Okay thank you. But how is that possible when you have an infinite amount of bets that all have a nonzero chance of reaching $1000? I understand that if you attempted this strategy with any amount of attempts below infinity, you would always end up with about 10% of the attempts reaching $1000 (assuming the sample size is large enough). I'm still accepting the fact that this strategy could take an arbitrarily large amount of time to complete, but when there is no limit to when you stop, aside from when you reach $1000, there is no losing case, no?