[TNixon]

Just came across this tidbit in another thread, from one of the authors of Professional No Limit Hold'em.

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For example, say you have $100. If you play the $100 as a 50bb stack in a $1-$2 game, your variance will be higher than if you play the $100 as a 200bb stack in a $.25-$.50 game. However, playing a $100 stack in a $1-$2 game will still be lower variance than playing a larger stack in a $1-$2 game.

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When you start a $100 sit-n-go on full tilt, you start out playing with a 75BB stack that is basically worth $100. At this point, any variance you experience in chips is equivalent to variance in dollars at a cash table if you were to buy-in for 75BB rather than the max 100.

As the tournament progresses, your stack is still worth the same $100, but the blinds have increased. Isn't this therefore a higher-variance situation? The swings in your bankroll are directly related to your winrate, but your winrate is dependent on the variance of the individual hands inside the tournament, just like a cash table. In fact, losing a big pot or two greatly increases the chances that you'll lose your entire buyin, even though you still have chips left, due to the pressure from the blinds.

Another train of thought: If "high variance" means that the results hit the outside ends of the spectrum more frequently, then lets say we only have $100. In this case, the the chance of going broke (the ultimate bad result of variance) playing a $100 sit-n-go would actually be greater than the chance of going broke playing $100 at a 0.5/1NL table, would it not? With a 60% winrate, you have a 60% chance of doubling up, and a 40% chance of going broke. On the cash table, there's a very wide possibility of results. At one extreme, you can lose your $100 and be broke. At the other extreme, you can double (or triple, or quadruple, or whatever, if he keeps rebuying), but most of the likely results over the same number of hands that you would play in a sit-n-go lie in the range between losing your buyin and gaining a buyin, for example, losing half your stack, or gaining 25%, or whatever. The chance of going broke here seems like it would have to be significantly less than 40%, I would think.

Call me crazy, but it seems pretty obvious that in this situation, the SNG variance is going to be higher than the cash variance.

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whereas in cash you win a few big pots and break even or lose a little in most pots. So in cash your results are swingy and spread deeply around the mean.

make sense?

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Not really, because you win and lose those same big pots in SNGs, with what I would guess is an even greater frequency, due to blind pressure. You start out playing $100 75BB stacks, but can very quickly end up playing $100 10BB stacks. Losing a big pot in a SNG isn't that much different from losing a big pot at a cash table. In fact, it should be a more painful blow in a SNG, because there's an increased likelihood that the rest of your chips will follow, as you are forced to gamble more and more. In a cash game, you can reload, removing this pressure, and although that does increase the maximum swings, it should reduce the *average* swings, should it not?

The *only* difference in absolute $ variance between the two, as far as I can tell, should be the ability for both sides to reload in cash, and as far as I can figure, that ability should have the effect of reducing the average swings, not increasing them, because there's less pressure to gamble. (Assuming, of course, that gambling on marginal situations is by default higher variance than not gambling, which only makes sense.)