Question

You are at a casino and have two dices to play with. You win $10 every time you roll a 5. If you play till you win and then stop, what is the expected payout

Answer 1

The expected payoff for one game is 5/3 as explained above.

If you play the game until you win (number of games tends to infinity), you are sure to win 5 or 10. At any round, the probability of winning 5 is 2*1/6*5/6 = (10/36) and the probability of winning 10 is 1/6*1/6 (1/36). So the expected payoff is then [5*(10/36) + 10*(1/36)] / (11/36) = (5*10 + 10*1)/11 = 60/11 as above.

I think the answer comes to 105/11