The Kleinman ratio is the basis for a probability (expressed as a number between 0.0 and 1.0) that you can use to assess the relative strength of your position in a running game.

The Kleinman ratio, K, is calculated by the formula:

K = (D * D) / S

where D = the pip count difference of the two players, plus 4 to compensate for the player on roll's additional pips, and S = the pip count sum, minus 4 to compensate for the player on roll.

The probability, P, displayed by MacFIBS is calculated from K as follows:

If K > 1.0, then P = 0.76 + 0.114 * ln(K)
If K < 1.0, then P = 0.5 + 0.267 * sqrt(K)

The Kleinman ratio was defined by Danny Kleinman, author of numerous books on backgammon emphasizing mathematical analysis. For more information, you can contact him at 5312 1/2 Village Green, Los Angeles, CA 90016.

Thanks to Øystein Johansen for the formula to convert the Kleinman ratio to a probability, which he described in a posting to the rec.games.backgammon newsgroup in February 2001.