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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:
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)
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