Mathematics

[Allen1]

Then, using approximately 5%, that means that if one is playing near perfect play that variance alone in the long term will make a player's outcome range between [using 101% return for the example] 96% and 106%.

That is a huge difference in terms of dollars. While I agree that near perfect play will insure, somewhat, a closer to positive return, it is no guarantee. It "seems" that slight variances of play have less of an affect on your total return that does SD. "If" that is true than SD, which I like to refer to as "luck" plays a bigger part that we want to admit.

That does not mean abandoning good or perfect play. For me personally, I've adopted slight variances. Those changes speed the play and decision making up for me, as well as making the game "more fun" to play while not costing me my bankroll.

These changes I have employed at both FPDW and DB. I can only argue results. I make 12 trips a year to LV. I started with a $500 bankroll four and one half years ago. I have taken out approx $2000 in that time for various projects or items of purchase and the fund is still bigger than what it started out. That's results, no mathematics. Could it have been higher with perfect play? Perhaps, but that is arguable. There are several instances where because of altered play [I keep fairly good records] that I have hit either four deuces on FPDW or a RF on other machines, DB.

These figures are based on about four and one half years, 12 trips a year, about 12,000 hands per trip at various casinos. That's far from a scientific distribution. However, 648,000 hands is a decent measure to base my conclusions. Keeping in mind that I play for pleasure with the goal of still achieving a profit. None of this includes my free rooms, meals, other discretionary comps or cash back.

I'm not saying I've made a living. Far from it!! But for the vacationer's standpoint, I can't argue about success. I don't suggest it as any system. I don't suggest it for the daily player. [local] I realize that the more one plays, the more likely the figures, math or "long run" will make the numbers ring truer to the percentages. Just one man's point.

···

At 10:14 AM 10/6/2003, you wrote:

According to the vpfree FAQ, SD is the square root of variance,
so the SD for 10/7 DB should be around 5.32.

[Lawrence_Boxer]

Then, using approximately 5%, that means that if one is playing

near

perfect play that variance alone in the long term will make a

player's

outcome range between [using 101% return for the example] 96% and

106%.

We also need to remember that the more hands played correctly, the
more liklihood that the expected outcome will result.

That said, is it incorrect to think that each session's results are
almost entirely the product of variance, and so are entirely
unpredictable, but the sum of all variance over time (assuming
perfect play) results in the expected outcome, or at least most
likely fell ("fell" not "will fall) within the SD, although the end
result might still be a net loss?

That is a huge difference in terms of dollars. While I agree that

near

perfect play will insure, somewhat, a closer to positive return, it

is no

guarantee. It "seems" that slight variances of play have less of an

affect

on your total return that does SD. "If" that is true than SD,

which I like

to refer to as "luck" plays a bigger part that we want to admit.

I think it might be more accurate to think of variance as being
analagous to luck. Just to clarify, did you mean that SD plays a
bigger role, or that variance plays a bigger role?

These changes I have employed at both FPDW and DB. I can only argue
results. I make 12 trips a year to LV. I started with a $500

bankroll four

and one half years ago.

I've seen your results, and I agree that the slight changes you've
made have been astoundingly successful, and make good sense. My only
comment would be that by making those kinds of changes, all long term
expectations based on "perfect" play are significantly affected.
iow, all long term bets are off. Not that you should mind, based on
your excellent results, which are much better than the baseline
expectations would ever be.

lb

[Harry_Porter]

Allen wrote:

>According to the vpfree FAQ, SD is the square root of variance,
>so the SD for 10/7 DB should be around 5.32.

Then, using approximately 5%, that means that if one is playing near
perfect play that variance alone in the long term will make a
player's outcome range between [using 101% return for the example]
96% and 106%.

There's some confusion in what standard deviation means here.

This value for SD represents 5.32 bets. 78% of wins will fall within
1 SD of one wager. Obviously when it comes to a single wager this
range makes little sense.

Quantitative application of standard deviation is practical only over
a large number of hands and requires a modestly complex forula to
determine what the SD is for the outcome of playing a given number of
hands (using the SD of playing a single hand).

For the typical player, the best application of SD or variance is as a
rough measure of the relative risk of play between two games.

- Harry