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Why do we minimise epc ?

Posted By: Timothy Chow
Date: Friday, 26 March 2010, at 10:26 p.m.

In Response To: Why do we minimise epc ? (Ray Kershaw)

Ray Kershaw wrote:

It seems obvious that minimising the number of pips we need on the average is the way to maximise the probability that we win the game. But can someone say why this is so ?

First of all, as you point out, it's not going to be able to give a watertight explanation of why this is true, because strictly speaking it's actually false. So a certain amount of hand-waving is necessary.

That aside, Trice gets the epc by multiplying the expected number of rolls by the average number of pips per roll. The average number of pips per roll is just some constant close to 8, so when we minimize epc, what we are really doing is minimizing the average number of rolls we need to bear off. It should, I think, be even more intuitive that minimizing the expected number of rolls (as opposed to minimizing the number of pips) is the best way to maximize the probability of winning the game.

In fact, maybe it seems so intuitive that you are wondering why it's not strictly true. As a rough analogy, compare money play to match play. In match play, we are trying to maximize the probability of winning the match. In money play, we are trying to maximize the expected amount of money we win. The two are similar in many ways, but there are exceptions, which become increasingly pronounced as you near the end of the match.

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