Proper "bankroll" in "short-term" play

[Dan]

Lawrence Boxer wrote:

>
> "Even in a very short session, a higher ER translates to a higher
probability of coming away a winner."

Let's all agree on that!

No Rob, with all due respect, let's not. The second part of the above
statement from the same poster was more applicable. It said, "In a short
session, however, variance becomes the dominant factor."

Short term results are almost entirely determined by variance and are
unpredictable. ER has little or no relevence in the short term.

The salient question is: can you predict results with any accuracy either
long term or short term? The answer is in the short term no, in the long
term yes.

I stick by my statement that even in a very short session, a higher ER translates to a higher probability of coming away a winner. But of course that's a generality.

And I retract my second statement, that variance is the dominant factor in a short session. I spoke without thinking on that one.

Let's take an example. The original Draw Poker game (circa mid 80's) was the same as today's 9/6 Jacks of Better except that it did NOT return your bet for a pair of jacks or better. The maximum payback was about 81.3%, but the variance was LOWER at only 18.7 compared to 19.5 for 9/6 JoB.

Suppose you decide to play for one hour (a short session). Would you have a better chance of ending up a winner on that game or on a 9/6 JoB? How's that? You prefer the JoB game in spite of the higher variance?

OK, that was a rather extreme example, but the principle is the same between, say, 9/6 JoB and 8/5 JoB, or any other similar games. The point is that variance by itself is not a dependable measure of desirability. ER is a better measure, but by itself it not always reliable either. That is why I defined my Attractiveness Quotient back in 1994.

The nice thing about the Sorokin formula is that, unlike other statistical measures such as variance or standard deviation, it is just a useful for the short term as for the long term. You can calculate Risk of Ruin for a $10 bankroll just as accurately as for a $1,000,000 bankroll.

Dan

···

--

Dan Paymar, author of the book, "Video Poker - Optimum Play"
Editor and Publisher of "Video Poker Times" newsletter
Web site at http://www.OptimumPlay.com

"Chance favors the prepared mind."
-- Louis Pasteur

[Lawrence_Boxer]

I stick by my statement that even in a very short session, a higher
ER translates to a higher probability of coming away a winner. But of
course that's a generality.

And I retract my second statement, that variance is the dominant
factor in a short session. I spoke without thinking on that one.

Dan, as I mentioned in my previous post, I'm willing to bend a little
because I think I was too stubborn in downplaying the role of ER in short
term play. To repeat, since ER is a per-hand computation it is valuable in
making a hold decision. I still maintain though that ER is a poor
predicator of short term results, as compared to long term play, and that
variance (volitality, deviations, whatever) are the primary factors in short
term results.

Let's take an example. The original Draw Poker game (circa mid 80's)
was the same as today's 9/6 Jacks of Better except that it did NOT
return your bet for a pair of jacks or better. The maximum payback
was about 81.3%, but the variance was LOWER at only 18.7 compared to
19.5 for 9/6 JoB.

Suppose you decide to play for one hour (a short session). Would you
have a better chance of ending up a winner on that game or on a 9/6
JoB? How's that? You prefer the JoB game in spite of the higher
variance?

Let me put it this way. If you gave me $100 and told me I've got only 5
minutes to bang out the biggest win I could, I'd choose the highest pay
progressive I could find regardless of variance and play as correctly as
possible and hope for the best outcome. otoh, if you gave me the same $100
and told me to make it last as long as possible, yes, I'd choose fpdw or
some other lower variance game. In either case, ER would be a factor
because it determines the proper holds, but in the first case I would be
hoping for variance to be the determining factor, while in the second case
I'd be rooting for the ER.

The nice thing about the Sorokin formula is that, unlike other
statistical measures such as variance or standard deviation, it is
just a useful for the short term as for the long term. You can
calculate Risk of Ruin for a $10 bankroll just as accurately as for a
$1,000,000 bankroll.

True, but as you've pointed out previously, a higher starting bankroll will
result in a significantly lower ror than a lower starting bankroll, assuming
the same positive expectation game. Why? Because in order to survive the
variance, you've got to have the proper bankroll.

But that bankroll size is less of a positive factor in short term play
because the ror in short term play *assumes* a smaller bankroll, and so it
seems to me that short term expectations and the increased ror are
analagous, which is to say that in short term play ror is higher because
variance has had a bigger effect on outcome...

...which leads me to say that there are no reasonable expectations in short
term play and that ER is not the significant factor that it is in long term
play.