Homework 4: Finishing Craps, On to Blackjack Due Tuesday April 26 (send by email to pasquale at cs.ucsd.edu) For homework this week, I simply want you to (1) complete your basic understanding of craps, and (2) get introduced to the next game we will study, Blackjack. If you are under time pressure with your other classes, do what you can. The non-optional parts are very easy. 1. Review the solutions to homework 3 at http://www.cse.ucsd.edu/classes/sp05/cse87-a/Solution3.txt. Answer the following questions: a. Outside of taking odds, a pass line bet is the best bet in craps (with the lowest house edge). What is the house edge? b. What is the second best bet? How much worse is it than the best? Express this as X times worse, where X = (H2 - H1)/H1, H1 = house edge of best bet, H2 = house edge of second-best bet. c. What is the third best bet? How much worse is it than the best? d. (Optional) Should you always take odds after a pass line bet (given that the house edge goes down)? Can you give a reason why you would not? e. (Optional) There is a free craps game at http://www.best-online-casino-guide.com/games/craps/01/index_craps.html . To get started, click on the pass line, and a $5 chip will appear there. If a point is established, you can click on your pass line bet to take up to 3 times odds ($15). To start the game over, simply reload the web page. You may want to put your craps knowledge to an experiment: try playing as a "smart" player, sticking to making only the best bet. After a certain amount of time, repeat but play as a dumb player. You may have to play for quite a long time to see the expected results, as little can be learned given only a few trials. You saw in Homework 1 that only after many tens of, or even a hundred, trials did the frequencies begin to approach the true probabilities. 2. Become acquainted with the game of Blackjack. Here is one source of instructions: http://www.wizardofodds.com/blackjack There is nothing to hand in for this question. a. (Optional) If you want to get some experience playing, there is a free blackjack game at: http://www.best-online-casino-guide.com/games/blackjack/01/ Click on the felt to put down some chips and get dealt a hand. b. (Optional) Learn the following simplified "basic strategy" that will help you cut the house edge down from about 2-3% or more (depending on how badly the player plays) to less than 1% (pure basic strategy gets it down to about 0.5%, but is significantly more complicated than this small set of rules): Say your total is T and the dealer's upcard is D Hard hands 9 or lower: hit 10 or 11: double down if T > D, else stand 12 through 16: hit if D is 7 or more, else stand 17 or higher: stand Soft hands 13 through 18: double down if D is 5 or 6 17 or lower: hit 18: hit if D is 9 or more, stand if D is 2, 3, 4, or 7 19 or higher: stand Pairs Always split a pair of aces or 8's Never split 10's, 4's, or 5's Split all other pairs when D is 6 or less These rules are based on those discussed in the book, "Mensa Guide to Casino Gambling: Winning Ways" by Andrew Brisman, which is an excellent reference.