# Lesson 12: Holding Game Doubles, Part 2 - Backgammon Blog

## Lesson 12: Holding Game Doubles, Part 2

by Bill Robertie
• 186
• 0
• 0

In some earlier posts we talked about doubling in high anchor games, and looked at some typical positions where White held an anchor on the 5-point and Black was trying to cash in on his racing advantage and bring his last checkers home to victory. All of those positions turned out to be takes.

From those examples, you might conclude that almost any 5-point game was a take, regardless of the race. But it’s not quite that simple. In this article we’ll look at some examples where small modifications to the position can produce big changes in the evaluation.

Let’s begin by looking once more at one of our previous problems.

Position Analysis

Position #1

#### Cube

##### Cubeless Equity: -0.53MWC: 0.4668Money: -0.529
Win 24.4%G1.9%BG0%
Lose 75.6%G3.6%BG0%
##### Cubeful Equities
• 1No double
-0.907 Eq.44.32% MWC
• 2Double, pass
1 Eq.56.26% MWC
• 3Double, Take
-1.812 Eq.38.65% MWC

Proper action is no double,take 32.18%

Black has a whopping 40-pip lead in the race (99-139), but White has an easy take, based on his chances of getting and hitting a shot as Black tries to clear both the 13-point and the 8-point.

With that position in mind, take a look at this one:

Position Analysis

Position #2

#### Cube

##### Cubeless Equity: -0.68MWC: 0.4574Money: -0.679
Win 17.5%G1.1%BG0%
Lose 82.5%G3.9%BG0%
##### Cubeful Equities
• 1No double
-0.997 Eq.43.76% MWC
• 2Double, pass
1 Eq.56.26% MWC
• 3Double, Take
-2.012 Eq.37.4% MWC

Proper action is no double,take 33.7%

Black has a 40-pip lead just as before (108-148), but the position is a little different. Black owns his 7-point in this example, and he has a big pile of checkers on his 6-point and 7-point. Is that enough to change the evaluation?

Indeed it is! In Diagram 2, Black should double and White has a big pass. There are two reasons:

• Black now has 7 rolls each turn that clear the 13-point without leaving a shot: 22, 33, 44, 55, 66, and 65.

• The many spares on the 6-point and 7-point mean that Black will have several turns to move without disturbing his position, while he waits to throw a number that clears the midpoint.

Seven rolls may not seem like a lot, but the cumulative effect is substantial. If he has four rolls to try to throw one of his seven numbers, his chances of success are higher than you might think: about 60%! And even after he leaves a shot, White still has to hit it, and then win the game after hitting. White’s winning chances in Diagram 2 are only about 17%, and he has to pass.

Now try this position:

Position Analysis

Position #3

#### Cube

##### Cubeless Equity: 0.614MWC: 0.5384Money: 0.613
Win 78.9%G5%BG0.1%
Lose 21.1%G1.4%BG0%
##### Cubeful Equities
• 1No double
0.964 Eq.56.04% MWC
• 2Double, pass
1 Eq.56.26% MWC
• 3Double, Take
1.099 Eq.56.88% MWC

Proper action is double,pass NaN%

Here Black leads by 29 pips. Certainly he has a double, and at first glance you might think that White can take here. But White has a big problem. Unlike the previous positions, White’s home board is no longer in such good shape. In those positions, White was on the verge of completing a full prime, which would win the game if he could hit a shot. But here, White’s home board is ragged, with the 3, 4, and 5-points still to be made. Because White has made the 1 and 2-points first, he can’t hope to make an outside prime and roll it home. Instead, he has to fill in all three home board points before he can claim the game after hitting. That’s a tall order, and it will give Black many extra opportunities to save the game even if he gets hit. The weak home board gives White a clear pass.

Remember: if your game plan depends on hitting an eventual shot, three separate events must occur

1. Your opponent must leave a shot.

2. You must hit the shot.

3. You must win after hitting.

If the best you can hope for is to get a single shot, then event (2) is never more than about 40%. To have a take, the probability of event (1) needs to be around 50%, and event (3) needs to be almost a certainty. Check all the features of a position before taking a cube in these situations.