20180701, 09:09  #12  
Jun 2003
5·307 Posts 
Quote:
Starting with $200 Assuming that at n turns the game stops then n=x+200 losses and x wins (min n=200) Or n=x looses and x + 300 wins (min n=300) Also note that n must be even Odd of this happening is 1 in n for reaching zero & 1 in n for reaching 500 Probability of loosing=1/200+1/202+....+1/infinity= infinity (divergent series) Probability of winning=1/300+1/302+....+1/infinity = infinity (divergent series) Probability of ending the game(winning or loosing)=1/200+1/202+....1/infinity+1/300+1/302+....1/infinity = infinity (divergent series) Probability of not ending the game=1infinity=0 (as probability cannot be negative) Of note, if n was not very large (limited turns e.g. 500 turns) then the series would not diverge. 

20180701, 12:57  #13  
"William"
May 2003
New Haven
2×3^{2}×131 Posts 
Quote:
I think the biggest problem is that you forgot to account for when the game ended previously. For example, 700 plays with 200 losses followed by 500 wins shows up as ending on both play 200 and play 700. 
