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.
I haven't read very many of Rob's articles, so I'm not really in a position to
compare my position with his position 
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.
That is close to what I mean, but I think I use the word "goal" differently
than you are using it here. When I talk about goals and/or objectives,
I'm talking about concepts that can be reduced to a mathematical
formula (or, at least, a computer program) which can *measures*, in
some precise way, the effectiveness of the strategy for meeting the
stated objective. It is hard to describe this without math, but I can
draw an analogy. Let's say that computing EV is for a VP game is
analogous to measuring a person's height in inches. There are many
other measures that can be applied to a person, and each measurement
describes a different aspect or characteristic of that person. We could
measure their circumference as interesting places, or measure their
weight or volume, temperature in/on/around different parts of their body,
all kinds of things. We could measure how fast they run, how loud they
can yell, hundreds of different things.
Now suppose we have a contest to determine who is the "best" person,
and we invite "experts" to measure the people who have entered the
contest and declare a winning. Some basketball player is picked as
the "obvious" winner based on their height, and NOBODY says "hang
"who is best". Well, that is somewhat like what is happening (and has
been happening for a great while) in the gambling community. We have
this measurement that the "experts" all like, known as EV. Whenever
anyone says "what is the best way to play" or "what is the best game"
the community all in harmony announce "Strategy X has EV of 100.39%"
or "Game Y has EV of 100.8% while game Z have EV of 99.93% so
clearly game Y must be better."
What has been lost, whether through tradition or lack of attention to
detail, is the fact that "what is best" isn't a meaningful question unless
we include "best at WHAT" as part of the question.
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?
I don't think that question is relevant. If your actual stated objective
is truly short term (example: 1 hour of tournament play) then what
WOULD happen in the long run isn't necessarily relevant. Different
situations call for different strategies, what applies to one situation
doesn't automatically apply to all situations.
That doesn't mean that I'm backing up Rob Singer. I don't know what
he has claimed, and finding mathematically optimal strategies is
a difficult task even for those who have the appropriate math
background.
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?
That is pretty much true, but it isn't necessarily relevant. Forcing the
short-term player to play a long-term strategy is mathematically
equivalent to forcing a player in a tournament to stick strictly to the
normal max-EV strategy. The correct tournament strategy is suboptimal
for casino play, and the correct casino strategy is suboptimal for
tournament play. Each strategy is suboptimal from the perspective
of the other situation.
I should also mention that it isn't as simply as short-term vs. long-term.
I think when people say "long term" what they really mean is that the
player is free to play indefinitely provided they have the funds to
continue. In other words, they aren't forced to stop playing after some
specific time has elapsed, or some fixed number of plays, or some
other event. There are different long-term objectives which yield
different strategies. Max-EV is well known. One alternative is to
play in such a way that you minimize risk of ruin. This calls for
a different strategy than max-EV, but places no other constraint
on how long the player is allowed to play. The max-EV strategy
is focused on winning dollars as quickly as possible. The min-ROR
strategy is focusend on reducing the probability of going broke. If
the game is favorable, then ANY strategy which yields a positive
EV will give the player some chance of having their bankroll grow
indefinitely. Maximizing this probability is equivalent to minimizing
the probability of going broke (a.k.a. risk of ruin).
In general, the min-ROR strategy will be slightly different than the
max-EV strategy. From the perspective of the min-ROR player,
the max-EV player is playing suboptimally by needlessly
increasing risk of ruin. From the perspective of the max-EV player,
the min-ROR player is playing suboptimally by needlessly
sacrificing EV. Each player is playing correctly for their OWN
objective and playing incorrectly for the other player's objective.
I don't believe there is any mathematically valid way to declare
one objective "superior" to the other. Each strategy is "best" in
its own way.
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.
Ask "computer-derived mathematically correct for WHICH objective?"
With an adjusted royal strategy you will lose more on your way to that
royal.
No, just the opposite (if I'm understanding you correctly).
What you describe above is ALMOST a comparison of max-EV and
min-cost strategies. The goal of the min-cost strategy is to minimize
total dollars lost, on average, while "waiting" to hit the progressive
jackpot. This causes the royal cycle to increase, so that it takes more
rounds of play on average to hit the royal, but at the same time it
reduces the "drain rate" averaged over the non-royal payoffs. The
"cost" of playing for the royal is (drain-rate * cycle-time). The min-cost
strategy reduces this value to a minimum. As a result, fewer dollars
are deducted from the jackpot to "pay back" the cost of doing business
while waiting for lightning to strike. The net result is to maximize your
average net worth, as measured just after you hit the royal and walk
out of the casino with the proceeds.
If you use a max-EV strategy, and continuously adjust the strategy
based on the value of the royal, then as the progressive increase
the strategy will "try harder" to win a royal. This causes the royal
cycle to decrease, but the "drain rate" actually goes up and the
overall cost per royal increases as well. The overall effect is that
you win royals more often, and you win money at a faster rate,
but your net gain PER ROYAL is lower.
