Testing ICM -- some questions for discussion

[eastbay]

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I've been mulling over this question for ages (if two people play an optimal strategy for HU freezeout tourney, is the equity function linear).

One observation: If each game in the match were fair (each player's expected chip gain/loss before they see their hole cards is zero) then the linear equity function is true, because the bankrolls will follow an unbiased random walk (this is provable).


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What's provable? That unbiased random walk leads to a linear function? Or that "if the each game in the match is fair" (you mean hand in the tournament?) it is equivalent to unbiased random walk?

The first is obvious and the second seems to be a big assumption.

There's a difference between the tournament having zero value (modulo button initialization) and _each hand_ having zero value. I don't have any reason to believe that chip disparity can't lead to non-zero value from that point forward. That big stack can threaten the tournament for little stack but not vice-versa seems like one mechanism by which this could be the case.

eastbay