Consider the following game. You pick a card from a standard 52-card deck and each time you select an ace, you get $520. For all other cards you must pay $26. This game is not a fair bet.

Question

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The expected value of the game is negative, indicating it's not a fair bet. With 4 aces in a 52-card deck, the chance of picking an ace is 4/52, or 1/13. The expected gain is (1/13)*$520 = $40. The expected loss for the other 48 cards is (48/52)*$26 = $24. Thus, the net expected value per game is $40 - $24 = $16 in favor of the player, contradicting the initial statement. However, considering the large payout for a relatively small probability event and the consistent loss for the more probable outcome, the game's structure can be perceived as unfair from a risk perspective, hence the confusion. My initial calculation was incorrect in assessing fairness solely on expected value; fairness also considers the risk and variance involved.

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