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