By Shalosh B. Ekhad and Doron Zeilberger
Using experimental mathematics and symbolic computation, we derive many moments for the duration of a 3-player (fair) gambler’s ruin.
It also gives you the special case A=B, and the limiting scaled moments of the latter.
[Note: this is contained in the file below, but since the latter file is so large, we keep it]
Warning: large file.