# BlackjackApplet

This applet allows you to "play" Blackjack (there is no dealer), and it tells you the odds of "busting" (card sum greater than 21) on your next card. The cards are dealt randomly from a simulated standard deck of 52 cards, that is reshuffled when half the deck has been used.

## Further Questions

1. Blackjack lends itself very well to statistical analysis. This applet will tell you the odds of busting, but it does not tell you the odds of winning. For a given hand, say perhaps 18, what is the probability that the dealer will beat you? Remember the following rules:

• Dealer must hit on 16 and below
• Dealer must stand on 17 and above
• If the dealer busts, you win
Note that this is a difficult question if you allow Aces to be 1 and 11, depending on which is more "useful". Therefore make a reasonable assumption to simplify your computation.

2. Do the odds of busting change remain constant? Jot down the probabilities of safe play for the following hands: 12, 13, 14, etc up to 20, each time you come across one. Offer a suggestion as to why the odds do change.

3. Say the odds of busting with a given hand with sum 17 is X. Now imagine a hand with sum < 17. If the latter hand plays a "hit" and brings its sum equal to 17, does it now have the same odds of busting? Why or why not?

4. This applet uses one simulated card deck. Why do Vegas casinos use multiple decks?

5. What is the maximum number of cards you can get and not bust? How many hands have this number of cards?

 6 a) Intentionally bust ten to fifteen hands in a row, and record the number of cards needed to bust each time. Based on this data, make an educated guess about the actual average. b) Mathematically derive the actual average (Hint: Make an assumption about the aces, as in problem 1)

Created by Andrew Freed, arf132@psu.edu on February 5, 2002.
Modified by Andrew Freed, arf132@psu.edu on April 15, 2002.

Development of this applet was sponsored by the Penn State Fund for Excellence in Learning and Teaching (FELT), project "Java-based Teaching of Mathematics in Information Sciences and Technology", supervised by Frank Ritter and David Mudgett.