October 30, 2013
Probability Problem Revised
- You are playing blackjack. The dealer is using only 1 deck of freshly shuffled standard playing cards. You are the only player at the table.
- The dealer must “Stand” (not take another card) at 17 or higher (even if one card is an Ace and hitting will only improve his hand) and must “Hit” (add a card to his hand) at 16 or lower.
- In this instance, the dealer may only receive 1 hit card. This helps simplify the problem, keeping the number of possible combinations manageable.
- You were dealt a 3 and a 4 of diamonds.
- The dealer is showing a 6 of spades. The other card is face down (unknown).
- It’s your turn and you decide to “Hit” and receive another 4, this one clubs.
- You decide to “Hit” again and receive an 8 of hearts.
- Your total is now 19 (3, 4, 4, 8) and you decide to “Stand”.
- Now it’s the dealer’s turn.
Q1. What is the probability that the dealer will bust (go over 21)?
Q2. What is the probability that you will win the hand?