A Conversation for How to Win a Pint by Using Binary Arithmetic


Post 1


The game presented here is the game Nim with one important difference. You are not allowed to take four matches from a row. In Nim the rule is that you can take any number of matches you choose from any one row.

The starting position 5 6 7 is not a strategic one. Therefore the first player to move can convert it into one under Nim's rules. But to do that would involve removing four matches from one of the rows, leaving

1 6 7 (1, 110, 111, totals 2, 2, 2)
5 2 7 (101, 10, 111, totals 2, 2, 2)
5 6 3 (101, 110, 11, totals 2, 2, 2)

But only permitting a maximum of 3 matches to be taken at once makes all three opening moves illegal and impossible for the first to play to ever win the game against best play.

It may be psychologically better to play with the following house rules

(a) one player can choose the starting line-up (there can be more than 3 rows but all rows of different sizes)

(b) the other player has first move

(c) these two roles alternate (as in a series of chess games where one player gets white, then gets black).

The winning strategy is to give your opponent a strategic position to have first move from, when you define the starting line-up

And convert the starting position he gives you to a strategic position when you have first move.

(He will occasionally stumble on a strategic position as what he lays down for you to respond to.) In such cases, just remove one match to give him the maximum opportunity to mess the position up.

A variant is to play the game so that the last player to pick up a match LOSES. You play with exactly the same winning strategy until the very last move.

The thing to do is avoid the idea that the starting line-up is fixed. And the suspicion that the game is fixed. Or your opponent will start to memorise moves you make and copy them in the next game.

Bruce Birchall

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