Backgammon Lesson – 8
Free Series of 13 Backgammon Lessons for Beginners
Paul Money
Beginners Please – Lesson 8
by Paul Money – October 2006
In this lesson we will look at match play for the first time. The skills required are different to those needed in money play, with many variations in checker play and cube actions. The score is the all-important factor, so let’s start by looking at the shortest match length possible, the two-point match.
These are of course often found at the end of longer matches, when both players are exactly two-points from victory, or 2-away, 2-away as it is known. The first thing to note is that matches are always played with the Crawford Rule in use. This states that when one player reaches a score one point from victory (1-away), then the cube may not be used in the next game.
A score where the Crawford Rule is in operation always mentions this; in our two-point match, 1-0 Crawford for example. Without this rule, cube actions at the end of the game become meaningless. At 1-away, 2-away for example, the leader would have no advantage at all, as the trailer could just double on the first turn and be 50% in the match whether the leader took or passed. Is that clear?
If not, let’s just make a Match Equity (ME) chart for a two-point match. Match equity is just the chances of winning a match from a particular score:
| Score | Winning chances for the leader |
| 0-0 | 50% |
| 1-0 Crawford | 70% |
| 1-1 | 50% |
Without the protection of the Crawford rule all the lines would read 50%!
Actually the leader would do minutely better at 1-0, because he could at least pass the cube at 1-0 if he felt that he was the underdog. This is known as a free drop and we will often see this in longer matches. It is worth about 1.5% to the leader, so the middle line would actually read 51.5%.
So, cube action in a two-point match. What strategy should you adopt? The main thing to note is that if the cube is offered, it is the last double of the match. If taken, the cube becomes dead, there can’t be a redouble. If passed, the next one or two games will be cubeless.
What can we deduce from this? If there is no chance of a redouble, then any advantage at all suffices for a double! If after the opening roll or rolls you think that you are a favourite, say 52% to win, you can double. If your opponent takes, then you become 52% to win the match. If she passes, then the score will be 1-0 Crawford and your match equity jumps to a whopping 70%. Very pure theorists think that you should still double even if you are a small underdog, as long as there is at least one market losing sequence.
Something else new, what is a Market Loser? A market loser is any sequence of rolls (one for you, one for your opponent), after which your opponent will no longer have a correct take. In our two-point match, you can lose your market if there is a sequence of rolls after which you will be better than 70% to win the game.
Why is losing your market bad? That’s because if you have doubled and suddenly go to 75% in the game, you are 75% in the match. If you haven’t doubled and suddenly go to 75% in the game, then doubling and getting a correct pass will take you to 1-0 Crawford and you will be 70% in the match.
At least one market loser (and outside the 2-point match usually more) is an essential part of any correct double. Why? Because if you can’t lose your market, then you have nothing to lose by rolling. If you get better you will still have a double and take, if you get worse you will be happy that you didn’t double. Technically speaking, market losers are a very complex subject, but in practice, this is all that you need to know.
So, correct strategy in a two-point match. If you double at the first legal opportunity, regardless of what has been rolled, you are either right to do so or making a tiny and unimportant error. That’s it. When you gain some more experience, you can often squeeze out a little extra equity against weaker opponents by waiting a turn or two, because they may make a bad mistake with the cube later. This is another excellent reason for doubling immediately against a stronger player, because she can’t then do this to you.
For now and until you become an advanced player, just double the first chance that you get regardless of the position. So, if your opponent starts with a 3-1, the best roll, should you double? Yes you should. You may reply with a terrific roll like 6-6 or 4-4 and be very glad that you doubled or you may do nothing special, in which case your opponent should double and you should still take anyway. You gain in a few cases and lose nothing much in the rest.
In our Match Equity chart above, the only non obvious number is the 70% figure for 1-0 C. How is this derived? The trailer, whose equity is of course 30%, can win the match if she wins the next two games. Her bald chances of doing this are 25%, which we find by multiplying her chances of winning this game and the next, 50% x 50% = 25%. However, she can also win a gammon in the Crawford game and win the match outright. Research has shown that about 24% of all games played to a finish, as this one will be, end in a gammon for one side or the other, so the trailer can expect that around 12% of her 50% wins will be gammons and this adds about 6% to her basic 25% to give her around 31% overall.
However, statistics show that 30% is nearer the mark, because the trailer will lose slightly more games than usual taking extra risks to win the gammon and that the leader will also make plays that reduce his gammon risk, for example, he will play 24/20(2) with an opening 2-2.
Some authorities think that the true figure is nearer 69% or 71% but this need not concern us unduly. In practice, the chances of players below World Class, i.e. 99% of us, being able to differentiate between 69% and 71% in the rare games where it is important is vanishingly small. This is actually true of most of the detailed arguments for against many checker and cube plays. The interesting positions don’t occur often enough to be crucial. Just concentrating on basic technique in commonplace positions will see anybody to the advanced level quite quickly. Once there, you can begin to sharpen your skills in the very difficult positions where it is sometimes possible to chisel out an extra 1 or 2%.
