vpFREE2 Forums

Holdem variance versus JOB

#1

I've started playing a little online Texas Holdem lately and trying
to understand some of the math behind it. Variance is as much a topic
on Holdem boards as it is here. People are talking about standard
deviations from their play of 15-17. I'm not sure how they are
measuring it but assuming that's correct and that it's based on
profit (loss) per hand, how does that compare to VP? The SD on JOB is
about 4, but then you play many more hands of VP in an hour than you
do Holdem. Yet I don't think of variance as being a function of time
so much as absolute highs and lows. Any thoughts on how to compare
the two?

The "rule-of-thumb" bankroll needed is 300 "big bets", or $1800 for
the traditional 3/6 casino game. Can anybody calculate the %ROR this
equates to? If you need additional assumptions for a full comparison,
you can assume a play rate of 40-60 hands per hour and an expected
profit of 2 big bets per 100 hands.

I know the wizard has some stuff on his site, I'm going there next,
just thought I'd stop here first. The Holdem message boards seem to
be great on how to play certain situations and reading your opponents
but math is kind of frowned upon (anybody else smell opportunity
there?).

#2

as generally used in video poker, variance means normalized per bet
per hand variance

standard deviation (sd) is the square root of variance

to get normalized per hand $sd multiply by dollars bet
for example, for 9/6job, er=.9954, var=19.51, $5/bet
$ev/hand=$5(.9954-1)=-$.02
$sd/hand=$5(sqrt(19.51))=+/-$22.09

to get standard deviation for any number of hands:

sd(hands)=sqrt(variance x hands)

for example, for blackjack you will often find sd(100) (standard
deviation of 100 hands, about an hour of play)

the caveat is that these are "normalized" numbers
obviously you can't lose two cents on one job hand nor can the sd be
+/-$22.09, the most you can lose is one bet
but, if you were to play a large number of hands, for job around
several royal cycles, you would approach these normalized ev and sd
values
for less than several royal cycles your expectation would be
significantly less (you don't expect to get a royal which is some 2%
of your expected return) and your sd is also less but significantly
skewed (asymmetric)

as for hold'em, which i think is off topic here, i'll just say there
are online sites with math and there are books with math
hold'em is a game that seems very simple, even boring, which is why
everyone thinks they can play it, but in reality it is very complex,
as far as i know no computer can yet beat the best humans at it