Re: Theorem of expected stack sizes
I don't see the theorem being refuted up until now. I didn't find any counterexample either.
Regardless, I was thinking about some interesting and very relevant IMO conseqences of it:
Even if there are 2 stack S1 and S2 (S1>S2), that for given expected stacks of S1' and S2' respectively, S2'-S2>S1'-S1 for _each and every hand played_ (!), still, according to the the theorem that still stands, it is always more advantagous to have stack S1 than having S2, for the simple reason that any MTT model that assigns a higher $EV value (or in other words, share in prize-pool) to a shorter stack (that is, a model that says that there could be cases in which S1>S2 AND (share of prize pool of S2) > (share of prize pool of S1) for same player) is absurd.
The above might look complicated but it is very simple. It means in simple words that no matter how much more chips you can make with each hand when you have a shorter stack, you should still prefer a bigger stack.
However, this is true ONLY for a MTTs. When we have this rare spot where S2'-S2>S1'-S1 for every hand played, and it's a _cash game_, we obviously better have the shorter stack, because we only care about the profit we make by playing the hand, and not where our stack is/was/will be.
I find it to be a rather interesting distinction.
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