Craps (Posted on 2003-04-18)

	Submitted by Charlie
Rating: 3.5000 (4 votes)
Solution:	(Hide)
Of the 36 ways the dice can come out, 6 produce a 7 and 2 produce 11, so the probability of an immediate win is 8/36 = 2/9. There are 4 ways of coming out as 2, 3 or 12, so the probability of an immediate loss is 4/36 = 1/9. Thus the probability of having to go for a point before getting a 7 is 24/36 = 2/3. Of the 24 ways that could happen on the first throw, the ways of getting each of the possibilities is: 4: 3 5: 4 6: 5 8: 5 9: 4 10: 3 As each of these must then be achieved before a 7, the probability in each instance is the number of ways of getting that number divided by that number plus the number of ways of getting a 7. For example, the probability of getting a 4 before getting a 7 is 3/(3+6) = 1/3. So just multiply each such probability by the probability that the given number would come up originally, and add this to the total probability of a win. Adding these onto the 2/9 probability of an immediate win, we get 2/9 + (3/36)(3/9) + (4/36)(4/10) + (5/36)(5/11) + (5/36)(5/11) + (4/36)(4/10) + (3/36)(3/9) which is 244/495, which is 49.2929… %.

	Subject	Author	Date
	Puzzle Thoughts	K Sengupta	2023-06-13 13:15:40
	re(4): My premise is valid, Correction on outcome.	Joshua	2011-09-07 16:52:31
	re(3): My premise is valid, Correction on outcome.	Charlie	2011-09-07 01:45:02
	re(2): My premise is valid, Correction on outcome.	Joshua	2011-09-06 19:43:50
	re: My premise is valid, Correction on outcome.	Charlie	2011-09-06 10:31:03
	My premise is valid, Correction on outcome.	Joshua	2011-09-06 04:49:05
	re(5): True Solution (Flaw in common answer.)	Charlie	2011-09-05 10:33:45
	re(4): True Solution (Flaw in common answer.)	Joshua	2011-09-05 05:08:47
	re(3): True Solution (Flaw in common answer.)	Charlie	2011-09-04 10:50:11
	re(2): True Solution (Flaw in common answer.)	Joshua	2011-09-03 19:55:30
	re: True Solution (Flaw in common answer.)	Charlie	2011-09-03 15:42:02
	True Solution (Flaw in common answer.)	Joshua	2011-09-02 22:06:04
	answer	K Sengupta	2007-09-01 05:24:24
	re: 49.2929… %.	logischer Verstand	2004-04-13 22:01:08
	49.2929… %.	qw	2003-06-20 09:31:48
	re(3): Okay odds, but a sucker's bet	Gamer	2003-04-19 10:33:28
	re(2): Okay odds, but a sucker's bet	Cory Taylor	2003-04-19 05:46:12
	re: Okay odds, but a sucker's bet	Gamer	2003-04-19 02:30:59
	Okay odds, but a sucker's bet	Bryan	2003-04-18 17:59:32