Googling “microsoft internet backgammon cheating”, I’ve found a lot of discussion about cheating on Microsoft Internet Backgammon. Silly, ill-informed, immature discussion.
Are there ways to cheat? Maybe, but probably not the way it’s discussed on the web forums.
Most of the people who complain about cheating, complain that the dice rolls favor the other player. From this, they infer that, somehow, the other player has a program that manipulates the dice rolls to give them doubles when they need them, rolls that let them make points more often than they should, or that block you from getting the roll required to get off the bar.
None of these players can point to a site where you can actually download these mythical cheating programs yourself. At best, they mention a friend of a friend who says that he could write such a program if he felt like it. But he never does.
Almost all of these posts about unfair dice rolls show ignorance about basic probability calculations.
One post stood out because it cited actual numbers. The writer had recorded the number of sixes rolled on the opponent’s first roll on over 2000 games. He found that the opponents rolled a six more than thirty percent of the time when the odds should have been one-sixth of the time. See his mistake? A six will come up one-sixth of the time on one die. But backgammon uses two dice. When you roll two dice, there are thirty-six possible outcomes. Eleven of them contain a six: 1-6, 2-6, 3-6, 4-6, 5-6, 6-6, 6-5, 6-4, 6-3, 6-2, and 6-1. Eleven out of thirty-six is about thirty percent. This guy didn’t prove that sixes came up too often, he proved that they came up about as often as random chance would predict.
But what did he do? He said that now, whenever his opponent rolls a six on the first roll, he concludes that his opponent is cheating and he immediately abandons the game. Now he wins more often. No shit. He only plays when he has a better than average chance after the first roll. Someone’s cheating, all right. But it’s not his opponent.
What should he have done? He should have recorded how often he rolled a six on the first roll, too. Then he would have discovered that he got sixes just as often as the other guy. And his abysmal understanding of probability theory wouldn’t have mattered.
If you’re going to play backgammon, you have to understand this table that shows all the possible rolls of a pair of dice:
Each row is a different face of the first die and each column a different face of the second die.
First, you can see that there are thirty-six possible outcomes. You can see that doubles, which are found on the diagonal occur six times out of thirty-six. Sevens are found on the other diagonal and also occur six times out of thirty-six.
Any single number occurs eleven times out of thirty-six: six times on the row and six times on the column, minus once where the row and column overlap.
You can also see that getting a six and five – 5,6; 6,5 – is twice as likely as getting double fives – 5,5 – but exactly as likely as getting either double sixes or double fives – 6,6; 5,5. That’s why it’s easier to advance out of your opponent’s one point to your safety point at his twelve point if you haven’t advanced your man to his two point.
This table also shows something more subtle and interesting. Look what happens as you move away from the top-left to lower-right diagonal. Rolls in which the dice are separated by one pip – 1,2; 2,3; 3,4; 4,5; 5,6; 6,5; 5,4; 4,3; 3,2; and 2,1 – are more common than rolls in which the dice are separated by two pips – 1,3; 2,4; 3,5; 4,6; 6,4; 5,3; 4,2; and 3,1. And those in turn, more common than three pip separations – 1,4; 2,4; 3,6; 6,3; 4,2; 5,1. And so forth. This means that you’ll more likely make points when you have men on the board that are adjacent than when they are separated by one or more empty points.
You shouldn’t be playing backgammon unless you can visualze this table in your head.
It explains why people often think that the dice are against them. The chances of a double are 1:6. Unlikely, but hardly rare. The chances of two doubles in a row is 1:36 and three doubles in a row, 1:216. If you play a lot of backgammon, you’re going to see your opponent get three doubles in a row once in a while. It does not mean that the dice are rigged. It means that he got lucky. And not lottery-win, struck-by-lightning lucky, only its-sure-to-happen-sometimes lucky. Frustrating when you’re neck and neck and bearing off, but it happens.
The chances of making a point on the opening roll – 1,3; 1,6; 2,4; 3,5; 4,6; 6,4; 5,3; 4,2; 6,1; 3,1 – is 10:36 or 28%. It’s going to happen a lot. By the way, expert players don’t recommend using an opening 6,4 roll to make a point because starting the game with a point that deep in your home table is not especially useful. I always know that I’m playing someone who has never read about backgammon strategy when I see my opponent do that.
So what do you do when your opponent gets lucky and you don’t? The stupid thing to do is to swear, claim your opponent must be cheating, and storm away from the computer. Stupid, not only because you’re almost certainly wrong, and very certainly immature, but because you never get a chance to learn about coming from behind to win a game. If you play to the bitter end, you’d be surprised how often you can manage to hit a blot as your opponent is bearing off, keep putting him back while you keep advancing, and squeak out a sweet, sweet victory.
How do people really cheat? They do it by getting a program like GNU Backgammon and using it to advise them on strategy. You won’t see them forcing good dice rolls for themselves more often than chance because that’s not what they’re doing. They’re simply playing better than you with fair dice. But they’re playing more slowly because they have to keep consulting the program to get advice before making their moves.
And you? Unlike chess, the best backgammon programs can still be beaten by great players. Forget about cheating and learn to play brilliantly. You won’t win when your opponent gets lucky rolls, but you will win far more often than not.
And you’ll enjoy playing a lot more.