Keeping it integer specifically was useful to avoid running out of precision using Python's multi-precision integers. You can show ruin without any flooring di

Keeping it integer specifically was useful to avoid running out of precision using Python's multi-precision integers. You can show ruin without any flooring division: #!/usr/bin/sage import random balances=[Rational(100)]*100 for i in range(10000): balances=[0 if x<=0 else random.choice([x*2+2,x/2-1]) for x in balances] #Yet all or almost all are bankrupt: print(len([x for x in balances if x<=0])) The key points are that there is a state that a participant can't recover from (e.g. ending up bankrupt) and you do enough trials that are reasonably likely to eventually wander into it. One that is the case 100 bets with 10000 betters and 10000 bets with 100 betters stop being the same thing. And this is a very realistic and physical assumption because real investments have integerization, fees, overheads, etc. You can't invest a femto-cent in the market, and certainly not get the same relative returns as someone investing 100k.