Lawrence Boxer wrote:
Dan wrote:
> I stick by my statement that even in a very short session, a higherER 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.
And I stick by my statement that ER by itself is a much better predicator of results, either short term or long term, than is the variance by itself. But it's much better to take both into account.
That's why I developed the Attractiveness Quotient, which combines the ER and variance into a single number. In case you're not familiar with the AQ, it's the player's advantage (the game's ER less 100%) divided by the standard deviation (the square root of the variance) and multiplied by 1000 to put it into a range that makes it easy to compare games. If you include any slot club rebate in the ER, it makes it easy to compare casinos as well.
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 situation you describe, trying for the biggest possible win in 5 minutes, is nearly identical to a VP tournament. That's very short term, probably about 100 hands. I'd look for a game with good medium term payoffs, such as Double Bonus or DDB, and hope to get lucky with one or more quads. A progressive royal is long term and not worth considering in this situation.
If you told me that I was in a contest to make the $100 last as long as possible (which I'll take to mean the maximum number of hands) I'd much prefer something like 9/7 Jacks or Better, but that game is now apparently extinct. Anyway, I'd be looking primarily for low variance, as you would. I'd probably end up on 9/6 JB at a casino with a really good cash back slot club.
But neither of these scenarios has anything to do with being a winner outside of the tournament environment. As an individual player starting with the same $100 and hoping to be a winner, I'd look for the highest AQ. Remember, that figure combines ER, variance and slot club rebates, all very important. Or, better yet, I'd use the Sorokin formula to evaluate the available games and slot clubs with a $100 bankroll. I'd want the lowest RoR, so I'd probably end up on the Fiesta nickel FPDW.
> 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.
That's just stating RoR a different way. You've reinforced my point.
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...
Most people playing only a short session are doing so because either they will only be in Las Vegas for a short time (e.g. a weekend) or they have a very limited bankroll. In either case, RoR calculations are important.
...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.
There are reasonable expectations in the short term, the long term, or any term. Even in a short term consisting of a single unit bet, the higher the ER, the better probability of being a winner.
And as I've shown with the example above, variance can be very misleading. I can't think of any situation where the AQ or the RoR (Sorokin) is misleading.
Dan
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--
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