Learning from mistakes 2: Is it too good to double?

This problem is from yesterday’s XGM match against Ole Nielsen. We are in the 4th game where I’m leading 5-1 to 17 (5-1/17). I hold the cube at 2.

The pip-count (race) is also strongly in my favor having only 64 pips against Ole’s 81 pips.

It was not at all clear to me what the right cube action was. Let’s try to dig into a deeper analysis of the situation I was faced with.

Match score

When leading a match you want to protect your lead by lowering the variance which in most cases means playing more conservatively with the cube – especially high cubes. More variance will benefit the person trailing because it will be easier to become lucky and turn around the course of the match.

This means that I should be less inclined to double than in money game where match score does not play a role.

Context – no gammon, no prime to jump

Let’s start by looking at another situation, that could arise from our original position, where the cube action is clear.

White is not behind the prime and there is no way of catching the second checker. White will lose a few games by being hit from the bar but Black will also lose a few gammons. See the theory section for reference positions.

Conclusion 1: It is clear that White has no incentive to play on for the gammon in position 2 and the correct cube action is for White to double and Black to pass both at the current match score and in money game.

Theory

I have two reference positions that are nice to know.

Context – gammon, no prime to jump

Let’s take a look at a position where we can win more gammons but we don’t have the issue of being behind a prime.

It is clear that we are in a much better position than in position 2. The question is if we should double now or play on for the gammon.

If White catch a second checker there will be a significant amount of gammon in the position. If not, White will jump out and end up in one of two situations.

1. If Black fans we have the same scenario as dealt with in “Context – no gammon, no prime to jump.”
2. If Blacks enters the position it will be a clear double for White and depending on the distance between the checkers Black has either a take or pass. See the theory section for reference position.

In scenario two Black’s cube action is as shown below.

In either case our cube decision is well defined if we do not double right away.

Conclusion 2: If we hit we play on for the gammon. If we miss we double and let Black decide what to do. By not doubling right away White gets a chance to try to win a gammon.

A good rule of thumb is that you need to win more gammons than you lose games to be able to play on for a gammon (the position is too good to double).

As seen in reference position 4 White will win less than 40% gammon if White hits the second checker (let’s say ~30% in position 3). It will happen ~1/3 of the time giving White close to 10% gammon chances. Another estimate is that white will win position 3 over 90% of the time.

Conclusion 3: The estimates above indicate that White will win ~10% gammon and lose fewer games than that. If White does not double there will be efficient cube action next roll. White should play on for the gammon in position 3. The decision is close though.

Theory

Rule of thumb: If you are in a position where you win if you run by your opponent or lose if you get hit, then

• you can double if you are 11 away
• your opponent should take if you are 9 or more away
• your opponent should take or pass if you are 8 away depending on other factors

If you have closed out two checkers you will win ~40% gammon.

Analysis of the original position

Looking at position 1 it is now clear that we are not thinking about playing on for the gammon. If position 3 was just good enough to play on for a gammon then position 1 is definitely not good enough. The question is then if White can double at all.

The fact that our position is not a lot worse than in position 3 it still has to be a clear double and a huge pass for Black. This conclusion is so strong that the match related adjustments does not change anything.

After thoughts

If you made it this far consider leaving a comment with feedback on the style of this blog. If I can make improvements I’d like to hear about it, so I spend the time writing these blogs as efficiently as possible.

Good luck with your training. See you at the tables.