I have been teaching beginner and intermediate backgammon players for about 20 years. I have stopped drilling match equity and take points into them. It just doesn't work for any but highly skilled players, and even many of them screw it up. Also, I have found that for that level of player, trying to learn these concepts thoroughly is frustrating and just makes the game "less fun." Many walk away thinking they can never enjoy tournament play because there's too much to learn and too much math that has to be done over the board to be fun.
The fact is, even most top-level players don't do the math over the board either ... they understand the concepts of the underlying math, and they have some general rules they follow at various scores, but then, they make their "best guess." You see, even if you have memorized all the take points at every score and are skillful and quick enough to do the math over the board, you still have to be able to look at the board and accurately estimate wins, losses, gammons and backgammons for both sides for the math to accurately apply. That kind of skill takes years of study and a huge internal library of reference positions.
So here is how I teach the concepts to beginner and intermediate players. (And if you are a more experienced player, this is not a bad refresher course for you, too!)
First we look at the concept of Match Equity and why we need to know anything about it in the first place. I start with a simple example. Let's suppose you are playing a match to 5 points and the score is 3-3. At this score, we say that both players are 2-away. When you are 2-away from winning, it doesn't matter whether it's 3-3 to 5, or 11-11 to 13, or 19-19 to 21 ... the match equity is all the same50% for each player.
At 2-away/2-away, before the first roll, each player has a 50% chance of winning the match (we always assume equal skill level in these computations, but you can adjust in your head if you believe you are far better or worse than your opponent). But after one or two rolls, usually one of the players has at least a slight advantage. If you were that player, and it is your turn to roll, your decision is simple: you should double. Why play a game for just 1 point when you are winning if you can turn the cube to 2 and a win gives you the entire match instead of just the game? If you don't double, you run the risk of getting so good that when you finally double, your opponent will drop.
Now, if you are ahead and don't double, of course there is the chance that your opponent will improve and get to a better position and become the favorite, and by not doubling you might lose only 1 point instead of losing the match. That's certainly possible, but the odds are, since you are ahead when you doubled, you are more likely to be the one to get further ahead and win the game. So play the odds when they are in your favor, and double.
There's another advantage to doubling when you have a slight lead ... your opponent might make a mistake and drop! Now, because of the Crawford Rule (he cannot double for one game when you are one-away from the match), he must win two games in a row, or win a gammon on the first game. Assuming equal ability, the odds of him winning one game are 50/50, so the odds of him winning two games in a row is half of that, or 25%. Now, he can also win the match by winning a gammon on the first game, and the odds of that are about 6%, so his true equity if he drops the cube is 31%. That means, if he drops your cube, you are now a 69% favorite to win the match. So if you got to the point at 2-away/2-away where you are a slight favorite, you're delighted if you double and he drops and now you become a big favorite (69%) instead of just a small favorite.
And that brings us to the take decision. If you are the one who is doubled, as you can see from the above, if you drop you have a 31% chance to win the match. Therefore, your "take-point" is 31 percent. You should look at the position of the checkers and try to estimate your winning chances. Gammons and backgammons don't matter if the cube is turned as you are both needing 2 points, and if you take the cube would be on 2so you only need to consider wins and losses. If you think you can win this game more than 31 percent of the time, you are going to win more matches by taking the cube than by dropping the cube. But if your opponent has waited too long to double, and he has an overwhelming position and is likely to win more than 69 percent of the time, you are better off dropping and playing more games.
So here you have one of the simplest examples of match equity, but when I go to major tournaments and watch intermediate and beginner players, and even some open players, I often see major cube errors at this score. To make it simple for us "idiots"at 2-away/2-away, double when you have even a slight lead, and if you're not quite sure if you should double or not, double anyway.
At other match scores, the doubling and taking decisions become much more complicated, as in addition to wins and losses, you have to take into account gammon and backgammon chances, both with the cube turned and unturned, and the affect of all of the risks taking into account the differences in the score.
Again, there is no substitute for learning the tables and concepts completely, but as I stated early, except for a few of the top players in the game, most of us apply some general rules of thumb to help us make the decisions.
- If you are ahead in the match, you should generally tend to be more conservative with the cube. If you give the cube too early, you generally benefit your opponent more than yourself, and you give him the cube, as a "weapon." Once he has access to the cube and you don't, he can use the cube to end the game and you cannot, or he can force you to take the cube at 4. The higher the cube, generally the greater benefit to the player who is trailing in the score. Whatever your winning chances when you doubled, they go down once your opponent has access to the cube and you don't.
- Conversely, if you are behind in the match, you should be more liberal both in giving and taking the cube. You need to take more chances, and you need to recognize that the higher the cube the better chance you have to catch up. However, giving away the cube too soon also reduces your chances of winning the game, as you can no longer end the game with the cube, so you don't just go wild with the cube.
- If you or your opponent is 2-away from winning the match and you are not, you generally want to be aggressive with the cube. If you lose, and he gets to 1-away (and it is Crawford) so your match equity, depending on your score, is fairly low anyway, so you don't risk that much by doubling. Further, when the cube is turned and he is 2-away, you now get the benefit of winning gammons and backgammons and he gets no benefit from gammons and backgammons. Now, that doesn't mean you should just wildly cube on the first roll ... clearly you should have an advantage and hopefully, some gammon chances before turning the cube. Conversely, if you are the one who is two-away and you are being doubled, most players get far too conservative about taking the cube. By taking you can now win the match with a simple win. The best reason not to take is if you are in the kind of position where you could get gammoned a lot, and then you probably should drop. But again, you must take into account your opponent's score when you make that decision.
- If it is post-Crawford, you should double on the first roll every game. You cannot double for one game, but don't forget to double immediately every game thereafter. (There are some scores and situations where expert players should hold the cube, but again, that should not be a consideration for the beginner and intermediate player.)
- If you are both 5-away or greater, the match equity is very similar to that of money games. That means that the take point is around 25 percent ... so take the cube if you win about 25% or more (considering gammons and backgammons in your decision), and give the cube when you are at least a 67% favorite or more, again, depending on gammon and backgammon risks. You can take with a little less than 25% if there is a reasonable chance you can get in a recube, or if enough of your wins also give you gammons.
- Your checker play also changes because of match equity. When there are differences in score, gammons and backgammons become more or less important to each side. If you determine that winning a gammon is extremely important, you might be right to take more chances to get a gammon. Conversely, if getting gammoned costs you the match, you should make plays that tend to protect against gammons, even if they might cost you some wins.
While I do advocate to beginner and intermediate players that they are better off applying the above principles than trying to "do the math" over the board, I still advocate, whenever possible, "checking your decisions" by constantly putting positions into Snowie (or Jellyfish or GnuBG) and seeing where you are making mistakes in your decisions. And I advise them to go a step further and actually look at what Snowie says the take-point is for both players and try to understand why a given position is a double or not, or a take or not. This will sharpen their judgment, and, along the way, more and more they will start learning the math and the math behind the reasoning and then, some day, they too can be too good to read articles "for idiots" like us.