Flipping for Dollars (Posted on 2002-10-09)

	Submitted by Jim Lyon
Rating: 3.9000 (10 votes)
Solution:	(Hide)
The probability that the nth flip is tails is 1/2^n. The amount of money won if the nth flip is tails is 2^(n-1). Mathematically speaking, the value of the game is: 1/2 * 1 + 1/4 * 2 + 1/8 * 4 + ... which equals 1/2 + 1/2 + 1/2 + ... So, mathematically speaking, the value of the game is infinite. In practical terms, however, you'll soon be limited by the amount of money I have. (That is, there will soon come a point where I am incapable of doubling the money on the table.) So, the series ends at that point. In reality, the series only has as many terms as log2 of the money I have, and the value of the game is 1/2 that. So, if I have about $1000, the value of the game is $5. If I have about $1,000,000, the value of the game is $10. If I have $1,000,000,000, the value of the game is $15. Even if I'm Bill Gates, the value is less than $20.

	Subject	Author	Date
	Puzzle Thoughts	K Sengupta	2022-12-27 22:15:50
	No Subject	cogitater	2007-01-14 03:20:53
	How much you play	Dan Porter	2004-01-15 02:49:15
	No Subject	Sara	2003-11-10 20:18:31
	The house	ratsnstuff	2003-10-14 05:30:05
	Try this	Ryan	2003-05-07 08:21:13
	No Subject	Alan	2003-01-04 14:18:04
	re Solution	Cheradenine	2002-10-14 03:02:08
	re(2): something missing	Cheradenine	2002-10-10 08:11:14
	re: something missing	Cheradenine	2002-10-10 07:37:38
	something missing	Cheradenine	2002-10-10 05:24:00
	My take	friedlinguini	2002-10-10 03:45:11
	re(3): Wait a second...(Another DOH!)	TomM	2002-10-09 20:08:27
	Doh!	TomM	2002-10-09 19:03:32
	re(4): Wait a second...	TomM	2002-10-09 18:24:26
	re: Is $100 high or low?	TomM	2002-10-09 18:12:19
	Is $100 high or low?	TomM	2002-10-09 18:07:29
	re(3): Wait a second...	TomM	2002-10-09 18:05:21
	re(2): Wait a second...	levik	2002-10-09 16:44:53
	re: Wait a second...	Jim Lyon	2002-10-09 11:49:16
	Wait a second...	levik	2002-10-09 11:37:23