View Full Version : Variance

09-25-2002, 12:46 PM
In blackjack, a person or team can reduce their variance by playing more than one hand at a table. In poker, it's impossible for one person to play more than one hand at a time at one table. My question is, does variance stay the same playing at two tables of the same limit in poker? Or does it double or decrease, if so how much?

09-25-2002, 10:42 PM
The variance per hand does not change if you play at two tables or one table IF the opponents have the same strength and character. (I am assuming all tables have the same number of players and the same limits.)

09-25-2002, 11:18 PM
Your variance per hand is the same, but you are playing twice as many hands per hour. This means your variance per hour will be twice as great. Your standard deviation per hour will be sqrt(2) times as great. Just as if you played twice as many hours.

09-26-2002, 01:10 AM
Dave wrote: "In blackjack, a person or team can reduce their variance by playing more than one hand at a table."

Just as an addendum to what irchans and BruceZ have said, the reduction in variance occurs when you proportionally reduce your bet size. For example, the blackjack team can reduce their variance by a factor of 2 if they choose to play two hands, each with 1/2 the bet size, instead of just 1.


09-26-2002, 05:54 AM
What if you changed the way you played poker on the 2 tables to more closely simulate the effect that blackjack counters have? What I mean is, play a more tight, lower variance strategy at poker, and use the fact that you are looking at more hands to find the higher percentage situations more often? Instead of looking for 1 big bet/hour earn, try to reduce variance and win .75 big bet/hour, on 2 tables. Is this plausible, or is there a factor I am missing that makes these situations non-comparable?


09-26-2002, 12:56 PM
Any statement that your variance per unit of time will change as a result of playing more than one hand assumes that all other things are equal, i.e. you are playing an identical strategy against opponents who are also playing identical strategies. Of course, this is not the case in the real world; the variance of your results will be affected both by the strategy you use and by the strategies your opponents are using, and since these variables are constantly fluctuating, there is no practical way to exactly calculate the variance of the population (the universe of all possible outcomes) at any given time at the poker table.

That being said, you can generally expect the variance of your results to increase by a factor of n when you increase the number of hands you play per unit of time by a factor of n, all other things being equal.

What I presume a 21 team does when it wishes to reduce variance per unit of time without reducing the mean result per unit of time is play an extra hand, but proportionally reduce the bet size. If they play twice as many hands, with each hand playing half the bet size, their mean result per unit of time should be the same, but their variance will be cut in half.

Now if you were to model that approach and play twice as many poker hands per unit of time at half the limit, theoretically your results would be the same. In real life, you likely wouldn't be able to play both tables optimally because of the extra distractions, so the mean of your results from each individual table would likely decrease as well.

So yes, your proposal is plausible.