't pass"
wager
can be treated like a coin flip that has p(win) = 949/1925. This is
a slight simplification that comes from doing an immediate replay
of pushes, but for this problem we would replay anyway since there
are no time constraints involved. With p(win)=949/1925, the
probability
of reaching a 36 unit bankroll before going broke is complicated to
compute, and I won't go into the details here (but I'll supply them
on
request). Bottom line: playing craps instead of roulette gives the
player a smaller probability of reaching the goal, and reduces the
overall probability of a win from 1/38 to 0.97757/38, so that the
players actual cash profit from this promotion is reduced by 2.24%
if they choose craps instead of roulette.
Is that clear? Playing the game with "better" EV actually reduces
the
player's profits in this example. This flies in the face of how EV
is
"supposed" to work. This isn't a case of sacrificing EV in order to
reach some non-monetary goal, it is a case of intentionally choosing
plays with worse EV in order to WIN MORE MONEY. EV is NOT some
kind of universal measure of "monetary goodness," as is widely
believed, and as Tom has repeated here. EV is only part of the
equation, and the other factors shouldn't be (but often are)
ignored.
Here's more strangeness. If we play the same "parlay 1 unit into N
units"
game with craps and roulette, but change N to a small enough number,
then craps becomes the better game. Roulette is better when N is
12 or
larger, and craps is better when N is smaller than 12. So,
the "best"
game depends on the extent to which the parlay represents a "long-
shot."
Risk and EV must both be considered, in the context of the overall
objective, in order to determine which bet is ultimately more
profitable.
VP is no different, but is much more complicated to analyze.
Maximizing
EV is sometimes (not always) a misguided concept, and it isn't
nearly
so "cut and dried" as it seems. The EV that is computed by the
programs
is the EV of single isolated wagers, but the overall results that
we achieve
are a result of a series of wagers that combine together into an
overall
result. The strategy which is optimal OVERALL is not necessarily
the
one which picks individual wagers with the highest EV, and this
remains
true even when your chosen goal is "maximum profit."
Max-EV does NOT guarantee maximum overall profit, it only maximizes
the "near sighted" profit on individual wagers. To focus purely on
EV
is to miss the forest because all you see is the trees.
>
> Short Term Playing Strategy
>
> How many hands a player will play in a session, a trip, or their
lifetime
> is irrelevant when playing a hand of video poker. Anyone trying
to maximize
> their profits will always use optimal EV strategy when playing a
hand.
> Players with different goals may choose other strategies, but in
doing so
> they lower their profit expectations.
Again, this is false and misleading. I know that wasn't your
intent, but
your statements have convinced me that you haven't fully grasped
what
I've been saying in my posts. It isn't merely that "alternate
goals" can be
mathematically justified, the very goal of "maximum dollar profit"
is a goal
that cannot always be reached simply by "always us[ing] optimal EV
strategy when playing a hand." The interaction between EV, risk and
overall profit is much more complicated than the picture you
paint. I know
you are simply following "common sense," but probability theory is
a domain
where common sense and reality do not intersect. It is truly
stranger than
you (and many many others) have always imagined it to be.
> The Dogma states vpFREE's view on video poker and provides
perspective
> for new members. Hopefully it will answer some routine questions,
> without suppressing future discussions of its contents.
It appears that my Karma just ran over your Dogma. Sorry about
that, it ran
out in front of me before I could hit my brakes. I know it was
probably
a cherished pet, and I'm really very sorry, but I don't think it
will survive.
···
--- In vpFREE@yahoogroups.com, Steve Jacobs <jacobs@x> wrote:
On Thursday 09 October 2003 11:57 pm, vp_FREE wrote:
