Running game doubles - Backgammon double
Doubling situations in running games can be divided into four types: last-throw situations, other calculable situations, no-miss situations and formula situations.
If you cannot get another throw, because Black is certain to get off on his next turn, you must double when you have any advantage at all. The closest situations are:
- those where you have one man on your five point and one on your two point, when you must double because you have 19 winning throws to 17 losing throws, and
- when you have either one man on your eight point, or one man on your four point and one on your three point, when you must not double because you have only 17 winning throws and 19 losing throws.
Other calculable situations
What is and is not calculable depends partly on how much trouble you want to take. To get the answer really accurate you would often have to work out what would happen in 1296 games, a convenient number because it is 36 x 36. But you can't do that at the table. You can only do it at leisure later, if you want to know what to do if the position crops up again. Most of us are not that interested, but even so there are some some simple situations you can work out easily.
Look at Diagram. 19 throws out of 36 win for you. You already know that if Black's one man were on the one, two or three points, so that he were bound to come off in one throw, you would double. But do not leap to the conclusion that, because his position is worse, you must double. If you do miss, Black has 27 throws which get him off and nine which do not (4-1, 3-2, 3-1, 2-1 and double 1). So, when you miss, he will win exactly three-quarters of the time. If you have doubled him, he will double you back. As you have exactly one chance in four of winning it is, as you know, immaterial in the long run whether you accept or drop. Let's assume you will drop. The result is that you lose the game on all those 17 throws out of 36 when you failed to bear off in one throw. But if you had not doubled, Black could not have redoubled you and so, on average, you would have won one-quarter of those 17 games, in addition to the 19 you won by bearing off on your first throw.
What does all that amount to? Just this. If you double, you win 19 games out of 36 and lose 17. If you don't, you win more than 23 and lose less than 13. So don't double. The advantage of winning twice as much, when you do win, nothing like makes up for the extra games you win by not doubling.
No-miss situations are ones where both sides have all their men on their one point, or most on the one point and the rest on the two point except for one or two on the three point. The effect is that any throw right to the end is virtually certain to bear off two men, and any double will bear off four men. The rules are simple:
- If you need one less turn, in the absence of doubles, than Black, double him.
- If each side needs five turns to bear off without throwing doubles, you should give a first double but not redouble.
- If each side needs four, three or two turns to bear off without throwing doubles, you should double or redouble.
- You should refuse a double, if you need more turns than Black. If you need the same number of turns, you should accept if that number is 4 or more and refuse if it is 2 or 3.
In all other running game situations you need a formula. I am going to give one for those readers who don't want to take things too seriously, and one for those who are willing to take more trouble.
The easy formula is this. If Black's pip count is 10 per cent or more higher than yours, double him. If he doubles you, take it unless your count is 15 per cent or more above his, in which case drop.
For the keen reader, I now give the most accurate formula yet published for running game doubles. Here is what you (White) do when deciding whether to double:
- Calculate your pip count;
- Calculate your adjusted pip count as follows: add two pips for each man you have left; add one pip for each man on your one point; subtract one pip for each point on which you have a man in your home board;
- Add 10 per cent, if your adjusted pip count is 25 or more. Otherwise add nothing. You now have 'D', the 'doubling number';
- If Black's adjusted pip count is D-1 or higher, offer him a double or redouble. If it is between D-2 and D-1, offer him a first double but not a redouble.
If Black offers you a double accept if your adjusted pip count is less than D+2. Otherwise drop. I admit this is rather hard work. But it is not as difficult as it looks, and, if you do it, you have the satisfaction of knowing that, in this area at least, you are playing better than 99 percent of players.