Backgammon Lesson

Lesson on Checker Play and Dice

Lessons analyzed by snowie that help show all the hidden mathmatics and skill that backgammon has, as well as some of the consideration taken during money plays and tournaments by the best players in the world

 Dice Action

This position is a good illustration of how the doubling cube can affect a checker play. This position came from a money game with the Jacoby Rule in effect, but the same principles would apply in a match where the score is close and each side needs at least 5 points or so.

As your position gets stronger, you move through this heirarchy:
1) Not good enough to double
2) Good enough to double, take
3) Good enough to double, pass
4) Too good to double

In terms of equity (average points won per game if played to completion) the breakpoint for a take/pass is about .550 points. With equity of minus half a point you would take, because you concede one point by passing, but you average minus one point if you play it out and never redouble. Since you own the cube and can redouble if things go well, your net loss would be less than a point. Once you get up to about .550, or minus 1.10 if played to completion with the cube on 2, it becomes borderline.

After that, there's a lot of room until you become "too good." If it were "double now or never" you would need equity of a full point to redouble, but of course as long as you have access to the cube, that's not your decision. As long as you have any gammon chances, and would always have equity above .550 next roll, you don't need to double this roll. Roughly, equity of about .800 is where you start thinking "too good."

In this position you have two very different choices. 11-6 9-5 is very safe. You can't be hit next shake, and will be up 13 pips in the race. It stacks up your checkers a bit, and you will have some trouble hitting the opponent safely anytime soon.

9-4 8-4 gives you a solid 5-prime. Next shake you have combinations of 3/4/5 to point on the opponent, and some pick-and-pass numbers. It has one significant risk though - an immediat 62 by the opponent that will hit you.

Risk Evaluation and Best Move

Let's look at Snowie's equity evaluation (not accounting for the doubling cube) after each play and all of black's reply rolls.  This is going to be White's equity at his next shake

The "wasteage" columns are the equity above .560 at white's next shake.  Notice that on average he wastes .041 of a point when he makes the safe play, but .127 when he makes the aggressive play.  This is because he is usually doubling and green is passing.  The rightmost column is the NET gain from the gammonish play.  He has a few stray gains, but they are offset by the HUGE loss when he is hit.

Let's look at the position if White has already doubled:

Final Lesson Notes for Player