vpFREE2 Forums

common fallacy: convergence to the mean

#1

it's a common fallacy in video poker to assume that the more hands
that are played the more likely the results are to be the mean

the mathematical reality is the central limit theorem which says that
the more hands that are played the more the results become normalized
(symmetrically distributed about the mean, not equal to the mean)

the fallout from the central limit theorem is the formula for
N0=variance/(er+comp-1)^2 which says that for a positive gamble
(er+comp-1>0) at N0 hands of play your chances of winning are 84% and
for a negative gamble (er+comp-1<0) at N0 hands of play your chances
of losing are 84% [for an even gamble (er+comp-1=0) N0 is infinite and
on a limited bankroll you face eventual bust, not convergence to the
mean as many think]

examples:
full pay (15/9/5) deuces wild and 0.25% comp:
N0=25.8/(1.0076+0.0025-1)^2= 252,916 hands
nsu (16/10/4) deuces and 1.25% comp:
N0=25.8/(.9973+.0125-1)^2= 268,638 hands
ugly ducks (15/9/4) and 2% comp:
N0=25.6/(.9891+.02-1)^2= 309,141 hands

at 4xN0 your chances improve to 98% (2sd)
at 9xN0 your chances improve to 99.85% (3sd)

[assumes perfect play, sufficient bankroll, random deal, central limit
theorem]

#2

--- In vpFREE@yahoogroups.com, "nightoftheiguana2000"
<nightoftheiguana2000@y...> wrote:

it's a common fallacy in video poker to assume that the more hands
that are played the more likely the results are to be the mean

The above is an Incorrect statement, overall results will TEND toward
the ev or mean of the game, as a larger number of hands are played
i.e. muliply you total wager times game ev

the mathematical reality is the central limit theorem which says

that

the more hands that are played the more the results become

normalized

CLT is that theorem that justifies using normal approximations to
distributions that are not Normal distributions...it's that simple,
nothing complicated.

(symmetrically distributed about the mean, not equal to the mean)

the fallout from the central limit theorem is the formula for
N0=variance/(er+comp-1)^2 which says that for a positive gamble
(er+comp-1>0) at N0 hands of play your chances of winning are 84%

and

for a negative gamble (er+comp-1<0) at N0 hands of play your chances
of losing are 84% [for an even gamble (er+comp-1=0) N0 is infinite

and

on a limited bankroll you face eventual bust, not convergence to the
mean as many think]

if you are playing a sub 100% game you face eventual bust given a set
amount of bankroll and infinite play that's what is meant by playing
a game where the ev(mean) is less than 100%...you slowly or not so
slowly as the case might be go bust..you don't need any formulas to
figure that out...I should hope not. I think trying to make the issue
more complcated than it is, has clouded your reasoning.