From: joltman@raisin-nut.ai.mit.edu (T. Andy Frakes)
Newsgroups: rec.games.board
Subject: Re: Winning isn't everything
Date: 21 Jan 93 16:08:00 GMT
Organization: MIT Artificial Intelligence Lab
NNTP-Posting-Host: raisin-nut.ai.mit.edu

In article <1993Jan15.051709.8535@netcom.com>, elvis@netcom.com ('kEvin') writes:
|> joltman@raisin-nut.ai.mit.edu (T. Andy Frakes) writes:
|> 
|> >Dan Shoham writes:
|> 
|> >>In our group, refusing to accept a serious "sporting chance" (i.e. 5% or more)
|> >>is considered un-game-man-ship-like. (But un-game-man-ship-like plays do not
|> >>prevent us from inviting the "offenders" back or encourge us to retaliate in
|> >>future games.
|> 
|> >I agree with this mentality.  One should not hold it against anyone if he
|> >declines such an "offer."  In the long run, one who declines such offers is
|> >only hurting himself. If, however, I find that a particular player consistently
|> >declines my offers, but accepts others' offers, I may threaten retaliation in
|> >future games in order to show the person that this is not a good strategy to
|> >adopt (since he obviously realizes that it is smarter to accept such offers and
|> >that he is only declining my offers because of some personal reason).  If that
|> >doesn't work I'd refuse to play with that player.
|> 
|> 
|> It's not necessarily smarter to accept those offers. If the player making the
|> offer has a slight chance of losing if you try for the titan kill and a
|> 100% chance of losing if you try to strip, then it depends on your position
|> as to whether the slight chance to stay alive is worthwhile. If allowing
|> you the opportunity for a "sporting chance" only prolongs a doomed existence
|> should you win, it is far, far better to strip, so that the player who attacked
|> you is eliminated as well. (Your intentions should probably be announced
|> ahead of time, since doomsday devices don't work well if your opponents
|> don't know about them.) This way, you are likely to survive much longer
|> than if you took a sporting chance, since your opponents will not wish to
|> sacrifice their titan stack to eliminate you. (This also assumes that
|> it takes a titan stack to eliminate yours.) I think this is part of the
|> revenge idea expressed earlier.
|> 
|> 
|> kEvin

If you indeed have a 100% chance of losing by trying to strip (you never REALLY
do) and you are playing solely to maximize your chances of winning, you should
always go for the titan kill (unless you also have a 100% chance of losing even
if you succeed in the titan kill attempt [which you also never have]).

Suppose you have a 1E-6 chance of winning if you go for the titan kill and
succeed and you have a 1E-3 chance of winning if you go for the strip and win,
but you have a 1E-1 chance of succeeding in the titan kill and a 1E-3 chance of
surviving while trying to strip.  Even though your chances of surviving the
battle are 100 times greater if you go for the titan kill, you end up better off
trying to strip.

However, in reality, the odds for your post-battle chances are usually opposite.
Normally, if you go for the strip, you will have nothing left in the end if you
manage to somehow win the battle, but if you kill his titan early by accepting
his offer of a sporting chance, you will have most of your stack left if you
manage to kill his titan.  Therefore, in reality, it is much better to accept
the sporting chance if you are playing to maximize your winning chances.
However, most humans will throw away a minscule chance of winning in exchange
for the emotional gain of revenge.

-- 
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=             T. Andy Frakes (joltman@ai.mit.edu)              =
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