[seqfan] Flipping 4 Penney's game sequences
Ed Pegg Jr
ed at mathpuzzle.com
Sat Oct 16 01:58:04 CEST 2010
I managed to calculate sequences for all of the 4 flip games, in Penney's game.
The count of ways HHHH beats HHHT on move 4, 5, 6, 7 ... leads to the sequence 1,1,2,4,7,13,24,44,81,149,274,504,927,1705,3136,5768,10609,19513
This is A000073 , the Tribonacci numbers.
In the attached text file, all the various types of 4-flip games are listed along with the odds of winning, a generating function or recurrence equation, and 30 terms of the sequence.
Outlier: HHTT beats HTHT seems excessively complicated.
HHHH beats TTTH has a chance of winning of 7/22, or about 1/Pi. It's A123908.
--Ed Pegg Jr
-------------- next part --------------
An embedded and charset-unspecified text was scrubbed...
More information about the SeqFan