Backgammon Stoplight Charts

Most cube reference positions that you will find in the literature, such as in Kit Woolsey’s Backgammon Encyclopedia, are for money games. As of this writing (October 2009), there seems to be no widely available compilation of cube reference positions for match play. However, I predict that it is only a matter of time before such compilations start to appear.

For anyone who is planning on producing such a compilation, I have a suggestion for how to summarize the cube action for a particular position: A stoplight chart. Here is the idea. First, let us associate a different color to each possible cube action, as follows.

No double, take Red    
Double, take Orange    
Double, pass Green    
Too good to double, take Blue    
Too good to double, pass Purple    

A stoplight chart for a particular position would look a little bit like a match equity table, except that the entries would not be match equities; they would be colors, indicating what the cube action would be for that particular position at that particular score. For example, here is a position and its associated stoplight chart, calculated using 1296-game GNU Backgammon supremo rollouts and the g11 MET:

|9X ' ' ' ' '|   | ' ' ' ' ' '|
|                   | 1X|                   |
|                 | 1 |                 |
|2O2O2O3O3O3O|   | ' ' ' ' ' '|
2 3 4 5 6 7

The first row and column have been suppressed because post-Crawford cube actions are not very interesting. Also, I have stopped arbitrarily at 7 points; naturally, the chart could be extended further. The stoplight chart tells us, for example, that if you are Black and are leading 2-away/4-away, then you should not double; however, if you are trailing 4-away/2-away then you should double and White should take.

To remember the colors, begin by noting that red means “no double”. That is, if you are tempted to double the position, STOP. Do not double. On the other hand, if you see green, then go ahead and double; in fact, your opponent should pass. Orange (or amber) is in between red and green on a stoplight so it represents “double, take”. The remaining possibility is “too good to double,” which may be thought of as lying beyond “double, pass,” so it is represented by either blue or purple (colors that lie beyond green on the rainbow). If we want to distinguish between “too good to double, take” and “too good to double, pass,” then we may use blue for the former and purple for the latter.

Stoplight charts do not, of course, tell you everything about a position. In the above example, the 4-away/3-away cube action is very close to the take/drop borderline, but the stoplight chart does not distinguish it from a clear drop. Nevertheless, I believe that a stoplight chart is a useful way of summarizing a lot of information about match cube actions.

Note: After coming up with the idea of a stoplight chart, I was informed by Bob Koca that Tom Keith had come up with a similar color-coding scheme many years ago. What can I say? Great minds think alike!

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