Undefined Equity - Part 2

by Douglas Zare
1 August 2004

In Undefined Equity, Part 1, we started to consider the Paradox Position.

The Paradox Position.

The mathematical model of backgammon breaks down in interesting ways. In this column, we'll see what happens if you play out the Paradox Position many times. We'll also look at match play and table stakes.

The Law of Large Numbers

If you roll a die, the expected value is 3.5. Of course, you would be very surprised if you rolled exactly 3.5 pips, but the average of the possibilities is 3.5. This is true even if you are only allowed to roll the die once. However, one consequence is that if you repeat the roll many times, the probability that the average is between 3.4 and 3.6 is over 90%. If you roll the die enough times, the average will be arbitrarily close to 3.5 with a probability arbitrarily close to 100%. This is called the Law of Large Numbers
 

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Article text Copyright © 1999-2010 Douglas Zare and GammonVillage Inc.

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