Proof that Better Backgammon Players are Luckier

by Phil Simborg
2 November 2015

A few years ago I wrote an article that stated that poor players who complain that the better players always seem to be getting better rolls are right. At first glance, this seems a little shocking, but the truth is, if you look at all the analyzed matches ever played, the players with the lower PR's (performance ratings) will have a higher luck factor. That means that they rolled better.

But the reason is NOT that they are luckier, as I stated in that article, the reason is that if you play better you set yourself up for more rolls that will help you and fewer rolls that will hurt you. Of course, it also means there will be more bad rolls for your opponent and fewer good rolls for your opponent.

Now, I am not about to say this is always true. In fact, for the most part, I think that players who play well are still very vulnerable to jokers. Most of the time, if you are playing well, you are better off assuming your opponent will not roll that 6-6 or that 6-1 from the bar and instead, assume that he will roll more of an average number. If you play that way, you will generally win far more than if you try to protect against the joker. And when the joker happens, well, that's backgammon.

Of course there are times this is not true. Take the situation in Figure 1 below where Red has to play a 5-1. There is only one thing that can really hurt Red, and that is a 5-5...the Joker. So Red should move off the 10 point so the 5-5 doesn't bite him.

A poor player might leave that checker on the 10 point and then when his opponent rolls 5-5 he spends the rest of the weekend telling everyone how lucky his opponent was to beat him. Neither he nor anyone he talks to realizes that the only reason Blue got so lucky is that Red gave him the opportunity to "get lucky." Of course this is an extreme example, but anyone who plays this crazy game knows that this kind of thing happens all the time (actually, about 1 out of 36 times). But the same principal applies to almost every play, even though the swings are usually not as extreme as this example.

Now take a look at Figure 2 below. Very similar, but now it is best to leave the checker on the 10 point. Yes, 5-5 hurts you, but if you move that checker and give your opponent a 5-4 you are twice as likely to get hit. In either case your opponent can only get really "lucky" and have a really good roll if you give him more of a chance to get it.

Okay, so these are two simple examples illustrating why you have more luck when you play better, and you also have more luck when your opponent plays worse. But again, it doesn't take extreme, obvious situations like this to create huge swings in the luck factor and the potential outcome of the game.

Take a look at Figure 3, below. Red has a 4-3 to play. Let's see what happens if Red plays the 4-3 well, and then Blue rolls an average roll and plays it poorly. And let's compare that to the reverse: Red plays his 4-3 poorly and Blue plays his next, average roll well. With the help of eXtreme Gammons "Dice Distribution" feature we can see the dramatic difference in the equity that is achieved, and in the number and quality of good and bad rolls that are likely as a result of the two scenarios.

The best play for red with the 4-3 in this position is to make his own 5 point. It would be a blunder to make his opponent's 5 point, although it is very likely that many players would make that mistake here. Now, if Red plays properly, an "average" roll for Blue, according to Dice Distribution, would be a 6-3. The best play for Blue with the 6-3 would be to make his bar point (7 point). But let's assume Blue makes a mistake and instead makes an inferior play: 24/18 13/10 (a blunder). After this sequence it is now Red's roll, and let's see what Dice Distribution has to say about all 36 of Red's rolls. As you can see below in Figure 4, Red's average roll yields an equity of .402 and he has 11% market losers. You can also see that 6-6 and 3-3 virtually end the game, and he has no rolls that give him a negative equity.

Now, let's take the same starting position and instead of Red playing the 4-3 properly, he makes his 20 point. And after doing that, 3-2 is an average roll for Blue and his best play is to make the 21 point. So let's have Blue play correctly and now let's look at Dice Distribution and see what the prospects are for Red.

As you can see below in Figure 5, the average roll will give Red a + .215 equity and he has 0 market losers! So comparing the two situations where the player skill is the only variable, Red is much more likely to "get lucky" when he plays well and his opponent plays poorly. On just this one play of the game Red's equity is about twice as high when he is more skillful and he can lose his market 11% of the time more often.

This is what can happen on just one sequence. Can you imagine the swing in equity and in the good rolls vs. bad rolls (luck factor) over the course of an entire game or match where one player consistently outplays his opponent?

I could, of course, provide many, many more examples, but I think the point is very clear and very obvious. So if it's so clear and obvious, why bother to write an article about it and even more, a follow up article about this? And the answer is: BECAUSE MANY PEOPLE JUST DON'T GET IT! You have to hit them over the head to see that BACKGAMMON IS NOT JUST A GAME OF LUCK. The more skill you apply, the less luck there is. It's that simple. And since telling people this over and over for years and years hasn't seemed to convince a lot of people, I thought I would give you some clear, mathematical proof and some illustrations so that you can beat those whiners and criers over the head with facts.

I know, there is a saying, "Never argue with a fool, people might not know the difference." But if you back up your opinions with logic and facts and illustrations, I believe people will know the difference, and maybe some of those fools will stop being fools and quit bitching about the dice when they lose. Nah!

Phil Simborg is a co-founder of TheBackgammonLearningCenter.com which consists of 10 highly skilled and certified teachers providing backgammon lessons on line and live in 7 languages. For more information go to www.backgammonlearningcenter.com