Reference positions in backgammon – Part I

One of the most useful tools a backgammon player can have is the reference position. A reference position is no more than a studied position that is close enough to a position that will arise in a game. The player can then use the reference position to make a decision should a related position come up.

We will begin with the simplest of reference positions :

referenceposition-1-1

Both players need three rolls here to remove all their checkers. Any double thrown will save a roll. The side who’s turn it is to play has been calculated to win 78.8% of their games. Also the other player can never offer a worthwhile redouble. The side taking the double in a real money game needs 25% without use of the cube. This situation calls for a double and pass.

Here is a position that is very closely related. If black fails to roll a double this is what will happen. Black is 74.5% to win the game.

referenceposition-1-2

But take a look at this play:

referenceposition-1-3

It is possible to calculate Blacks chances of winning here.

White is very likely thinking that the position is the same for a lot of rolls. If Black rolls 11 it will be as good as any double unless he rolls a 21 next and white throws doubles. Its a very small difference.

If White rolls 22 it will not save him a roll letting White stay in the game with about 25% chance of winning 3% of the time. This gains White about 0.7% wins.

If Black rolls a 21 things change drastically. Instead of being 25.5% favorite to win White becomes 100% favorite. White will double and black will drop. Black will roll 21 5.6% at any given time so this gains me 75% of 5.6% which is 4.2%.

In total with ownership of the cube included white gains 5% in wins from 21.2 to 26.2% and is now able to take the double.

Before we leave the subject of reference positions, let’s show just a few more racing positions.

referenceposition-1-4

In this position both players need 2 rolls. The side whos turn it is is 86.1% favorite to win the game. if you take 1296 rolls (36 for each side) the player throwing the dice first will win on the first throw 216 times. The opposing player will roll doubles 180 of the last 1080 rolls. This means that the player throwing second will win 180/1296 times or 13.9% of the time. This matters because there might well be a situation where you are playing White and trailing 5-1 in a best of 9 series and your opponent has the cube and doubles to 4.

You can also take a black checker and place it on your 3 or 4 point. As you have seen you can always calculate your odds of winning if you know what the odds are n the reference position.

referenceposition-1-5

A position which requires 4 rolls for each player leaves the side who’s turn it is roll 74.5% favorite to win.In a money game this translates into a double and a take. You should double in this situation because most of the time neither side will roll a double and then your opponent will have a pass next turn ensuring you get maximum cube value.

referenceposition-1-6

A 5 roll position will leave the players who’s turn it is favorite 71.7% of the time. You should not double in this position as both players will not roll a double the majority of the time leaving you with a better double on the next turn.