Casino Card Counting

Probability Level 3

A Casino offers the following card game which uses a standard deck of 52 cards. Each time, you turn over 2 cards.
- If both cards are red, you keep them.
- If both cards are black, the dealer keeps them.
- If both cards are different colors, they get discarded.

You win the game if you end up with (strictly) more cards than the dealer. If so, you get X times of the amount that you bet. Should you play this game?

Yes! (It's free money) Maybe! (Depends on the value of X) No! (Casinos are evil)

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Calvin Lin by Calvin Lin

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2 solutions

A very simple solution is to change the game a little. Instead of the cards being discarded in Case 3, take the red card for yourself and give the black card to the dealer. This does not change relative standings and hence does not change the outcome. At the end of the game, you will hold all the red cards and the dealer will hold all the black cards. Since the number of black cards is equal to the number of red cards cards, you both have the same number of cards and you lose, always. Therefore, you shouldn't play the game.

Also, typo in the question. Last word of the second last line should be "bet", not "be".

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice solution!

Thanks, fixed the typo.

Calvin Lin Staff - 6 years, 4 months ago

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I don't understand...This cant be correct... What if x= 99999999? If the cards are discarded if one is red and one is black then its potentially possible to end up winning if you get double red a few times and the dealer doesn't get double black cards. As long as the cards aren't recycled until the dealer or the player have all the cards.

Dylan Scupin-Dursema - 6 years, 2 months ago
Anshul Sanghi
Jan 31, 2015

Red and black cards are of equal number.At the end of the game both the players have equal number of cards.the amount of red cards player 1 has will be always equal to the amount of black cards player 2 has.As the number of red and black cards is equal in the deck you will always draw and hence loose the game.

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