Question 1142815
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The probabilities of drawing any one of the 13 cards are all the same.  So the expected value for a play is the average of the values of each card.<br>
The only losing card is the ace; the player loses $20 if that card is drawn.<br>
Each of the 3 face cards wins $10; each of the remaining 9 cards wins $2.<br>
So the average value of each draw is<br>
{{{((-20)+3(10)+9(2))/13 = (-20+48)/13 = 28/13}}}<br>
On average, the player will WIN (28/13) dollars; to be a fair game, the player must PAY (28/13) dollars for a game.<br>
That of course is not possible, unless the game must be played in groups of 13 draws, with a cost of $28 for the 13 draws.