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"Hey, George!" I say. "Wanna play a game?"

"Always. What've you got?"

I take out a deck of cards, pull out the A, 2, 3, 4, 5, 6, 7, 8, and 9 of spades, and place them on the table.

source: wikipedia snip

"So these cards represent the numbers 1 to 9---"

"In what order?" asks George. He's a little pedantic.

"The obvious one," says I. "We take it in turns to pick up a card from the table. The first person to get three cards that add up to 15 wins."

"Oh," George sounded disappointed.

"What?"

"It's so trivial. Easy draw."

"Really? I thought it was quite interesting."

"Not at all. It's basically just a game of ..."

George then explained how this game was simply a disguised version of another well-known game, long since solved.

What well-known game is it, and how does the equivalence work? Bonus for the best opening moves if your opponent plays randomly rather than strategically.

And when I say "bonus", I really mean the admiration of your peers on PSE, because I'm not going to be giving any other bonuses.

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  • $\begingroup$ I didn't even realize it worked like that! Such a weird bijection! $\endgroup$
    – Someone
    Commented Jan 11 at 20:05

1 Answer 1

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This is a card version of

Tic-Tac-Toe (AKA Naughts and Crosses)

If we arrange the cards like this:

2♠ 7♠ 6♠
9♠ 5♠ A♠
4♠ 3♠ 8♠

We get a

Magic Square, where each row, column, or diagonal sums to 15.
Drawing a card is equivalent to placing your mark ('X' or 'O') in that cards spot in the magic square.

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    $\begingroup$ I thought that Roshambo was another name for rock-paper-scissors, not for this. $\endgroup$ Commented Jan 11 at 23:06
  • $\begingroup$ @JaapScherphuis You are correct. I even googled it ahead of time, but apparently my brain just decided all three-word-name children's games were the same... $\endgroup$
    – DqwertyC
    Commented Jan 12 at 14:21

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