Crawford and Beyond
Kit Woolsey, 1982
Las Vegas Backgammon Magazine, April 1982

Kit Woolsey
It would seem that once the Crawford game in a match is reached or passed, cube decisions are trivial and checker play is considerably simplified. This is not necessarily the case. An understanding of the intricacies of the Crawford game can give the knowledgeable player that little extra edge which might make the difference. In the following examples, assume an eleven-point match.

In Position 1, Black must decide whether or not to play for the gammon. If he runs by without hitting, gammon chances are negligible, but the win is virtually assured. If he hits with 12/7*, 6/2, he will almost surely lose if White hits back. If White misses Black's gammon chances are very good — I would estimate about seventy-five percent. So of the thirty-six possible rolls we can say that Black loses eleven times, and of the remaining twenty-five rolls he gets about eighteen gammons. 18 to 11 odds would not be sufficient for money play; you need to be twice as likely to score up the gammon as to lose the game to make it worthwhile.

 11 10 7
Position 1.
Black to play 5-4.

The match score changes the picture. This is the Crawford game, and Black is behind 10–7. If Black wins a single game he must then win two straight (or one gammon), with a probability of about 30%. However, if Black wins a gammon the next game will decide the match (the value of the free drop is probably about 1%) so Black's equity to gain 19%, and at 18 to 11 odds this is a worthwhile gamble. Of course had the score been 10–8 the gammon would be practically worthless, so hitting would be lunacy.

I had Position 2 in a late round match in the jackpot tournament in Monte Carlo. What could be simpler — 6/off, 5/1 seems automatic. However this was the Crawford game, and I was trailing 10–6. A close examination of the score shows that a gammon is virtually no better than a win (I have to win two games or one gammon in either case), while a backgammon is very valuable, as the next game would then decide the match.

 11 10 6
Position 2.
Black to play 6-4.
I chose the unusual play of 6/off, 6/2. The idea is to hold the five-point board as long as possible while taking men off. There is little risk of losing the game, for even if White rolls 6-6 Black is still a favorite. White it could be argued that my ploy is not the best play for the backgammon, it is an interesting consideration since the gammon is meaningless. This type of situation can only occur in the Crawford game of a match. As luck would have it I was rewarded and did win a backgammon (and the match!).

## Opening Rolls

What could be simpler than an opening roll, right? Wrong! Suppose you are behind 10–9, Crawford game is over with, and you have an opening 4-1.
 11 10 9
Position 3.
Black to play 4-1.
Do not slot the five point! The old fashioned 13/9, 24/23 is clearly correct. The reason for not slotting the five point is that you will never get a chance to make it. Your opponent has a free drop available, and he will use it if he fails to hit the blot or roll some super doubles. Your goal should be to play your opening roll so that not too much is swinging on the response. You don't want your opponent to know whether his winning or losing when you double on your next turn.

Some other examples:

 11 10 9
Position 4.
Black to play 6-3.
Play 24/18, 13/10 rather than 24/15. If you run, your opponent will pass if he misses the blot (unless he rolls a good set), and take if he hits. If you slot his bar point and he hits it loose, it is not clear who is the favorite.
 11 10 9
Position 5.
Black to play 5-3.
Make the three point; don't bring two men down. You can't let your opponent roll a 9 to discover that he is winning.

## Free Drop

The use of the free drop takes some care. The principle is that if you have a free drop available (i.e., your opponent has an even number of points to go, so losing a single point is meaningless since he will presumably double every game), you should drop if you are an underdog when he doubles.

The next game of the match in which I scored the backgammon (score now 10–9) started as follows: I rolled 6-5 and ran, he rolled 3-1 and made the five point. I now doubled, of course. Should he take?

 11 10 9
Position 6.
Black doubles to 2. Should White take?
It is a close decision, but I think that opening 6-5 plus the roll is better than an opening 3-1, so I feel the double should be dropped. (In practice, he did take.)

## Mandatory Double

Obviously, the player behind in the match should double as soon as legally possible after the Crawford game is over, right? Not necessarily! Consider the following situation: You are behind 10–8, having just won the Crawford game. Your opponent does not have a free drop available, for if he loses as much as one point you can double the next game for the match. Consequently, he should take any double unless he is more likely to get gammoned than to win the game, and a position has to be pretty bad for that to be the case. Consequently, if you double on the opening roll he will surely take, and that will be that.

Now, picture the following scenario: You wait a few rolls, until your position gets strong. If a real gammon threat looms you must double before it materializes, and he should take, of course (but you never know). If there is no gammon threat, you can play on until you are a substantial favorite (say 85%) to win the game. Now you double. He should take, of course, but it can't cost to give your opponent a chance to make a mistake and drop. If he does, your 85% becomes 100%, since the extra point you would get if he had taken and lost is of virtually no value.

I have had several opponents err in this situation. A weak player might not know better, and even a strong player may go wrong if he underestimates his opponent and thinks that he doesn't know enough to double after the Crawford game. Imagine his surprise when his adversary whips it on the opening roll of the next game!

At a 10–9 score, the trailer obviously must double immediately, it seems. However, even this is debatable. Suppose you opening with 3-1 and make your five point, and your opponent counters with 5-2, bringing 2 men down.

 11 10 9
Position 7.
Should Black double?
If you double, he will drop, since he has a free drop available, so there is a lot to be said for rolling on and playing for the gammon! The point is that your opponent should only take at this score if he is a favorite, and this is very unlikely to be the case after the next roll. As usual, when playing for a gammon you must reevaluate the position after each roll, and if there is much danger that in one roll he will have a take (i.e., become favorite in this case) you must double, but as long as your advantage keeps growing it is correct to play one.

I think that it is, in fact, correct to play for the gammon in this situation. Paul Magriel disagrees, feeling that the gammon chances are outweighed by the cost of becoming the underdog in one roll if your opponent rolls a lucky number at some point in the game. Judge for yourself.