Variance Again

For some reason I went back to re-read this old post and noticed that I left out a key part of the explanation about the effect of multitabling on variance.

What I was trying to say is that your variance as measured in some normalized unit - say, big blinds or big bets - isn't reduced by multitabling.

However, if you play, for example, four tables of $25/$50 NLHE instead of one table of $100/$200 NLHE, then your variance in terms of absolute dollars will probably be lower, assuming the quality of your play doesn't deteriorate significantly.

To understand why, we can use a simple coin flip problem. You have a choice between betting $5 on a single coin flip or $1 each on five flips. The probability of the final result being +/- $5 is 100% in the first case, but only 6.25% in the second. That's oversimplifying the issue of variance, but it gives you the general idea of why, if all else is equal, you should see smaller swings if you multitable at lower stakes than if you play a single game at higher stakes.

Usually it's even better than that, because as a general rule, the weaker the opposition, the lower your variance and the higher your EV. And most of the time, the lower the stakes, the more poorly your opponents play.

On the other hand, if your play deterioriates significantly when multitabling, then these benefits are likely to be offset. You may still have lower variance, but your EV is likely to take a big hit.

You also have to factor in games that are playing higher than the notional stakes. This is a fairly common situation in live big bet games, less so online. For example, you're playing live $1/$2 NLHE but everyone's straddling and some drunk is raising to $20 preflop on every hand. A game like that is playing way bigger than $1/$2 and shouldn't be treated as $1/$2 if you're trying to figure out whether your bankroll is adequate. This game is likely to have huge EV for the skillful player, but it could also do a lot of damage to your bankroll if the cards don't cooperate.