So, double as early as legally possible and if doubled, you can take if you estimate that you can win a minimum of 30% of the games. You will always have a take if your opponent doubles on the first turn that she can.
How about checker play? Is this likely to be different from money play? Indeed it is. At 0-0, where the cube has been turned or is just about to be, then we need to make the same pure plays that are good in a one-point match. We need to concentrate on good positional play, trying to build a prime and of course making plays at the back that reduce our opponent’s chances of priming us. We don’t need to worry about the risk of being gammoned and of course winning one is pointless. The same is true at 1-1 of course.
In the Crawford game, we will see both sides making unusual plays, as the trailer presses hard for a match-winning gammon and the leader tries extra hard to avoid losing one. This is where the third and fourth columns in our response charts come in. The trailer should select plays from the GammonGo column and the leader of course uses the GammonSave column. Often of course the plays are not radically different from the norm, but they can be. Look at this position:
For money play and also at DMP (1-1 in our 2-point match) it is well known that 13/7*(2) is clearly right. However if Red is trailing 2-away, 1-away Crawford (GammonGo) then he should play 13/7*, 8/5(2). If he leads 1-away, 2-away (GammonSave) then he must play much more conservatively and shouldn’t even hit! His best play is probably 24/21(2), 13/10(2) although 24/21(2), 6/3(2) is a close alternate. The 24/21(2) play is the important bit. Red will lose far fewer gammons once he has a high anchor, typically here 7 or 8% gammons, rather than the 11% he could expect to lose if he played 13/7*(2).
In the gammon literature, in print and online, there are many interesting articles on two-point matches. However, we have covered just about all that you need to know for now, except this. If you find yourself playing a much stronger player, then it is likely that she won’t double on the first turn. She isn’t making a mistake. What she hopes to do is to work her position up to somewhere in the 60-70% range, then double hoping to get an incorrect pass. You can forestall this by doubling yourself, at the first legal opportunity. It is correct even between equal players, but where you are the underdog for skill, then it is hugely correct, because you are removing any chance of her outplaying you with the cube later.
In money play, the threat of gammons often leads us to pass doubles, even though we can win the position 30-35% of the time. A typical example comes when we have split on the opening roll and been pounded with a 5-5. Incidentally, many of the old text books dislike splitting with the opening roll, precisely because of this risk, but it is usually a risk well worth taking. Anyway, look at this position:
This is a common position. White opened with 6-3 played 24/18, 13/10 and Red rolled 5-5. White danced and Red doubles. For money, Red will win about 65 out of 100 games from here, including around 47 gammons (!), but White’s 35 wins will include 10 gammons of her own and cube ownership will count for a lot. Some people take this, some don’t but all agree that it is very close. In our two-point match though, White’s 35 wins are easily enough for a take and to pass would be a big blunder. A lot of people faced with this as Red like to play on for a gammon, but doubling now is correct. You can reach a stage in a two-point match where it is correct to try for a gammon, but invariably you will have missed at least one and probably several chances to double along the way.
Should Red have doubled before rolling the 5-5? Yes. More interestingly, should White have doubled from the bar? Yes in my opinion, although she actually loses nothing by waiting. On the bar and on roll in this position, she wins the game about 45% of the time, but it doesn’t matter if she doubles or not, because she has no market losers.
So, if you should, technically speaking, double immediately anyway, what’s the point of playing two-point matches? Because however often you demonstrate to people that immediate doubling is correct, most people won’t do it! They just hate to put the match on the line straight away if they are beginners and think that they can do better by waiting if they are advanced players. This last is often true, although not everybody who thinks that he is advanced really is! Until you get there, just turn that cube as soon as you legally can.
A point to note that will be repeated again and again with regard to the correctness of double and take decisions; in this column we always assume that the players are equal in strength and will both play the position as well as the best humans. Of course this is rarely the case and a moment’s thought will show that it can make a big difference to the decision. In the above position for example, a very skilful White player playing an intermediate Red player in a money game, might well decide that Red would make some mistakes before the end of the game and thus justify a take.
Some positions also require a great deal of skill on one side and almost none on the other, which should be taken into account. Some games require almost no skill to play perfectly, races are the most common example, so they offer ideal doubling and taking opportunities for weaker players, who get to up the stakes in a game where they will play as well as the master. This doesn’t even scratch the surface of a very complex subject, so for now, just be aware that this exists.
That’s plenty for anybody to take in. Read and re-read it until you understand it well, as it will pay dividends the first time that you come to a 2-away, 2-away score.
Let’s finish this lesson with a look at another of our response charts. This one has all the replies to a 6-2 played 24/18, 13/11 as it usually is of course. There are a few surprises here, notably the times when it is right to hit on the ace point and the times when it is wrong. Print this off or save it somewhere handy. Playing the replies well starts the game off on the right foot and most importantly, makes life as difficult as possible for your opponent.
Note: The moves suggested above are the #1 results of rollouts, however, sometimes other possible moves for a dice roll may have been listed as very close or as a reasonable alternate.
Until next time, enjoy the game!