Variance?

[J.R.]

When playing online you can play two tables at once. Does playing two tables at once effect one's variance?

I have read conflicting reports one this- my gut feeling is if it has any effect, it would reduce one's variance. What ye say?

[droidboy]

Your variance per hand is the same, your variance per hour is higher.

[Bozeman]

But variance/EV (hour) will remain the same, and SD/EV (hour) will go down.

[J.R.]

My bad, I equated SD with variance. /forums/images/icons/confused.gif

For bankroll purposes, I need to consider my win rate and my variance (or standard deviation?). My general thought was the more hands per hour I play, the less of a bankroll I would need because my variance/standard deviation (swings) would be reduced. Is my gut feeling correct?

[BruceZ]

My general thought was the more hands per hour I play, the less of a bankroll I would need because my variance/standard deviation (swings) would be reduced. Is my gut feeling correct?

No. Your bankroll requirement for a given risk of going broke depends on variance/ev, not sd/ev. See the formulas for bankroll and risk of ruin in the general forum under the thread titled "bankroll". As Bozeman said, playing more hands per hour keeps variance/ev the same, so your bankroll requirment is the same. Playing more hands per hour does not reduce your risk of going broke. All you are doing is speeding things up. If you go broke, it will likely happen sooner. If you don't go broke, you will earn money faster, and your winnings will have a smaller spread (by percentage of win) for a given amount of time. That is, you will reach the long run faster due to the lower sd/ev.

Note that the situation is different for blackjack, where it is possible under certain conditions to increase your ev without increasing your risk by playing more than one hand against the dealer. This is because the results of the hands are not independent of each other since they are played against the same dealer hand. In this case, we consider not only the variance, but something called the co-variance between the two hands.