Backgammon Records

by Douglas Zare
3 March 2014


Douglas Zare

Some backgammon events are extreme. You might have your largest box run ever, make the largest blunder, get the luckiest exchange, play the longest game, or face your strongest opponent. We'll call it a record if it was the best/worst event ever at the time it occurred, even if it was surpassed later. Records are fun, and people like tracking how results compare with the records, including in the Winter Olympics which just concluded and extreme weather events. How often should you expect to see a record-setting performance?

Marking records can be amusing, but it also has some value. We can model how frequently you should see a record if current games are like past games. Exceptionally many records indicate that the games have changed. Of course, there may be more powerful tests, but sometimes aggregate statistics are harder to track than the extreme events. I can't remember the average error rate of my opponents, but I can remember the largest blunder an opponent made against me:





Red leads 8-0 to 11.
Red misplays 6-2.


A Simple Model

Suppose we repeatedly draw a number between 0 and 1. Assume our random number generator has no memory, and the numbers are all different so there are no ties. Suppose we draw 100 numbers: 0.812, 0.855, 0.604, 0.006,... How often should we get the highest value so far? How about if we make 1000 draws?
 
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Article text Copyright © 1999-2018 Douglas Zare and GammonVillage Inc.

 
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