[gumpzilla]

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(I'm assuming you meant U and D) So what you're asking for is that U and D are vectors rather than scalars, and turn the whole system into a matrix equation? Whee. This would be a nice expansion, but the simple model is still pretty good.

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That's a fine point, too, but I was just thinking that I have no idea where these specific numbers are coming from. The qualitative result "The games get less populated as you go up in buyins" in a model where we consider a closed system of SNGs can be derived (I'm 99% sure having not done this calculation) with the simple proviso that U<D; that is, that fewer people move up than down. The existence of the rake seems like enough to make this true.

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I agree the rake should be included. I did some backo-da-envelope calcs a while back and decided the rake was fairly important.

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I think this is right. There are probably more big losers than big winners (at least at the lower levels, and probably all levels), so without the rake I would expect that if you assume that all winning players move up, you'd see pretty drastically different results.

It also occurs to me that there is a relatively long timescale involved before winning players know they are winning, if we assume rational behavior. But there is probably a shorter timescale involved in busting back down. I wonder how this would affect things? Obviously this is a fanciful amount of overcomplication for a dinky little problem.

EDIT: One painfully obvious thing I didn't think of until just now: the rake means that in order for an equilibrium to be reached, there has to be an influx of new money into the system, otherwise the equilibrium that is reached is the trivial "Party Poker = 100%, everybody else = 0".