Match Play

 The Doubling Cube Made Simple by Phil Simborg, 2008
I am going to talk to you about something that I consider to be one of the most irritating things that can happen in backgammon. You are rolling the dice and playing along and having a really nice time, and then all of a sudden your opponent does something extremely irritating and rude: He doubles you! What a nasty thing to do, especially since you are probably not really happy about how the game has been going.

Now, thanks to your extremely inconsiderate opponent, you are often faced with a very tough and ugly decision. You have a lot to think about, and it's often very complicated. You have to look at the board and you have to try to guess just how often you are likely to lose the game. You also have to estimate the number of times you might get gammoned or backgammoned. And when you've done that, you're still not finished, as you have to take into account how often you might gammon or backgammon your opponent if things go well for you. And you're still not through—you have to think about the volatility of the game and how much opportunity you might have to give the cube back if things go well.

Coming up with decent estimates of the above factors is a combination of science, art, memory, experience, and intuition, and believe me when I tell you that even the best players in the world—even the computer programs—often get it wrong. Most players below the Championship level (and even some in the Championship level) believe that once they have done the above estimations, they are done. But the truth is, they are only half done!

So what if you have come to the conclusion that you would win the game about 40% of the time and you might get gammoned about 20% of the time, and if things go well you might gammon your opponent 10% of the time? Even if you are extremely accurate in those estimates, unless you know what your take-point is at the match score, you have no idea whether to take or drop the cube. At some scores you should take if your net winning/gammon chances are around 31% (2-away/2-away), and at other scores your take point can be as low as 18% (2-away/4-away).

The same thing applies to your decision in giving the cube. How do you know when it is right to give your opponent the cube unless you also know what his take point is? If his take point is 18% you really should have an extremely strong game before you give the cube (or have excellent gammon chances, depending on your score), but if he can and should take the cube much higher, you should be giving the cube sooner.

One of the major reasons it is so irritating when your opponent gives you the cube is because you are often in a quandary about whether to take or drop. It's not fun being put in a position where you know you will often make the wrong decision. I have decided to make this situation far less irritating for you, by helping you do a better job of making the right decision.

Now, I'm not the first to try to do this—there are hundreds of books and articles advising how to use the doubling cube and how to figure take points and match equity. Why haven't more players read, understood, and memorized them? I think it's because most of those books and articles are written for very advanced players and they are far too complicated for the average player.

While I cannot help you, in this article, to do you estimations of wins and losses and gammons in a given position—I know no other way to get good at this except for experience and study and the good old school of hard knocks. I can help you understand your take points in a more simplified manner so that at least half the battle becomes clearer for you.

At the beginning of every single game you play, you should stop and think about your cube strategy. If you wait until after you start and wait until there is cube action, you are too late—for two reasons. First, your cube strategy at any given score affects your checker play—it even affects many plays on the first and second rolls of the game! Secondly, you are, in effect, making a cube decision every time you roll. If you don't know the strategy from the start, you are more likely to pass up a cube opportunity.

Put simply, if you want to play backgammon well, you must know, or have a good approximation of your take point and your opponent's take point every game you play. Few players do this, again, because it is complicated if you use exact numbers, and difficult to remember all those numbers. I hope to make this a little easier for you.

The important thing about the score in a match is not how many points you or your opponent has, it's how many points you or your opponent needs to win the match. That is called the away score. If you are playing a match to 7 and you both have 3 points, you are both 4-away from winning. The same is true if you are playing a match to 5 and you both have 1 point, and it's true if you are playing a match to 21 and you both have 17. The cube and checker strategy and takes points are the same in all three matches. And that is why, when you are playing, you need to think in terms of away points.

To further simply the strategy, I am going to give you some simplified cube strategies and take points for matches that are 5-away/5-away (both players are 5 away from winning) or less. It is at those scores, when the match gets closer, that the cube decisions generally become more complicated and are more critical, as a wrong cube decision is more likely to cost you the match. Also, I am only going to deal with initial cubes in this article. Redoubling is a whole 'nuther ball of wax. (I recently read a great article on that subject by Steve Sax—call him if you want a copy!)

If you will study and learn this summary, I promise you that you will play better, win more, and not feel quite so irritated when you get the cube in the future. (By the way, I make no guarantees about my promise.)

Since most of us are familiar with the cube strategy for money games, we use that as a basis for many of our decisions. In money games, we know the take point is around 25%. If you take every cube and win 25% of the time you will break even. We know that this 25% number must be adjusted to account for gammons and backgammons, and we also know that since there is an advantage in holding the cube (you can end the game or double the game any time and he can't), the take point can actually be as low as 23 percent if you are in a game where there could be reasonable opportunity for a redouble.

At most match scores, you will not be far off using money cube strategy to make your doubling and taking decisions. Around 25% applies pretty well if you are both farther than 5-away/5-away, or if you are tied at 5-away/5-away, and 4-away/4-away.

If you are winning 3-away/4-away, you can actually take around 20%, as the score gives you a much bigger advantage in the match if you win than the disadvantage you have if you lose. If you happen to be the losing 4-away/3-away, you're still around that 25% money game range. A big factor at this score is the gammon risk. If you are losing and there is a double, gammons win you the match and you get the full value of the 4 points for winning a gammon. The leader only needs 3 points to win the match, so the gammon does not give him as great a value. Therefore, if you are losing, be much quicker to give the cube if there are reasonable gammon risks, and if you are the leader at this score, be much quicker to drop the cube if there are reasonable gammon risks.

