Backgammon Takepoints and Gammon Prices in a 15-point match
This is an article from John O'Hagan, who is available for backgammon lessons at the Backgammon Learning Center and member of the US Backgammon Federation.
John has won far too many tournaments to list, and he is currently ranked No. 11 in the World on the Giants list. He recently took 1st place in the Howard Ring Memorial Quiz, which was a pure test of backgammon knowledge and skill. John has retired and is now devoting his time to playing and teaching backgammon-he has placed 2nd in the World Championships is currently ranked No. 1 on the U.S. ABT tour.
Below are some rules of thumb that you can use to estimate your takepoints and gammon prices (or values) in a 15-point match. They are the combination of being simple enough to use OTB and accurate enough to usually lead you to the correct cube action. They are based on the Rockwell-Kazaross MET. These rules do not apply to scores where both players are within 5 points of victory (they do however apply to any score where the trailer is 6 or more away even if the leader is 5a or less). I recommend that players memorize the takepoints and gammon values for these 5a or less scores on their own. Also, don't use these rules for Crawford or Post-Crawford scores.
Perhaps someone smarter than me can come up with a "one size fits all" formula for takepoints and gammon values. Something like the takepoint is 25% plus a% if a win by the opponent puts him at Crawford, plus b% if a win by the opponent wins the match with no overage, minus c% if a win by the opponent wins the match with overage, minus d% if a win by me puts me at Crawford, minus e% if a win wins the match with no overage, minus f% if I'm way behind in the match, etc. Similarly, the gammon price formula could be 50% +/- factors a-f plus factors g and h for one being way ahead or behind in the score. I haven't been able to come up with a formula like this, but maybe someone can?