A Variance Wager
 

Imagine this proposition was set forth.

The talk is about variance and here is the wager (this is sort of a discussion on FCP's forums but it's invariably better suited here as I'm there infrequently):

Player A plays at the Party Poker $0.50-$1.00 game for X time and then plays at the Party Poker $10-$20 game for X time.

Where would the variance in terms of BB be highest?

You can pick either side. Where do you bet? Why? Does the amount of "X" matter? When doesn't it? What range? Why?

People always talk about the everyone-seeing-the-flop aspect of the micro-limits increasing variance, but does the truly horrendous play make up for it? Or doesn't it?

Where would you put your money? What would X have to be to sway it?

Barron Vangor Toth
BarronVangorToth.com

Re: A Variance Wager
 

If you measure variance in terms of BB's per 100 hands then increasing X only reduces the variance of your variance and not the actualy value after 100 hands.

Variance will always be higher in the typical low-limit verus typical higher-limit. Bad play doesn't reduce variance, it simply increases your win-rate. If I played a slightly +EV lottery with you where you had a 1 in a million chance of winning or if I played a zero EV coin flip game with you where you had a 50% chance of winning the variance is obviously higher for the lottery.

If you use a different measure for variance the answer to your questions is much different.

Re: A Variance Wager
 

[ QUOTE ]

Player A plays at the Party Poker $0.50-$1.00 game for X time and then plays at the Party Poker $10-$20 game for X time.

Where would the variance in terms of BB be highest?

[/ QUOTE ]
Variance may be associated with loose games, but microlimit games are also very passive. People will limp in, then just call on each street with AA. The result is that the average standard deviation reported in the microlimits forum is lower than the average standard deviation in BB/100 reported in the small stakes forum.

People also play much more slowly in $0.50-$1, so the standard deviation in BB/hour is significantly lower.

Re: A Variance Wager
 

I would bet on the $0.50/$1.00 game, regardless of what value 'X' may have. I think, under most circumstances, the absolute value of the expectation, and variance, should be proportional in hold'em.

The way I think of it: When your opponents (or you) are playing poorly it is generally because they (you) are calling down without the proper odds. If they fold correctly when not getting proper odds you take the pot down 100% of the time, so there's no risk of an 'unlikely' event occuring which would increase variance. However, when you get a huge number of people in every pot calling down with anything and everything, the 'unlikely' event has a non-zero chance of occuring, so the variance must be higher. So... even though you generally want your opponents to be making these -EV plays against you, as it increases your expected profit, it also will increase your variance as there will be times when they outdraw you.

Re: A Variance Wager
 

[ QUOTE ]
People also play much more slowly in $0.50-$1, so the standard deviation in BB/hour is significantly lower.

[/ QUOTE ]


Good point. Assume that my original post says X # of hands, NOT X amount of time.

Barron Vangor Toth
BarronVangorToth.com