The limiting (normalized) prob. distribution for the r.v. duration of game f\ or a Gambler's ruin starting with 50 dollars and quitting when you either get broke or have 100 dollars looks like: AAA + AAAAA 1.4 + AAAAAA + AAAAAAA + AAAAAAAA 1.2 + AAAAAAAAAA + AAAAAAAAAAA + AAAAAAAAAAAA1 + AAAAAAAAAAAAA + AAAAAAAAAA0.8A+ AAAAAAAAAAAAAA* AAAAAAAAAAAAAA*AA AAAAAAAAAAA0.6A*AAA AAAAAAAAAAAAAAA*AAAAA AAAAAAAAAAAAAAA*AAAAAAA AAAAAAAAAAA0.4A*AAAAAAAAAA AAAAAAAAAAAAAAA*AAAAAAAAAAAAA AAAAAAAAAAA0.2A*AAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAA*AAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAAAAA*AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA -**********************************************************- -1 1 2 3 The limiting (normalized) prob. distribution for the r.v. duration of game f\ or a Gambler's ruin starting with 30 dollars and quitting when you either get broke or have 90 dollars looks like: AA + AAA + AAAA 1.6+ AAAAA + AAAAAA 1.4+ AAAAAA + AAAAAAA 1.2+ AAAAAAAA + AAAAAAAAA 1+ AAAAAAAAAA + AAAAAAAAAAA+ AAAAAAAA0.8* AAAAAAAAAAA*AA AAAAAAAA0.6*AAAA AAAAAAAAAAA*AAAAA AAAAAAAAA0.4*AAAAAAAA AAAAAAAAAAAA*AAAAAAAAAAA AAAAAAAAAAAA*AAAAAAAAAAAAAA AAAAAAAAA0.2*AAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAA*AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA -************************************************- -1 1 2 3