Score	Match equity
0-0	50%
1-0	60%
2-0 C	75%
1-1	50%
2-1 C	70%
2-1	51%
2-2	50%

 

There are many published opinions about match equities and I am sure that some charts have slightly different numbers to those above. It isn’t important. It is very rare for the differences to have an effect on correct cube action and even then, the effect will be very small. So, let’s take a look at good cube strategy at 0-0. Why is this different to money play?

In Lesson 3, I showed you how to do a risk/gain analysis for money play. Go back and refresh your memory if needed. When we do a risk/gain analysis in match play, we use the match equity chart to assess what we stand to win and lose. If offered a cube at 0-0 (3-away, 3-away), passing means that our match equity will drop to 40% when we trail 0-1(3-away, 2-away).

If we take and win we go to 75% (2-0 C), take and lose we drop to 25% (0-2 C). Our risk is 40-25=15%, our gain is 75-40=35%. Risk divided by risk + gain is 15/15+35 = 15/50 = 30%. We need to have around 30% cubeless winning chances to take a cube at 3-away, 3-away, rather than the 25% that is the norm for money play. Just as in money play we can take a little deeper because owning the cube will win some games for us, but in general at 3-away, 3-away you can be more aggressive in doubling, particularly with an enhanced gammon threat and will want to be more reluctant to take than usual.

Many manuals will give you far more detailed guidelines than these, sometimes down to two places of decimals (!!), but the information is of relatively little value because over the board we can’t put such an accurate price on a position. Almost everybody relies on instinct and experience in this sort of situation and you must try to do the same. Here is a typical example of aggression at 3-away, 3-away.

 

 

Not quite a double for money, but at 3-away, 3-away you can turn the cube as Red. He’ll win about 65% from here, including 18% gammons. Note by the way that that is 18% of the games, not 18% of the 65 wins. You must double now, because there are more chances to lose your market from here than there are in money play, because your opponent’s drop point is closer. Also, the cube has less value for her than usual. She can redouble to 4 if things go her way, but your take/pass decision will be easier than usual. You won’t have to allow for gammons, just can I win the game 25% of the time?

 

At 1-0, things change somewhat, depending on whether you lead or trail. The trailer at 3-away, 2-away has to seek out an attacking position with some gammon threats, so that he can offer an aggressive cube. This is because after a double and take by the trailer, the cube will be dead and the gammon threat will be one way. Gammons for the trailer win the match, gammons for the leader are useless. Here is an example of the sort of thing to look for.

 

 

For money, this is just about a minimal double. Red will win around 68%, including 16% gammons. I would probably double this for money, but if a partner wanted to wait, I wouldn’t argue. The game has a long way to go, White will win some gammons too and cube ownership will count for a lot, so the take is very easy. Trailing 3-away, 2-away though, this one is a powerhouse double.

Now White’s gammons are worthless and so is the cube, whereas Red’s gammons win the match. At this score, White must pass! Without doubt, failing to recognize this sort of opportunity costs beginners and intermediates loads of match wins. If this is already a pass, something much less threatening must be a double and take. The above position relies heavily on the number of wins rather than the number of the gammons, so a great part of the threat is just to go to 2-1 Crawford, a very powerful score to reach of course.

A different type of position occurs when the win rate is nothing special, but there are a lot of gammons around. In the position below, Red has attacked two blots with a 6-6, making the ace point in the process. This is the sort of play that you have to try at this score, but White has managed to enter both her checkers.

 

 

For money, this is no double/take. Red only wins about 57% of the time, including 29% gammons. This just isn’t enough to give the cube away for money and he should wait. At 3-away, 2-away however, strong double and a clear take. The double is based on the gammon threat rather than the number of wins.

For the leader at 2-away, 3-away things are rather different. With a strong gammon threat he will often find himself playing on for an un-doubled match-winning gammon. In the position above for example, a double would be a terrible mistake. When the gammon threat is small or non-existent, he will want to get as close as possible to 75% before doubling, as of course a take means an automatic redouble to 4 putting the whole match on the line.

Is there a way to add up the chances of wins, gammons and losses and arrive at a mathematical answer to the doubling question in these positions? There is indeed. There are several ways to do this and I want to devote a whole article, perhaps even two articles, to it later on in this series.