The score of 2-away/4-away is one of the most interesting and complex scores in backgammon. The main thing to remember is that no matter which player you are, your take point is around 18 percent. The biggest difference in the strategy between the leader and the trailer is the value of gammons. If you are ahead and the cube is turned, winning gammons doesn't mean a thing--you only need 2 points to win the match. But if the cube is not turned at all, you can win the match by winning a gammon. If you are the trailer and you need 4 points to win the match, obviously a gammon is of huge importance to you once the cube is turned. Also, once the cube is turned it doesn't matter if you get gammoned, but before the cube is turned, getting gammoned is fatal. These factors should be taken into account in all of your checker plays and cube decisions.

Now, whether you are the leader or the trailer at this score, since you know that your opponent's take point is 18 percent, far below that of a money game, and since you know your opponent is likely to take all but very, very tough positions, you probably should not turn the cube until you get to a pretty strong position. One of the most common mistakes that beginner and intermediate players make at this score is when they are losing they think they should turn the cube quickly. When you give the cube too early at this score, you are giving your opponent a major edge in winning the match. Another very common mistake is often made by players who are ahead at this score, as they often drop too quickly, thinking that is the best way to preserve their lead. When they get the cube too soon, they are given a golden opportunity to win the match with a relatively smaller risk if they lose the game, and they often throw this gift away. Again, you have to be careful to consider gammon risks in your decisions. If you are trailing and have strong gammon potential, you might well give the cube even if you are only a slight favorite in the win/loss department.

2-away/2-away is one of the most misunderstood scores in backgammon, but it is one of the easiest to handle. If you are ahead at all, even as little as 1 percent, you should double. The reasoning is simple: if you are winning, wouldn't you rather play the game for the entire match than just for one point? If you are getting the cube you should take as long as you think you will win more than 1/3 of the time (actual take point is 31.5%). The reason is that if you drop, your odds of winning the match are 31.5% (you have to win two games in a row, or win a gammon or backgammon on the first game). So if you win the match more by taking the cube than by dropping, take it. Gammons don't matter at all after the cube is turned, so you only have to consider wins and losses.

Free drops. Another consideration in cube strategy is the post-Crawford cube strategy. If you get to 1-away from winning, because of the Crawford rule, you cannot be doubled for one game. After that game, it makes sense for your opponent to double every game immediately. So if you are the one who is losing, you should turn the cube right away. If you are the one winning and you are given the cube right away, or even later in the game if your opponent did not choose to double quickly, you have a decision to make.

For the purposes of this discussion, let's assume your opponent doubles you after the first roll of the game, as he generally should. If he needs 2, 4, 6, 8, 10, 12, or any even number of points to win the match, you have what is known as a free drop. It costs you very little to drop the cube, so if he has a favorable position, even very slight, after the first roll, you should drop the cube. If he needs an odd number of points to win the match, however, a drop is very costly, and you would take any cube he gives you after the first roll.

Let me give you a couple of examples and some explanation to illustrate this thinking. Let's suppose you are winning 4 to 1 and it's post-Crawford. Your opponent wins the opening roll and rolls a 6-1 and makes his bar point, and you roll a 5-3 and make your 3 point. Now, he doubles. You should pass. According to Snowie, he is only 54% to win the game, but you lose very little by passing, and there is no reason to play if he has any kind of edge at all. The same is true if you were winning 4-3 and he doubles in this situation. You have a free drop. The reason is this: if you take the cube a 4-3, then whoever wins the game wins the match. If you drop the cube and the score becomes 4-4, whoever wins the next game wins the match, but maybe on that next game he won't have an advantage after the opening roll!

With a score of 4-1, in order for him to win the match, he has to win 2 games with the cube turned or one gammon with the cube turned. If you drop the cube, it's the same! He still has to win two games in a row, or a gammon on the first game.

Now that you have the basic take point factors down cold (I'm sure you've memorized everything I've written), let me give you some of my favorite Rules of Thumb to apply to your cube decisions.

1. Use Woolsey's Law. If you are thinking about doubling, first put yourself in your opponent's shoes and ask yourself if you would take or drop. If you are sure it's a drop, then for sure it's a double (unless you are too good because of gammons.) If you are sure it's a take, you might still have a double, but be careful. If you think it's a take but you are not sure it is right to take, or if you think it's a drop but are not sure it is right to drop, then for sure it is a double. If you are unsure, hopefully, your opponent isn't sure either, and he might well make a mistake and make the wrong decision. There is no chance for him to make a wrong decision if you don't cube.

2. Use Simborg's Law. If you are thinking about doubling, put yourself in your opponent's shoes and ask yourself if you are really hoping your opponent will not cube. If you think your opponent would hate getting the cube, the for sure, give it to him. The basic fundamental of Simborg's Law is that you want to cause as much pain as possible for your opponent. (It's a lot like my first two marriages.) You should apply the same thing to taking or dropping cubes. If you are given the cube, put yourself in your opponent's shoes, and if you think he would love to see you drop, then it's probably a take; and if you think he'd love to see you take, then it's probably a drop. Your goal is to make your opponent unhappy as much as possible.

3. Study. The best way to learn about when to cube or not cube, and when to take or not take, is through study. Unless you constantly check your decisions by seeing what the bots (Snowie, GnuBG and Jellyfish) say, you will not improve in your judgment. There is no way around it—if you want to be a good backgammon player, you must make good cube decisions, and the only way to sharpen those skills is through experience and study.

I want to close by saying that this is a highly simplified discussion of cube strategy that I believe will be helpful for beginner and intermediate players to understand and apply. Once you get your game to a more advanced level, I strongly urge you to study take points, match equity, price of gammons, and other theories relating to cube handling, in a much more thorough and detailed fashion. Again, there are many books and articles to help you, and many really great teachers and coaches. One that just happens to come to mind at this moment can be reached at the email address below.

 Phil Simborg is a fulltime backgammon player and teacher. You can contact Phil at: psimborg@sbcglobal.net or visit his web site: http://www.thebackgammonlearningcenter.com

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