Let’s Make this Match Equity Stuff a Little Simpler

Backgammon Cube Strategy Made Simple
by Phil Simborg – 25 June 2008

(This article is intended to serve as a simplified guideline for players of all levels who have not yet completely mastered the art of the cube. These guidelines are extremely useful simply because there is so much less to memorize or calculate or try to remember over the board.)

As all experienced backgammon players know, understanding take points and value of gammons at every possible score is critical in match play. It affects not only your cube decisions, but your checker play as well. Knowing when it is important to protect from getting gammoned and when it is important to try to win gammons affect even the opening moves. Knowing when you are at a score where you should be thinking about giving the cube quickly, or giving it as soon as there are reasonable gammon chances is critical.

Top tournament players understand these issues and know exactly what their take points and opponent’s take points are. You can do this too: just sit down with a chart and memorize all 50 different combinations of take points and gammon values for all the scores you are likely to be playing at in any given match.

Does this sound too hard to do? It’s far too hard for me. I doubt that there are many people in the world who can do this. Even most of the best players in the game don’t memorize all those numbers at all those different scores, but the top players are good enough at math to be able to calculate or estimate those numbers over the board.

So an alternative to having a photographic memory is to be a math genius and be able to do complex calculations over the board. If you are like me, and don’t happen to be a math genius, let me suggest another approach that has worked well for me, and many others, for many years.

Simply round off the numbers so they are easier to remember and apply the Money Game take points and gammon values to every game EXCEPT those few scores where the values are different. For those few scores, memorize those values.

For most scores we can use Money Game numbers where we know that the break-even on a cube is 25%. If we can win more than 1 out of 4 games (25%) we are better off dropping instead of taking. That’s simple to remember, and it’s also simple to remember that this also applies to what I call “Normal Match Scores (NMS).

We also know that if our break-even is 25%, we can actually take the cube if we are a little less than 25% because we have an advantage in holding the cube. There will be times we will be able to win the game with a redouble, and there are times we will redouble where the opponent takes, and most of the time he takes we will win 4 points instead of 2 (and sometimes even 8 points with a gammon). So depending on how much potential there is for a redouble, we can take the cube with around 22 percent winning chances, and in some instances even lower. But let’s use 22 percent for Money Games and Normal Match Scores (NMS).

Now, we also know that in a Money Game, we must also consider the gammon risks. Hopefully, you already understand why the value of gammons is half as great as a win in a Money Game, so we apply ½, or .5 as the value of gammons. This pretty much applies to NMS as well.

So if it looks like you can win a game well over 22% you have an easy take unless the number of gammons, times .5, brings you down to under that number. For example, if you have 30 percent winning chances but you are likely to get gammoned 20 percent of the time, you subtract 20/2, or 10, from 30, and you net 20%. Since 20% is less than 22, you should drop. If you are the person doubling, it is just as important to know what your opponent’s take points and gammon values are, as that determines when you should be giving the cube and how likely he is to take or drop.

Now, in a money game, as in most NMS, when you subtract your gammons from your wins, you must also take into account the number of gammons you might win. So in the above example, let’s say your gammon losses are 20 percent, but when you win, you will win gammons about 10 percent. In that case, you subtract 10 from 20, and that means that your “net” gammon losses are 10 percent, and you multiply that times .5, and that’s 5. Then you subtract 5 from your 30 percent winning chances and that leaves you with 25, or a take (since your minimum take point is 22).

Now, in a game, over the board, can you actually do all these calculations? The answer is PROBABLY NOT! Even the best players in the world are usually guessing and estimating wins and gammons. Sometimes we can be very accurate because of reference positions or because the game is a simply race and not very complex. But most of the time we must estimate and make our best guess. We survey the position and weigh the strengths and weaknesses of each side and try to come up with a reasonable guess. There are tools to help us make the guess more educated–consider Race, Opportunities, and Threats; consider your own and your opponent’s potential game plan and likelihood of success; consider Most Common Variation of what is likely to happen on the next roll or two; and consider the potential for recube. Good players even consider the comparative complexities of playing each side and the comparative skills of themselves to their opponent.

I generally ask myself these questions: “Do I think I can win this game more or less than 1 out of 4 times? About how much more? Do I get gammoned a lot? Do I win some gammons when I win?” I guess at about how many wins I might have and about how many net gammons I might have (after multiplying by .5) and see if I think that is over or under 22 and then make my decision accordingly.

The MORE you go through this exercise of guessing what number you end up with, and the more you check that against what a computer program says (I use ExtremeGammon many times a day to do this), the better you will get at making these estimates. DON’T GET DISCOURAGED if your estimates are often not very accurate – you don’t have to be as good as a computer program to win – you only have to be better than your opponents!

Once I have these numbers estimated, I then apply a methodology to deciding whether to take or drop that always includes applying Woolsey’s Law and Simborg’s Law and Robertie’s Law of Market Losers. If you don’t know or understand those strategies, I recommend some research as they will all help you enormously in your cube decisions.

That is what I do for a money game, and for all Normal Match Scores. Again, I apply these specific values to pretty much all of the possible scores of a match with the exception of those that are not NMS.

Now, all we have left to do is define what scores are not in the category of NMS, and how to apply take points and gammon values at those scores.

We know, right off the bat, that whenever one of the players needs only 1 point to win the match, this is not an NMS. If it is Crawford, there is no cube, and the importance of your winning a gammon depends on your score. Naturally, if you are 2-away, winning a gammon wins you the match, so the value of a gammon is huge – in fact, it is 1.0. If it is Post-Crawford, the cube should generally be turned immediately and the value of gammons again depends on how many points you need to win the match. If you are 3-away or 4-away and the cube is on 2, you can see that the value of gammons is very high again, as a gammon wins you the match. So we know that every score where one player is 1-away is not a Normal Match Score.

