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Message from discussion Going Too Far & Implicit Collusion
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Erik Reuter  
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 More options Apr 7 1997, 3:00 am
Newsgroups: rec.gambling.poker
From: e-reu...@uiuc.edu (Erik Reuter)
Date: 1997/04/07
Subject: Re: Going Too Far & Implicit Collusion
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In article <JBURNS.97Apr7204...@wildcat.monmouth.com>, jbu...@monmouth.com

(Jazbo Burns) wrote:
> 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.

>                 p > p_c = (a+b)/c.

>                (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!).

It's not symmetrical since A gets all of C's outs if C folds, and B gets
none of C's outs. B wants C to call, no matter what the pot size, since
b(p+1) > b(p)

> 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).

This must be restated in light of the above. (SOME of the other players,
namely B, DO want him to call). Also, it isn't true head's up, since then
b = 0 and p_c = p_a, but as stated above it isn't this isn't crystal
clear.

"If the best hand bets and is called by a drawing hand, there is a range
of pot sizes such that the next player's maximal EV play is to fold, yet
the best hand has a higher EV when this player folds."

I'm more interested in applications of the theorem to poker strategy. It
would seem one application would be that certain situations may arise
where slowplaying is not correct based on the theorem, but slowplaying
would have been correct if the theorem were not considered.

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


 
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