My Great Aunt "Myrna" (Erdman Bowe, pictured at right) used to call this game Arizona Ann. Mom says she wrote my grandfather about it during World War I.

Nowadays everyone calls it Nim.

Here's a nice flash version: http://www.transience.com.au/pearl3.html

Myrna's strategy was to memorize some combinations, and you always try to leave a combination. But you don't talk about combinations -- to confuse your opponent, you talk about how many you take: "You took 3 from that pile, so I'll take 2 from this pile".

When Myrna played it, there were always 3 piles of cards to start with. But the game can also be played with more.

Some of Myrna's combinations:

• 1,1,1 (actually, an odd number of ones)
• 1, an even number, and the number above it. (this includes 1,2,3 and 1,4,5)
• Two piles equal (the other pile empty)
• 2,4,6
• 3,4,7

Against human players who don't know the system, that's sufficient to win most of the time. If there's large numbers of cards/stones/pearls (whatever), you just take a few and let the game whittle down to something you know.

But to always win, there's a system involving binary numbers and the XOR operation. If there's more than 1 card in any pile, you have to leave a combination such that the XOR of the numbers is 0. When there is no more than 1 card in any pile, you have to leave an odd number of cards. If you don't leave a valid combination, the other play will be able to do so, and to beat you.

-- strick (at the yak)