[LearnedfromTV]

Hey guys. I'm just a lurker here and not even a limit player but I've done a decent amount of analysis of and thinking about variance, and there is one thing that isn't usually directly stated in these threads:

Whatever risk of ruin/probabilities of different sized downswings are implied by a given winrate and standard deviation, the actual swings you'll experience will be much wider. The reason is that you don't play all your hands with the same expected winrate and variance, but the simulations often quoted assume that you do.

This goes a lot deeper than the obvious case of tilting or chasing losses higher. If you have, say, a 1.0 bb/100 winrate over 1,000,000 hands, at any random table you sit down at you may usually have an edge between 0.5 and 1.5 bb/100, with different standard deviations depending on the type of play at the table. The fact that your wr/sd aren't constant means that over any shortish sample size, you'll be more likely to have an unusual distribution of tables, plus even if "it all averages out," you'll be playing a lot of hands in a more high-variance scenario than whatever your average expected wr/sd are. So the ror and downswing probabilities from simulations that assume wr/sd are constant will always underestimate.

Also, as many have said, with reference to very large sample sizes, your relative skill to that of your opponents will very widely over long periods of time.

The flip side, which I think aba is getting at, is that many of the things that affect whether a table is 0.5 bb/100 and high variance vs 2.0bb/100 and low variance are in fact under your control. That is, playing in good games, leaving when the game gets tough or you play bad or get tired, etc.

Thanks all for a good thread.