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Merrigan's Metric Formula

by Douglas Zare
1 February 2012

Douglas Zare

Nigel Merrigan wrote an interesting article on backgammon races. This article discusses some work on racing theory by others first. The main addition is a formula for estimating the probability of winning a long race, which he calls the Metric formula, with the name from MErrigan and TRICe. This percentage can be used for take/pass decisions in money play and match play.

The formula asks you first to compute the maximum number of pips at which the trailer can take for money, or PLT (Point of Last Take). One of the easiest and most accurate method for this is the Nack58 rule due to Nack Ballard:

Start with the leader's pip count.
Subtract 32.
Double the result.
Take the square root.
Round.

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Subject: Re: Merrigan's Metric Formula

From: Grant Hoffman

Date: 02 Feb 2012 14:33 EST

Putting epips to one side the formula 50 + (62-PLT)/(L+PLT) x L is very interesting. The article I saw on Nack58 said to round DOWN the square root result so in the examples the PLT would therefore be 11 not 12. This means example 1 & 2 = 77.6% = 78% (remember no epips) which is very close. In the 3rd example we have to use the Keith count adjustment of there being no men on Whites 4 point so add 1 to whites pip count. Therefore the calculation is 50 + (62-11)/(14+11) x 14 = 78.56% = 79%. This is a lot easier to calculate than Kleinman. Does this calculation hold for other race pipcounts? And where does the formula come from?

Subject: Re: Merrigan's Metric Formula

From: Timothy Chow

Date: 04 Feb 2012 21:14 EST

Doug, have you communicated your criticisms to Nigel Merrigan directly?

Subject: Re: Merrigan's Metric Formula

From: othello

Date: 23 Feb 2012 20:01 EST

Kleinman count is easier to me.

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