Much the most difficult part of the job is to accurately estimate the numbers that form the raw material of the calculations. This is the first skill that you need to learn before you start to get into the mysteries of match equity calculations including gammons. How is it done? It’s all right for me to casually say, “57% wins, 29% gammons”, because I’ve used a powerful computer program to do the work. How is it possible to do this over the board?

First, you don’t need to be absolutely accurate. If you can even get down to fairly round numbers for this sort of position, you will be doing fine. Here, if you could guess 55% wins, 30% gammons, that’s great. Only a very few players in the world could do better. In this position, which is quite complex to assess, there are no ways of saying, “This feature of the position equates to so many wins, that feature adds a few more”. Getting a good estimate is much more a matter of experience and feel. I’ll let you into a secret. Most expert and world class players won’t do much calculating here. Their thought process will be something like, “Well I’m ahead, on roll and hitting something somewhere for sure. This reeks of gammon to me, so I’ll ship the cube in and see what happens.”

It is White who has the problem then and it’s not hard to imagine some wrong passes here. However, if she keeps her head she will say to herself, “Well I’m going to be blitzed for sure, but if I can hit something back and/or anchor, I’ll be in good shape. His midpoint has gone, his back men haven’t moved and two checkers are out of play on the ace point. I can probably have a go at this one.”

That’s how it’s done! As I say though, there are ways of doing proper mathematical calculations and I will show them to you another time. For now, double these aggressively, take thoughtfully. Be prepared to make mistakes, for the person who never made a mistake, never made anything. If in doubt as White, should you take or pass? I advise taking. It means that the doubler has got to go on and win the game, whereas passing will give him his point. That may be correct of course, but as far as learning is concerned, taking has a fringe benefit. When you take and lose, you will at least have seen what happens beyond the doubling point and perhaps learned something. The passer never gets to see this. If you take too aggressively, you can learn to be a little more careful. If you pass to easily, I don’t see how you can learn from that and somehow become more aggressive.

We have digressed slightly, but I hope usefully. Let’s move on and look at the other scores. At 2-0 Crawford, it’s just like DMP. Winning a gammon has no value for the leader and almost none for the trailer. Why? Because winning a gammon will get him to 2-2 and 50%, but if he wins a plain game, he gets to 1-2 and will double on the first roll anyway, so he will be very nearly 50%, actually about 48.5%. You can see that a gammon that only gains 1.5% of ME isn’t worth a lot, although you will take if you can get it without any risk of course.

This brings us again to the concept of the free drop. At 1-away, 2-away post-Crawford, the match winning chances of the leader are about 51.5%. If he passes, he only goes down to 50%, so if he is any sort of underdog, passing is correct. Strictly speaking, it’s not quite free, but it’s as cheap as it gets!

- At 1-1 we are playing a two-point match, which we covered last time.

- 2-1 Crawford is exactly the same as 1-0 Crawford in the 2-point match.

- 2-1 post Crawford is summarized above, it’s a free drop situation.

That’s it! The three-point match, bagged and tagged. Of course that’s not all there is, nothing like it, but it gets us started. To summarise, double aggressively at 0-0 and take a little more conservatively. At 2-away, 1-away, the trailer can double very aggressively with any sort of gammon threat and the leader often has to pass positions that she could usually take. The leader should play on for an undoubled gammon while there is a reasonable chance of one and double non-gammonish positions conservatively.

The other scores are handled as in two-point or one-point matches. Give all that a try and play lots of three-pointers to get a feel for them. There is a strong tendency for beginners and intermediates to try and avoid cube decisions that shorten the match. This makes them slow to double and quick to pass. Bold cube play will wreak havoc against these, so go for it. Practice makes perfect!

For your homework I want you to play out some of the positions above so that you can gain confidence with your play and cube actions. You can do this on your own, but it is much more enjoyable with a buddy, ideally somebody of your own standard, so that you learn together. Set yourself to play each position 10 times, more if you have the time and the patience. Record you results and see if they concur with the sort of figures that I give, although for small numbers of games, they may be quite different of course.

This time our response chart looks at what to do when our opponent has rolled 6-1 and made the bar. It looks like this: