Exercise #10a

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?

Justin

Justin Holman is CEO of Aftermarket Analytics, where he leads efforts to develop cutting edge sales forecasting and inventory optimization technology for the Automotive Aftermarket. Prior to joining Aftermarket Analytics, Justin managed corporate consulting for the Strategy & Analytics division at MapInfo Corporation, leading major projects for retail clients including The Home Depot, Darden Restaurants, Bridgestone-Firestone, Sainsbury’s and New York & Company. Before that, Justin served as Vice President of Software Development at LogicTools, now part of IBM's supply chain application software group. Justin holds a B.A. from Claremont McKenna College, a Ph.D. from the University of Oregon and an Executive Management certificate from Northwestern University's Kellogg School of Management.

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