The min-cost strategy is different than either the base strategy or
the max-EV strategy. The min-cost strategy can be found as
follows: pretend that the royal jackpot is just barely large enough
so that the max-EV strategy gives a break-even game. The
max-EV strategy for this break-even jackpot is the min-cost
strategy. The break-even point is usually above the base game,
so the base strategy is "too conservative" relative to min-cost.
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.
True. But, if these opportunities are few and far between, so that
you essentially win a fixed number of royals per year (with lots of
idle time in between) then the min-cost strategy will give a higher
annual rate of return. Do you want more money for the year, or
do you want to play fewer hours in order to win the money? If
it is your only source of income and you like to play anyway, then
the min-cost strategy gives you more playing time and more dollars
to spend. Unfortunately, that only holds for "one machine"
progressives -- not very common.
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.
That isn't quite right. In effect, the break-even point divides the jackpot
into two chunks. The first chunk is what "pays back" the playing costs.
After you cover the playing costs, the rest of the jackpot is expected
profit. So, whatever base strategy you start with, if the jackpot is $500
above break-even and you stick with that strategy, your expected
profit is $500. You can do better than the base game by using the
min-cost strategy to reduce the average playing cost to the lowest
possible level, making the expected profit as large as possible. This
gives maximize dollars per royal flush.
The min-cost strategy maximizes the expected value of final bankroll,
without regard to the number of rounds played. Min-cost doesn't care
how long it takes to reach the goal. Max-EV doesn't care about the
size of the overall net win, it only cares about winning the most money
per play. $$$/royal vs. $$$/decision is the fundamental tradeoff
between these two strategies, and again each strategy is "best" in
its own way.
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.
The objective also matters. If you specifically wish to maximize average
dollars per game played, then max-EV meets that objective. If instead,
your specific objective is to maximize the number of dollars won per
royal flush, then the min-cost strategy is optimal. Both are totally founded
in mathematics.
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???
You are right and wrong at the same time (how is that for a baffling
response). The problem is the phrase "THE optimal strategy". If EV
per play was the only conceivable way to measure the "goodness"
of a game, then it would make sense to talk about "THE" optimal
strategy. But, in reality, there are many aspects of a strategy that can
be measured in a meaningful way. I hope the min-cost vs. max-EV
discussion above has helped clarify. If not, please ask more questions
and keep thinking about this. I know it is a difficult concept. It takes
time and effort to really come to grips with how this works. But, it is
just like measuring people -- who is "most extreme" depends on what
aspect you measure, whether tallest/heaviest/loudest/smartest/fastest
or whatever. Which is "best" is always relative to the objective.
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!!!!)
Right, people do a make a lot of choices that can't be described by math,
and I don't know how to measure such things. I also don't believe for a
minute that "all plays are optimal for SOME strategy," so that isn't what
I'm saying either. But I am saying that deviation from max-EV strategy
isn't automatically justification for declaring a play as "wrong."
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.
The "minimize cost of hitting a royal" strategy described above is just such
an example. Part of the reason that you can't think of one is that you're
conditioned to thinking that max-EV is the "only TRUE way" to play. That
way of thinking becomes an ingrained habit that is hard to break. I think
the hardest part is to let go of the idea that there is some "universal" best
way that is right no matter what situation comes up. I think we instinctively
want there to be "one right way" to do things that are mathematical.
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.
I agree, but you also should understand that this door swings both ways.
If someone has a short-term goal, such as "turn $30 into $80 or go bust
trying" the optimal strategy may in fact be mathematically different than
the optimal strategy for your chosen goal (whether long-term or not). The
phrase "short-term" shouldn't be thought of as a code phrase for "non-
mathematical".
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."
I agree that this is important, but I don't think this can be cleared up
quickly. It is very hard to shift one's thinking away from "there is only
one way" to "there are many right ways." Some here won't even try,
because it will be easier to them to simply claim (to themselves, if not
in the forum) that I'm off my rocker. I'm glad to know that you are willing
to make an effort to understand what I'm saying.
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.)
I don't have any issue with that statement. It is correct to say "...one way
to compare games...". Some would claim it to be "the only way" or "the best
way" to compare games, and then I'd take issue with the statement.
But, the more I learn, the more I believe that EV isn't always a good way to
compare games. If EVERYTHING else is equal, then the game with higher
EV is the better game. But, people tend to forget the "everything else" part
and only remember "higher EV is better." That is where much of the trouble
comes from.
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."
A rose by any other name....
Thanks for the discussion, I hope I've been able to clarify some things.
···
On Saturday 04 October 2003 02:00 pm, Jean Scott wrote:
on here, who declared "height" as the only meaningful measurement?" It is just "accepted" that height was what we all meant when we said