# FOM: truels, reproduction, consistency

Fred Johnson johnsonf at lamar.ColoState.EDU
Sat Jan 17 12:03:20 EST 1998

```Singh, in his book on FLT, mentions a variant of the following
math puzzle:

A, B, and C are involved in a truel (a three-party duel)
where their chances of hitting their target are 1/3, 2/3, and 1,
respectively.  A shoots first, B second, C third, A fourth, etc.
The "game" only ends if two people are shot (and thus the game
may go on forever).  The parties are rational, want to survive,
and always try to hit their target.

Should A's first shot be at B?  at C?

According to my calculations if A's first shot is at B her chances
of survival are 2/27 + 4/21.  Otherwise they are 2/27 + 5/21.

I'm confident that anyone who uses Logic will *reproduce* my
results.  I'm even more confident that anyone who uses Logic
will obtain a result that is *consistent* with mine (for example,
by concluding that A's first shot should be at C).

Fred Johnson, Professor, Philosophy, Colorado State University
(My work has appeared in JPL, NDJFL, HPL, Studia Logica,
Analysis, ....)

```