Doubling in bear-off racing conditions (intro to iSight)

The pip count isn’t everything when it comes to doubling decisions in non-contact racing positions. Consider the following position:

Here, your pip count is 10, and Gary’s is 12. You are actually leading by more than 10%, which would mean you have a reasonable double based on our original racing game doubling rule. However, you have 10 checkers remaining on the board; no matter what, it will take you at least 3 rolls to bear off all of your checkers. Compare that to Gary’s 2 checkers, which will be borne off in 2 rolls on average. Even though you get to roll first, he actually has a 98% win chance. This contrived example is meant to show you that there are more things that need to be considered once you’ve started to bear off checkers.

Over the years, many different methods have been developed for accurately assessing these types of cube decisions using “effective” or “adjusted” pip counts that penalize additional checkers on the lower points (such as in your board above), gaps in the bear-off structure, and additional crossovers.¹ We could write entire book chapters on the history and pros and cons of each method. Since our aim is solely to improve your practical playing, we’ll just cut to the chase and learn the simplest one, called the iSight method. It was developed using a fancy computer algorithm, and was designed to be accurate yet simple to implement over the board. Just know that there is a lot more to learn on this topic for a motivated student.

This article will be separated into 3 parts. First, we will learn how to use the iSight method to determine effective pip counts. Next, we will learn how to use effective pip counts to make informed cube decisions. Finally, as a bonus, we will use iSight to calculate game win chances.

Calculating the effective pip count using iSight

The algorithm to calculate your effective pip count is:

1. Calculate your ordinary pip count
2. Add 2 pips for every checker more than 2 on your 1-pt (e.g., if you have 4 checkers on your 1-pt, add 4 pips.)
3. Add 1 pip for every checker more than 2 on your 2-pt
4. Add 1 pip for every checker more than 3 on your 3-pt
5. Add 1 pip for each empty space on your side of your 4-, 5- and 6-pts that are filled on your opponent’s side of the board
6. Add 1 pip for each additional crossover you have compared to your opponent
7. Add 1 pip for each additional checker you have compared to your opponent

Looking at the board above, you would start with your 10 pips, add 16 pips for the extra checkers on the 1-pt, add 1 pip for the extra open space on your 6-pt, and add 8 pips for your extra checkers. Your opponent’s pip count would remain unchanged. Now instead of leading the race 10 pips to 12, you’re trailing the effective race 35 to 12! The effective count does a much better job of assessing the race than the direct count.

Let’s try this exercise on a more realistic example:

In the race above, the pip counts are 58 for Gary, and 71 for you. What are the effective pip counts? Your board is fairly simple, with no gaps anywhere or wastage on the low points. You have a crossover, but it’s fewer than the number Gary has. Your effective count remains at 71. What about Gary? Gary has an extra checker on his 1-pt, a gap on the 5-pt where your board has none, and one additional crossover compared to you. Following the algorithm above will add 4 pips to his count, up to 62 pips.

Before moving on to the next question, a brief discussion — why do these rules work? Each one corrects for a “slow-down” in your racing. For example, checkers that need additional crossovers cannot be borne off until you bring them in. Imagine you rolled a double-6 — on your board, one of those 6s will be completely wasted; on Gary’s board, the crossovers will waste two of them. However, the most unintuitive rule is adding pips for checkers on the 1-, 2- and 3-pts. Those checkers are the closest to being borne off, why are we being penalized for them? The answer is that the dice are equally likely to roll 6s as 1s, but regardless of the number you can only bear off a single checker per number. Therefore, the small pip count contributions from these closer checkers underreport how much of your race is actually left. Correcting for this allows you to make more accurate cube decisions.

Cubing decisions

The straight racing formula suggests that this adjusted pip lead of 62 to 72 is a double/pass for Gary. What does iSight propose as a method?

First, the player on roll adds 1/6 (rounded down) of their effective pip count. Here, we’re adding 62/6 ~ 10 to 62, resulting in 72. Then they subtract their opponent’s effective count. Here, 72 – 72 = 0.

The cube criteria state that: Gary should double if this number is 6 or less (redouble if it’s 5 or less), and you should take if it’s 2 or larger. It seems iSight agrees that this position is still a double/pass.

Win percentage

The effective pip counts above can be used to estimate the win% of the race within a few percent. The formula is as follows:

p = 80 – (adjusted pipcount on roll)/3 + 2 × (pipcount difference)

In the position above, Gary’s effective pip count was 62 and yours 72, so the difference was 10. Plugging these values into our equation leads to a win probability of ~ 80 – (63)/3 + 2×10 = 79%, beyond the doubling window for an unlimited game.

The iSight method isn’t perfect, getting 10-15% of races wrong. However, it acts as a great starting point for some extremely tough decisions. In practice, like in the second example above, you often notice that most corrections don’t apply at all, or that the difference is so large that it is a clear double or a clear pass. This makes its application even easier. It also gets easier and easier the more you use it, so it pays to practice it.

Further reading:

• The article where the iSight method was first introduced by Axel Reichert
• The article describing the Keith count, a precursor to the iSight method
• A video by Goeff Hall describing how to use the iSight method
• A video by Joseph Heled comparing iSight to other models

1. I suppose that it’s easier to “solve” these positions analytically because there is no contact, leading to a lot of interest from mathematicians. ↩︎

Next lesson: Opening blitz doubles