That is also true of every score when either player is 2-away. We know that when a player is 2-away, winning an undoubled gammon wins the match, so that puts the value of the gammon to 1.0 again. The value of gammons to the other player depends on how many points he needs – and the take points for both players depends on how many points each player needs.

To apply the cube process properly at the many scores where one or both is 2-away does require a little more work, but you only have to remember the reasoning and numbers for 3 key scores and you’re done. It really isn’t that hard to remember, particularly if you keep referring to this article or a take point chart until you’ve got it. Let’s go through the list and see if we can find some easy ways to remember the key numbers.

2-away/2-away – When you are both 2-away from winning, cube strategy is relatively simple. If you are up even slightly, give the cube. You’d simply rather be playing for the match when you are winning. Once the cube is turned, gammons don’t matter to either side. Before the cube is turned, you could win the match by winning a gammon, but it is rare to get into a gammoning situation where you should not have already cubed. If you are doubled, your take decision is simple. If you were to drop, because of the Crawford Rule, you would have to win 2 games in a row. That’s 25 percent. But you could also win a gammon the first game, and most experts agree that the odds of that is about 7 percent. So if you drop your chance of winning the match is 32 percent. That 32 percent is the only real key number you have to remember. So say it 20 times right now, or write in on your left toe, or do whatever you need to in order to remember this number. If you are offered the cube and you are in a position where you think you can win more than 32 percent (or about 1 out of 3 games), take the cube. If not, drop. Again, gammons don’t matter after the cube is turned.

2-away/4-away – This is a little more complex. If you are the one 2-away, you know that if you can win a gammon without the cube being turned you win the match. So that’s a very good reason not to double if you have good gammon chances. Another good reason not to double is that if your opponent takes, he will immediately redouble and with the cube on 4, then whoever wins the game wins the match. If you turn the cube and he redoubles, you have lost all of your advantage of being ahead in the score, so you should only double if you have very strong winning chances. In fact, if your opponent drops he only wins the match about 18 percent of the time, so he should take any cube and redouble where he thinks he can win over 18 percent, or only 1 out of 5 games. So now you know what his take point is and why you should not double unless you think you can get a drop, or if, by taking, you are better off than simply winning 1 point and playing on. 18 percent is the key number to remember here. (This goes on your right toe.) So you double when you are somewhere close to that 18 percent winning chances for your opponent (provided you don’t have some strong gammon chances).

If you are the one who is 4-away, it’s a different story. If you win a gammon without the cube being turned, you only get to a score that is tied 2away/2away and you then have 50 percent match winning chances. But if you turn the cube and win a gammon, you win the match. So your strategy is to make sure you turn that cube if you have some reasonable gammon chances. Remember, if you cube and lose 2 points and lose the match, you are only 18 percent worse off than if you just lost one point. So you don’t have that much to lose by doubling even if things go wrong. But if they go right and you win a gammon you win the match. And if you just win 2 points, again, you are far better off than just winning 1 point. So your strategy is to be pretty quick on the trigger at this score, particularly if the gammons chances are high.

Now, if you are the one who is 2-away and you are being doubled, it is important to know that your take point is pretty low… about 20 percent. You should be willing to take more games than you would at NMS because, in effect, you are getting 2 to 1 odds. If you win the game at two you win the match you get to 100 percent. If you lose the game at 2, now the match is tied, and you are at 50 percent. So you have a lot to gain by taking, and you should take if you can win 20 percent, or 1 out of 5 games.

The above would be true ONLY IF there is no chance for a gammon – in a pure race situation or if you are both bearing off. But in most games, you do have to worry about gammons, and if your opponent is 4-away and the cube is turned, if he wins a gammon he wins the match, so the value of gammons is very high…1.0. So you must estimate gammon risks and subtract 1 point for every possible gammon. If the number is still over 20, take, otherwise, drop.

2away/5away – Logic tells us that many of the same basic ideas for 2away/4away apply to the leader at this score – a gammon without the cube is very valuable. You don’t want to give the cube unless you have extremely high winning chances because if your opponent takes he will immediately redouble to 4.

If the trailer (5away player) turns the cube and wins a gammon, it is not quite as good as if he were 4 away because a gammon does not win him the match, but it’s still pretty strong to get take the lead at 2away/3 away Crawford. In fact, at that score he has 70 percent match winning chances.

So again, when gammon chances become a factor, it’s usually right to turn the cube. Getting a 2-cube should be thought of as a gift to the leader, and that’s why his take point is very low at this score… about 17 percent. Just think about this from the leader’s perspective – if he takes the cube and wins the game he wins the match, and if he loses the game, he’s still winning 2away/3away and is still a favorite. So the only thing that should really stop him is if the gammon risks are high.

Now, I know that “experts” may look at this advice and say it is far too simplified. They will say that there is much more to these numbers and many other scores that have differences in take points and gammon values, and therefore strategy. They are absolutely right. This article is intended to serve as a simplified guideline for players of all levels who have not yet completely mastered the art of the cube. These guidelines are extremely useful simply because there is so much less to memorize or calculate or try to remember over the board.

Approaching the game in this manner has helped me tremendously, and has helped many that I have taught over the past 20 years, who are now playing at the highest levels of the game and still approach their cube handling in this manner. I hope it helps you, too.