A gambler has $256, Estimate the probability of winning $80 within 1000 sequential bets in American roulette. Note that once the gambler has lost all of his money (i.e., episode_winnings reaches -256) , he stops betting. Also, the gambler stops betting if his total winning amount reaches $80. Gambler bets on black all the time (i.e. 18 out of 38 possibilities). $1 is the starting bet.

On a lose event: Betting amount is doubled for next spin. On a win event: Betting amount is set to $1 for next spin.

Below algorithm is followed for sequential/subsequent 1000 spins :

while episode_winnings < $80: won = False bet_amount = $1 while not won wager bet_amount on black won = result of roulette wheel spin if won == True: episode_winnings = episode_winnings + bet_amount else: episode_winnings = episode_winnings - bet_amount bet_amount = bet_amount * 2