Skill versus Luck in Backgammon
Is backgammon 5% luck? 10% luck? 90% luck. To me, that's like asking how many angels can dance on the head of a pin. But I will say this, with 100% certainty:
Take two players, B and W, where B is a better player and W is a worse player.
B will win more than 50% of the 3-point matches against W.
If B wins x% of his 3-point matches against W, he will win y% of his 5-point matches, and y will be greater than x.
If B wins y% of his 5-point matches against W, he will win z% of his 7-point matches, and z will be greater than y.
And so on.
B will probably also win more than 50% of his one-point matches against W, and this percentage will probably be less than x%, but it's possible this could be untrue if there is a great difference between the player's checker play and cube skills.
What are reasonable values for these percentages? Well, it depends on the difference in skill between B and W. I'm not going to try to quantify the difference. But I am as sure of the above statement, and that 100% of all top-level backgammon players would agree with it, as I am that the sun will rise tomorrow.
Example of a skilled and a lucky player
Consider this position:
X on roll
It is possible to calculate the chances of winning exactly, since there are at most four more rolls in the game. I'll save you the math and say that x wins 75.4% of the time.
Now, suppose that x rolls 4-1. I would call this an unlucky roll. If he plays this roll best, he will have 67.1% chances of winning the game. So I would say he was unlucky on this roll by 8.3%.
However – he might not play it best. It is clear that the right play with the ace is 2-1, not 4-3. He can’t control what o does, but if he plays 2-1, he will get both checkers off next roll when he rolls anything but 1-1, 2-1, 3-1, or 3-2. That is 7 of the 36 possible combinations (since each non-double can come up either of 2 ways; i.e. 3-1 or 1-3.), leaving 29 good rolls. If he plays 4-3, he will get both checkers off only if he doesn’t roll an ace. That is 11 bad rolls and 25 good ones.
1/6 of the time o will roll doubles and it won’t matter. 5/6 of the time he will have the chance to have his mistake cost 1/9 of the time. So 5/54 of the time he will lose because of skill. Thus, if he plays 4-3 instead of 2-1, I would say he was unskillful by 9.3%
If you believe that it doesn’t matter because “Either you’ll get good dice or you won’t” then I have a proposition for you. We will each put up $100,000. In the middle of the night we will go down to the highway, wearing black. You will lie down in the middle of the road, and I will sit on the shoulder. One of us will be hit and killed. The survivor gets all the money. Now, it might be a car that comes down the middle of the road and hits you, or it might be one that happens to veer out of control and hits me on the side. But – well, it doesn’t matter what you do, because either you’re going to be lucky or you’re not.
You see my point. There are no guarantees, but if you play the odds – you will live longer and will win more backgammon games. If you refuse to play the odds and lose, don’t blame it on bad luck. And if you refuse to learn and use the odds, then don't blame your losses on bad luck or on your opponents.
So how to Improve Your Game
Practice Your Game
As you might have guessed the best way to try these concepts and views is going an online gaming site and start playing for fun. Gammon Empire has a great backgammon school that helps learn more about these strategies as well as a stable software platform, which makes playing easy and fun. Here is a review of the Gammon Empire site.