Backgammon position of the day (as requested by Anonymous below)

Zoe and I were playing a 7-point match. Zoe had lucked her way to a 2-0 lead, had given a risibly early cube, had mistakenly taken a recube to 4 and then rolled her way into the position below (at least this is how I remember the turn of events).

Zoe owns the cube at 4 on roll leading 2-0 match to 7 - cube action.
















Zoe cubed and I took. Zoe rolled a non-double so did I and it was all over.

To work out the correct cube actions for both sides here you need to know the chance of black winning in this position and the match equities associated with taking and dropping.

First the match equities:

Black can drop to trail 6-0 with about 10% mwc. Given that if he takes he either definitely wins or definitely loses he needs over 10% winning chances in this position to take.

White is risking 35% mwc (her chances trailing 4-2 match to 7) to gain 10% (her increase in winning chances from 90% to 100%).

Double Point = Risk/Risk + Reward.

Zoe has a doubling point of 35/45 which is approximately equal to 78%.

What are the actual chances in the above position? Well for Black to win White needs to roll a non-double followed by Black rolling a double. i.e. 1/6 X 5/6 = 5/36 = 14%

So Zoe has 86% chances of winning if she doubles which is greater than her averaged 78% winning chances if she doesn't double and as such she should double (this is a last roll position so Zoe should double as soon as she is in the window). I have 14% match winning chances if I take and only 10% if I drop so I should take.

A good example of how drastically cube action differs from money play with big cubes close to the end of a match.