Re: A theoretical draw question
I finally found an example lowball hand for two players in which the order matters, even with both players having perfect information.
A has Qc 8c 6s 4s 2s. B has Qs 9c 7d 5h 3s. 5s and 5c are dead.
If both stand pat, A wins. If both draw (A to an 8, B to a 9), A is a small favorite (0.512/0.488). If A draws and B is pat, or A is pat and B draws, A and B are in a dead heat (0.5/0.5).
Thus if B goes first he should draw, and A draws behind him. If A goes first he may either stand pat or draw; B will always do the opposite and gain a 1% advantage over going first.
I just thought it was neat to work out a somewhat paradoxical situation like this, where there is a positional advantage even though both players know all the cards. It's an embedding of the penny-matching game into poker!
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