Question 1128750
<br>
His expected payouts and the corresponding probabilities are<br>
$0.75 * (1/52) for the ace of hearts
$0.70 * (3/52) for any of the other aces
$0.50 * (12/52) for any of the other hearts
$0.00 * 36/52) for any of the other cards<br>
His total expected payout is<br>
{{{.75(1/52)+.70(3/52)+.50(12/52) = 8.85/52}}} = 17.01923 to 5 decimal places.<br>
So he can't realistically expect to EXACTLY break even.  If he pays $0.17 to play the game, then in the long run he can expect to come out very slightly ahead.