GamesGrid Backgammon FAQ

backgammon frequently-asked questions

Thorp Metric

What is the Thorp metric?

The Thorp metric is an adjusted backgammon pipcount, designed to give a more accurate depiction of game winning chances than a simple pipcount. The formula was developed by Edward Thorp, author of Beat the Dealer, a guide to blackjack strategies and tactics. Correct use of the formula is described through examples in Robertie's Advanced Backgammon, pages 191-194 and 231-247.

In medium races, the Thorp metric typically gives the same results as a simple pipcount.

The Thorp metric is especially useful in bearoff situations where one (or both) of the home boards is not smooth, since the formula is designed to adjust for holes in the distribution and penalize stacking on the 1 point. (A "smooth" bearoff position refers to a position in which all six home board points contain two checkers each, with the spares on the 4, 5, and 6 points.)

As with any reduction of a complicated position into a single number, the Thorp metric should be used with caution, with full awareness of the cases in which the results might be interpreted incorrectly. In particular, the Thorp metric makes no assumptions about positional considerations or contact, so it is totally inappropriate in many situations.

How is the Thorp metric calculated?

Thorp metric is calculated by

T = P + 2*C + A - H

where

P = simple pipcount

C = number of checkers in play (i.e., not borne off)

A = number of checkers on ace (1) point

H = number of home points covered

For the leader, add 10% if T is more than 30.

If the leader is less than or equal to the trailer+2, then the leader should offer an initial double.

If the leader is less than or equal to the trailer+1, then the leader should offer a redouble.

If the trailer is greater than the leader+2, then the trailer should pass; otherwise the trailer should take.

last modified: 2002-10-04