An outstanding post, Andy.  It's articles like these that make r.g.p. one
of the best newsgroups on the net.

In the original post, Andy Morton <andr...@ix.netcom.com>
demonstrated that David Sklansky's claim that his Fundamental Theorem
of Poker applies to multiway action is false.  The particular example
he used is from hold'em where there has been a bet and a call and the
third player is faced with a decision on whether to call or not.
Assuming you are the bettor and have the best chance to win the pot
(you have the most outs), Sklansky says you want the last player to
call whenever the pot odds from his point of view are insufficient (FToP).
Andy showed that there is a region where it is incorrect for the third
player to call, yet it costs you money if they do.  I will take the
liberty to recast things from Andy's original to simplify the
notation.

There are three players A, B and C, having a, b and c outs on the
river, respectively.  A has bet one unit, B has called and C must
decide whether or not to call with p units (including the bets of A
and B) in the pot.  Pot odds dictate that C should call if and only if

                p > p_c = (a+b)/c.

Player A would prefer that C fold whenever p is large enough so the
A's fraction of the pot with one more bet on it (we assume no bets
after the flop -- perhaps A is all-in) is worth more than his fraction
when C calls.  Algebraically this reduces to

                (a+c)p > a(p+1), or

                p > p_a = a/c.

Note that unless Player B or C has no outs (b=0 or c=0), p_a < p_c, so
there is *always* a region where Player C should fold from his point
of view but Player A would prefer that C not call (and, symmetrically,
the same holds for Player B!).  Also note that this result holds for
more than three players (just consider the players that have called as
a collective named B and the players to call as a collective named C).

I propose we name this result appropriately:

Morton's Theorem:  Ignoring future betting rounds, there is always a pot
    size such that the next player should fold to the bet according to
    the Fundamental Theorem of Poker, yet the other players do not
    want him to call (unless he has no outs).

When another betting round must be considered, things become more
complicated.  I doubt we can come up with anything as crisp as
Morton's Theorem, but this is an excellent topic for discussion.
Thanks for starting it, Andy!

--jazbo
--
- - - - -
Video poker strategy cards for sale:
 http://www.monmouth.com/~jburns/vidpoker.html