This is the type of discussion I find most interesting on r.g.p. Thanks
for the post, Andy!

Despite a small mistake in the EV calculations, I think that the "middle
region" concept you point out is true. There are no doubt multi-way poker
situations where the hand with the largest pot equity would prefer a
drawing hand to make a correct fold (correct fold = folding is the play
which maximizes the folder's EV).

In article <33442BD0.6...@ix.netcom.com>, Andy Morton

However, the interpretation of this concept in practice is difficult.
Suppose the pot is in the "middle region" and another hand is added to
your example which is also drawing to the flush (Jh2h). In this case, the
AK clearly has a higher EV when the lower flush draw calls (given that the
higher flush draw calls) since the lower flush draw has no chance to win.
If the only way to get the Q9 to fold also gets the J2 to fold, then the
change in the EV of the AK is the sum of a positive from the Q9 folding
and a negative from the J2 folding. In general, I think this will go both
ways in different situations, so it is not possible to say that one ALWAYS
(or even usually) should try to eliminate or not eliminate players. It
depends on specific holdings and specific situations.

If I have AdJd pre-flop, my intuition is that I would like to have AcTs
and Td8d playing against me, and it may be beneficial to not raise
pre-flop if raising would chase them out. The concept is that of a
"dominating hand", where I expect to make extra money in later betting
rounds by giving up some in early betting rounds in order to encourage
dominated hands to play with me. On the other hand, if the dominated hands
would have called a raise anyway, or if there are lots of hands with live
draws out, raising to get more money or eliminate players is surely best.

In article <33442BD0.6...@ix.netcom.com>, Andy Morton

[example EV calculation deleted]

Nicely demonstrated.

Getting back to the "middle region" concept, I think this is the clearest
demonstration I have seen of the problems with the FToP when applied to
multi-way pots. I remember having an email discussion some time ago where
it was suggested that Sklansky's Fundamental Theorem of Poker wasn't
fundamental, and often wasn't even correct. I believe I added my opinion
that it is also vague in its phrasing ("you lose...you win": compared to
what? how much?) and difficult to apply quantitatively.

Nevertheless, the FToP does have its conceptual uses for heads-up pots.
Perhaps what is needed is an additonal theorem: the Fundamental Theorem of
Poker for Multi-way Pots. Without careful thought, I offer for discussion:
"In a multi-way pot with knowledge of all opponents' hole cards, there
exists a mathematical expected value (EV) for each possible way of playing
a hand, and the best play is that which has the maximum EV." Is it true?
Is it useful?

--
Erik Reuter, e-reu...@uiuc.edu