backgammon

In looking at doubling decisions we have so far ignored the possibility of gammons, but in the vast majority of early-or middle- game positions, this is a very important factor. It is commonly accepted that 20 per cent of all games played to a conclusion - not ended prematurely by a double being declined - end in gammons. What impact should this have on our cube decisions?

Consider today's position: White rolled 6-3 and played 24-18, 13-10. Black has rolled 5-5 and played 8/3(2); 6/1*(2). White rolled 3-1 and stayed on the bar. Should Black double, and if so, should White take?

In 100 games starting from the above position, Black will win 31 gammons and 35 single games and White will win 34 single games (how these figures are derived will be the subject of my next article). This gives White 34 per cent winning chances, well above the 25 per cent needed to accept a double.

Therefore, it looks as if White has a take. But look at the arithmetic. If White takes, he will lose 31 gammons at four points each, and 35 plain games at two points each, while winning 34 games at two points each. His net loss will be 128+70-68=126.

If he declines the original double, he will lose only 100 points. Thus we have the answer to our original problem: Black should double and White should pass. This clearly demonstrates the impact gammons can have on doubling decisions. Ignoring the "gammon factor" accounts for more wrong doubling decisions than anything else. There is a simple rule of thumb for adjusting your take point to allow for gammons. Take your expected gammon loss and divide by 2. Add this to 25 per cent to get your new take point; so if you expect to lose a gammon 10 per cent of the time, you will need to win 30 per cent of all games to justify accepting a double.