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- Thread starter Steel_City82
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http://www-2.cs.cmu.edu/~pattis/15-1XX/15-200/programs.html

look for this...

Download: Craps Statistics

This program prompts the user for the number of craps games to play (craps is a dice game whose rules are explained in the opening comment in the Application.java file). It then simulates that many games of craps, printing the number of wins, losses, dice throws, elapsed time, and playing speed. This program uses the DiceEnsemble and Timer classes.

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mathwonk

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craps is easy. in fact the correct odds, which are against the shooter, are even published in the webster unabridged dictionary under craps! even after 40 years i think i still remember them as 251 to 244.

a good book on this stuff, fascinating in its coverage of cheating, is john scarne's "scarne on dice", pub. about 1945.

ok, there are 2 dice, and each die has 6 sides, so by the fundamental principle of probability, there are 36 possible outcomes for one throw. now craps is concerned with the sum of the two numbers and these are not equally distributed.

12 can come up only one way, 2 can come up only one way. three and eleven can each come up two ways, and seven can come up 6 ways. If you check these assertions you will be well on your way to understanding craps odds.

now i forget the rules momentarily. does 3 lose on first roll? as well as 2 and 12? i suppose so.

and 7 and eleven win? well if so, there are 4 ways to lose on first roll, and 8 ways to win. and the possible points are 4,5,6,8,9,10, which occur in respectively, 3,4,5,5,4,3 ways. So there are 24 ways to go into point, 8 ways to win, and 4 ways to lose on first roll. that gives the odds on the first roll. i.e. you have an 8/36 chance of winning on the first roll.

then if you throw say a point of 10, you have only a 1/2 chance of making it afterwards since there are only three ways to make 10 and 6 ways to make the now deadly 7.

etc etc...... this is fun but simple once you get the idea.

more interesting are combination bets like: should you bet me that I will not throw either a seven or an 8 in 2 throws of the dice? (you should not, as the odds are 671 to 625 against you, if i am correct here. i have not done this since freshman year in college.)

and so on. check out scarne, you may be entertained.

a good book on this stuff, fascinating in its coverage of cheating, is john scarne's "scarne on dice", pub. about 1945.

ok, there are 2 dice, and each die has 6 sides, so by the fundamental principle of probability, there are 36 possible outcomes for one throw. now craps is concerned with the sum of the two numbers and these are not equally distributed.

12 can come up only one way, 2 can come up only one way. three and eleven can each come up two ways, and seven can come up 6 ways. If you check these assertions you will be well on your way to understanding craps odds.

now i forget the rules momentarily. does 3 lose on first roll? as well as 2 and 12? i suppose so.

and 7 and eleven win? well if so, there are 4 ways to lose on first roll, and 8 ways to win. and the possible points are 4,5,6,8,9,10, which occur in respectively, 3,4,5,5,4,3 ways. So there are 24 ways to go into point, 8 ways to win, and 4 ways to lose on first roll. that gives the odds on the first roll. i.e. you have an 8/36 chance of winning on the first roll.

then if you throw say a point of 10, you have only a 1/2 chance of making it afterwards since there are only three ways to make 10 and 6 ways to make the now deadly 7.

etc etc...... this is fun but simple once you get the idea.

more interesting are combination bets like: should you bet me that I will not throw either a seven or an 8 in 2 throws of the dice? (you should not, as the odds are 671 to 625 against you, if i am correct here. i have not done this since freshman year in college.)

and so on. check out scarne, you may be entertained.

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