[ExI] who should white shoot?

[Mike Dougherty]

On Thu, Aug 28, 2008 at 12:49 AM, spike <spike66 at att.net> wrote:
>
> In the old days when two guys just couldn't take each other they would have
> a duel.  Suppose three guys couldn't settle matters peacefully, so they
> decide to have a go at the pistols, taking turns firing until only one walks
> away.  Mr. White can hit his mark a third of the time.  Mr. Brown hits two
> thirds of the time and Mr. Black never misses.  Mr. White goes first,
> followed by Brown, followed by Black.

I assume this question to be not only about the probability of
accurate marksmanship, but also about each person's estimation of who
the remaining shooters would choose to shoot.  Are we to assume that a
successful hit necessarily means death?  If not, the scenario could
become quite absurd when a fatally wounded-but-not-yet-dead gunslinger
waits for his turn to shoot another nearly dead gunslinger.  I guess
we also don't worry about either White or Brown killing Black on their
first shot, then running out of bullets from missing either other
repeatedly (assuming that 1/3 probability does not guarantee that
White will definitely hit by his 3rd attempt in the same way a 1/2
coin toss may show a 3+ occurance sequence of heads or tails)

In the cases I considered (below) White has the best chance for
survival if he shoots at Black first:  he is either lucky and gets rid
of the deadliest opponent himself or misses Black but Brown kills
Black.  Even if Brown were to miss, if Black shoots Brown first then
White gets one more chance to kill Black.  If White kills Brown, Black
kills white = game over.

WR1, Rx, BW1, Wx, Rx :: B wins
WR0, RW0, BW1, Wx, RB0, BR1, Wx, Rx :: B wins
WR0, RW1, BR1, Wx, Rx :: B wins
WR0, RB0, BW1, Wx, RB0, BR1 :: B wins
WR0, RB0, BW1, Wx, RB1 :: R wins
WR0, RB0, BR1, WB0, Rx, BW1, Wx, Rx :: B wins
WR0, RB0, BR1, WB1, Rx, Bx :: W wins
WB0, RW0, BW1, Wx, RB0, BR1, Wx, Rx :: B wins
WB0, RW0, BR1, WB0, Rx, BW1, Wx, Rx :: B wins
WB0, RW1, BR1, Wx, Rx :: B wins
WB0, RB0, BR1, WB0, Rx, BW1, Wx, Rx :: B wins
WB0, RB1, Bx, WR0, RW1, Bx, Wx :: R wins
WB0, RB1, Bx, WR1, Rx, Bx :: W wins
WB1, RW0, Bx, WR1, Rx, Bx :: W wins
WB1, RW1, Bx, Wx :: R wins