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## Counting Cards

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #2378 Fun: (2.53) Difficulty: (2.77) Category: Probability Submitted By: rayneeday Corrected By: Swordoffury1392

Slick Willie is trying his hand at blackjack on a two deck table in Las Vegas. The dealer rolls through 3 hands in which Willie counts 17 face cards and 29 non face cards. On the fourth hand he sees 4 face cards and 9 non-face cards, of which he has a SEVEN and a FIVE and the dealer has an ACE showing. What are the odds that Willie will bust if he takes one card?

There are 32 cards that can make him bust. (Don't forget the non-face TENS) 21 face cards have already been seen. And of the 37 non face cards played anywhere between 0 and 8 could have been TENS. So of the possible bust cards, between 21 and 29 have been played. This leaves between 3 and 11 bust cards still in the deck of 44 remaining cards. (Remember: The dealer has one card down but we know it is not a face card or a 10 because the dealer would have already shown a blackjack). So his odds of drawing a bust card are between 3/44 and 11/44 or 6.8% and 25%. He has to take a hit.
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