### Tallies

December 15th, 2007
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Decent amount of stuff happening lately, including a surprise engagement contra dance for me and Julia on Tuesday. It was a lot of fun and we were both completely surprised. We have fun, though devious, friends.

I was thinking some about tallies. David Chudziki is visiting and brought with him a new game: Jaguar. It's an Italian trick taking game, quite bridge like. There are all sorts of cool things about it, but one interesting thing is the scoring. The score is set up so it's completely zero sum. In the normal situation the Jaguar and the friend are going against the three other players. If the Jaguar side wins, the Jaguar gets 2, their friend gets 1, the other three get -1. If it goes the other way the Jaguar gets -2, the friend gets -1, the other three get 1. In a tie everyone gets 0. If the Jaguar and the friend are one and the same, the Jaguar gets + or - 4 and the other people get - or + 1.

This is a game in which your score goes up and down by small amounts. If it only ever went up, a classical tally system (vertical line for one, two lines for two, a lower left to upper right slash for five, repeat on a new block) would be great. Tallies give fast write performance and pretty good read performance, but do not support subtraction. So how do we add subtraction?

Consider these tally marks:

The pattern is simple. We add horizontal and upper left to lower right slashes. These added marks are negative. So (a) is 3, (b) is 0, (c) is 4, (d) is -3, (e) is -4. Negation (if we needed it) would be a quarter rotation. And its completely backward compatible with traditional tallies.

Chudziki and friends had been keeping score in arabic numerals and scribbling out each number to write the next. That's a lot slower because the actions involved are more complex. You need to perform addition and subtraction in your head. No fun. You get slightly faster read times, but I don't think that's worth it. Because of the typically small adjustment size, I believe these tallies are also much more space efficient.

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