Daddy's board came with a doubling cube, ivory-colored, with the corners worn round. He used to say the checkers are how you play backgammon and the cube is how you win at it. It took me forty years and a computer to understand what he meant.

How it works. The cube has 2, 4, 8, 16, 32 and 64 on its faces. It starts in the middle with the 64 up, which means the game is worth one point. Before your roll, if you think you're winning, you may double: turn the cube to 2 and offer it across. Your opponent has two choices:

  Take (on FIBS, accept): the game goes on, worth twice as much, and the cube now sits on his side. He owns it. Only he can double next, to 4, when things turn his way.
  Pass (reject): he gives up the game right there and loses what it was worth before you doubled.

Gammons and backgammons. If you bear off all fifteen of your checkers before your opponent has borne off any, that's a gammon, and you win double the cube. If he still has a checker on the bar or in your home board at that point, it's a backgammon: triple. So a game with the cube on 4 that ends in a gammon is worth 8 points. That's how matches turn around in one game.

This is the arithmetic every beginner should know, and I'll do it the way I'd have done it for a loan customer.

Say you're doubled. If you pass, you lose 1 point. Certain.

If you take, the game is worth 2. Suppose you'll win it one time in four. Play it four times: you win once (+2) and lose three times (−6). That's −4 over four games, or −1 a game. Exactly the same as passing.

So one chance in four is the break-even point. Better than one in four, take. Worse, pass. Owning the cube makes a take a little better than that, because you can double back later. Gammons make it worse, because when you lose a doubled game by a gammon, you lose 4. Every position is a little different, but one in four is where you start.

Which means you should take a lot more doubles than feel comfortable. A position where you're losing 70% of the time feels terrible. It's a take. Daddy took doubles in positions that made my uncle laugh out loud, and he won enough of them to keep my uncle from laughing for long.

How to read my boards. I'm always X. My checkers move from the 24-point down to the 1-point, and my home board is points 1 through 6, on the bottom right. O moves the other way and bears off past my 24-point. A number with a letter, like 3x, means three of my checkers on that point, and 2o means two of his. Here is the starting position, so you can get your bearings. Each side's pip count is 167.

 13 14 15 16 17 18  | 19 20 21 22 23 24
 5x  .  .  . 3o  .  | 5o  .  .  .  . 2x
 5o  .  .  . 3x  .  | 5x  .  .  .  . 2o
 12 11 10  9  8  7  |  6  5  4  3  2  1

Position 1: a pure race. Everybody's past everybody. No more hitting, just rolling. I'm on roll. Should I double?

 13 14 15 16 17 18  | 19 20 21 22 23 24
  . 1o 2o  . 2o  .  | 3o 2o 2o 2o 1o  .
  .  . 1x 1x 2x  .  | 3x 3x 2x 2x 1x  .
 12 11 10  9  8  7  |  6  5  4  3  2  1

Count it. My pips: 84. O's pips: 91. I'm ahead by 7, and it's my roll, which is worth something on its own (about four pips, by the usual reckoning, since an average roll moves a little over eight).

The rough rule I learned for long races: you want to be ahead by something like eight to ten percent of your count before you double, and the other side can take until they're about twelve percent behind. Seven pips on 84 is a little over eight percent. So: a double, just barely, and an easy take for O. If you're O and you pass this, you've thrown away a point you didn't have to. This is exactly the kind of position where beginners pass and shouldn't.

Position 2: the blitz. O has a checker on the bar and another stuck on my 1-point. I've made five points in my home board. I'm on roll.

 13 14 15 16 17 18  | 19 20 21 22 23 24
 2x  .  .  . 3o  .  | 4o 2o  .  .  .  .
 4o  .  .  . 2x  .  | 3x 2x 2x 2x 2x 1o
 12 11 10  9  8  7  |  6  5  4  3  2  1
 O on the bar: 1

My count is 88, his is 159, but the count barely matters here. He can only come in from the bar with a 1, onto his own checker on my 1-point, and 11 rolls out of 36 have a 1 in them. The other 25, he doesn't move at all. Meanwhile I'm bringing my last four checkers around to hit that blot and close the board.

If I double, he should pass, and I win one point. If I don't double and just play it out, I'll win most of these, and I'll win a lot of them by a gammon, two points. That's what people mean by too good to double: when your chances of a gammon are big enough, offering the cube actually costs you. You play on, and you take the cube out only if things start to go wrong. (In money play, that is. In a match, it depends on the score, and the score changes everything. Which brings me to Crawford.)

On FIBS you play matches: first to 5 points, or 7, or 11. Here's the problem the Crawford rule solves. Say we're playing to 7 and I lead 6 to 4. I need one more point. You need three. If the cube were allowed, you'd double me on your very first roll of every game, because it costs you nothing: you're losing the match anyway if you lose any game. Every game would be worth 2 and your one good game would win you the match.

So: the first time either player gets to one point away from winning the match, the next game is played without the cube. That's the Crawford game. If the leader wins it, the match is over. If the trailer wins it, the cube comes back for every game after that (people say "post-Crawford"), and the trailing player should double right away, at the first chance, every game, for the reason above.

FIBS applies the rule automatically. It still comes as a surprise to new players when the cube won't move.

At the kitchen table, of course, it was money play, a nickel a point, and no Crawford rule because there was no match. Daddy and my uncle played beavers: if you're doubled and you think the doubler is wrong, you can say "beaver," take, and immediately turn the cube one more time, keeping it on your side. A nickel became a dime became twenty cents before the dice were rolled. My mother made them stop at a dollar. I'm told it went over a dollar exactly once, in 1958, and nobody would ever tell me who won.