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BGonline.org Forums
EPC Explanation
Posted By: Kevin Whyte In Response To: EPC Explanation (Max Levenstein)
Date: Tuesday, 9 August 2011, at 4:22 a.m.
Since no one else has responded and I've been looking in some detail at race models, I'll take a stab at it. I'm not sure if you're asking for an explanation of what EPC is, or details on how to calculate and use it. Since I can't answer the second part with any authority, let me just take on the first. My apologies if you know all this already and were asking for something else or specifically for a source in the literature to give as a reference to someone else. Anyway, here's my take (which is a slightly different point of view than seems to be the norm, but it's equivalent):
EPC is the average number of pips you need to roll to completely bear off. To give an example, the position with a single checker on the 1-point will bear off immediately whatever is rolled. Since the average pips for that one roll is 8 1/6, that's also the EPC for the position. Any position that is guaranteed off in 1 roll has that same EPC.
More generally, a stack of checkers on the 1-point is easy to calculate too. Each checker bears off with one die (counting a roll of doubles as 4 dice), with the exception of an odd number of checkers where a die is always wasted. So for 2n or 2n-1 checkers on the 1 point (what is usually called an n-roll position, although I can't get used to that name) we get almost get an EPC of the total average of 2n dice, namely 7n. There's one slight flaw there, namely that when we're down to a 1-roll position we might roll doubles whcih wastes an extra two dice (so an average of 7 extra pips). This happens 1/6 of the time, so the EPC of an n-roll position is 7n + 7/6.
Just to make sure things are clear, one more example: one checker on the 4 point. This is off in one except if the roll is 21, when it is off in 2 no matter what is rolled. That means 8 1/6 pips for the first roll average for sure, and another 8 1/6 for the second 1/18 of the time, for a total EPC of 931/108 or around 8.62.
As the last calculation suggests, and a drop of math will verify, EPC is the same thing as the average number of rolls it takes to bear off multiplied by 8 1/6 (the average pips/roll).
The difference between EPC and the actual pip count is call the wastage, and it is the main thing one needs to estimate to make the pip count an accurate reflection of the race, at least for longish races.
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