»  Solutions to puzzles in my National Review Online Diary

  January 2009

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January's puzzle concerns the card game known as War. A reader had told me:

One night a friend and I decided to kill some time before dinner with a game of War. I won the game in one pass through the deck.

What is the probability of this? I asked.  (Note: My reader was playing ace high, though it seems to me this doesn't make any difference.)

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Solution

Most notable from a thin response was this one:

"Dear John — Concerning your January math puzzle … I have no idea how to compute that using my limited knowledge of probability. So, I opened a DOS window and wrote a short FORTRAN program to do it for me. I ran 10,000,000 simulations and found 1,561 times where one side or the other swept the game. I assumed the Ace was the same as the other face cards, but, as you said, I don\'t know if that matters …"

What struck me about that was the reader's use of FORTRAN. I used to teach FORTRAN, a lifetime ago. Clunky language, in my opinion, but engineers loved it. I still have my Microfocus COBOL on old disks somewhere. Perhaps I'll try a COBOL simulation. (I once, for a bet, wrote a COBOL program to compute pi to 100,000 decimal places. Piece of cake.)