**POLYA027: Probability of winning a solitaire card game
**(proposed
by Antreas P. Hatzipolakis, 1/19/02).

In a solitaire game, a player deals one card (from a deck of 52) at a time and counts 1, 2, 3, 1, 2, 3, ... in succession. He loses if he counts a number same as the card dealt at the same time. [For this purpose, an ACE is regarded as the same as one]. What is the probability of winning the game?

**Discussion. [SCL]: **The probability of winning is
**24,532,967,512
/ 3,004,641,364,725. **Explanation follows in postscript
or pdf file.

**Bibliography.**

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