[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
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