Homework 5: Understanding Why Basic Strategy for Blackjack Works

Due Tuesday May 17 (send by email to pasquale at cs.ucsd.edu)


At the last seminar meeting we discussed the logic behind basic strategy for Blackjack.  A key to developing your understanding of it is seeing the patterns in the following table [from Mensa Guide to Casino Gambling by Andrew Brisman]:

Probability of Dealer's Final Hand Based on Upcards (Excluding Blackjacks)

Dealer's
Upcard		17	18	19	20	21	Bust

2		14%	13%	13%	13%	12%	35%
3		13%	13%	12%	12%	12%	38%
4		13%	12%	12%	12%	11%	40%
5		12%	12%	12%	10%	11%	43%
6		17%	10%	11%	10%	10%	42%
7		37%	14%	 8%	 8%	 7%	26%
8		13%	36%	13%	 7%	 7%	24%
9		13%	10%	36%	12%	 6%	23%
10		12%	12%	12%	36%	 4%	24%
Ace		19%	19%	19%	18%	 8%	17%

Some observations:

1. If the dealer's upcard is low, 2-6, the probability that the dealer will bust is high (35-43%).  So, you should play conservatively and stand, even with not-so-good hands, as the dealer may simply bust and the total of your hand will not matter.

2. If the dealer's upcard is high, 7-A, the probability that the dealer will bust is low (17-26%).  So, you should play aggressively and hit, as your hand is competing with the dealer's hand.

3. If the dealer's upcard is X in the range 7-10, then the dealer's final hand with the highest probability is X+10.  For example, if the dealer's upcard is 8, the highest probability final hand is an 18.  This gives you an idea of how aggressive you need to play.


HOMEWORK

For each of the following simplified basic strategy rules, provide a short reason why it makes sense.  Use the above table for justification wherever applicable. 

1. If you have a hard 9 or lower, hit

2. If you have a hard 10 or 11, double down if your cards total more than the dealer's upcard, else hit (previously said "stand" which was an error)

3. If you have a hard 12 through 16, hit if the dealer's upcard is 7 or more, else stand

4. If you have a hard 17 or higher, stand

5. If you have a soft 13 through 18, double down if the dealer's upcard is 5 or 6

6. If you have a soft 17 or lower, hit

7. If you have a soft 18, hit if the dealer's upcard is 9 or more, stand if it is 2, 3, 4, or 7

8. If you have a soft 19 or higher, stand

9. Always split a pair of aces or 8's

10. Never split 10's, 4's, or 5's

11. Split all other pairs when the dealer's upcard is 6 or less