In article <334C9F3B.2...@ix.netcom.com>, Andy Morton

I think that often the best posts in r.g.p. are like the tip of an
iceberg: all the thinking and calculation that is behind such a post is
not readily apparent. The best posts have more background work supporting
them than the general run of the mill posts which generate lots of
replies. This leads to a constant quality-response figure for each thread:
post quality x number of responses = constant (holds for quality > 0). So
if a post gets few responses then it is of high quality. Either that, or
the post was worthless :-)  

I'm not so sure. I believe you will find that in most realistic cases such
situations occur only occasionally, and for a fairly small range of pot
sizes, and make a small fraction of a bet difference. When all this is
taken into account, the overall effect on strategy should be small.

As Jazbo demonstrated, if the outs of the folder get distributed to the
remaining players proportionally to their chances of winning, this
situation does not come up. Morton's example (29/9/4) gave an uneven
distributions of the outs (33/9/0). In the situations where the outs get
distributed more evenly, the range of pot sizes where this phenomenon
occurs will be smaller. Note that if we give just 1 of C's 4 outs to B
(32/10/0) then A no longer benefits by C folding correctly. I suspect that
in many realistic situations where X benefits from Y folding correctly, X
will be trailing another hand. If so, there aren't many situations where X
can raise to fold out C without losing more money to the leading hand. And
to have an image where a mere call strikes fear into the hearts of your
opponents is probably not good for maximizing your EV in other situations.

Most importantly, we have to consider how this theory could be applied in
practice. I can think of two ways: raising more often with relatively
weaker hands, or developing an image that encourages opponents to fold
more frequently when you bet or call. However, THE ISSUE IS NOT A
COMPARISON BETWEEN 0 AND WHATEVER CAN BE GAINED FROM THIS STRATEGY DUE TO
THIS PHENOMENON ALONE! It is likely that if you take either of these two
strategies, you will lose more due to other effects than you could ever
gain by influencing your opponents to make correct folds against you in
situations where those correct folds benefit you. In other words, the
change in your EV due to these strategies may include a positive term from
the issue under discussion, but a much larger negative term due to loss of
income from loose (incorrect) calls.

Admittedly, I have no data or calculations to back up my qualitative
assertions, and I don't plan to work on it. Of course, if you disagree, I
would be interested seeing your arguments (or better yet, numbers).

Not convincing, but it may help in developing your intuition for the
situation and suggesting how to further analyze the issue.

I suggest trying examples spanning the entire range of distribution of C's
outs: you already have one extreme (all outs going to A). The other
extreme (all outs going to B) is somewhat interesting. And everything in
between. (I am always assuming that A is the player with the most outs).

That would be an interesting demonstration. If you do it, make sure to
record enough data to figure out the EV of all players in the pot, and the
delta(EV) under various circumstances such as: player x folds, player y
raises.

It may be difficult to keep track of gains from this issue and properly
offset losses from other effects caused by implementing the strategy
necessary to obtain said gains. I can't think of an elegant simulation to
do it. Maybe someone else can.

Bad comparison. It is more meaningful to compare to, say, the change in EV
when a calling station stops paying you off when you have the nuts because
you projected an image to get this player to fold to you.

Once again, the problem is in finding a strategy that reaps the gains from
this issue without suffering greater losses from other issues. I think you
will have difficulty clearly identifying strategies that do this.

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