Cube Thoughts.

Here are some thoughts on cube action, taken from a recent five point match. I'm playing the Black checkers, trailing 5-away, 3-away. White is on roll and on the bar. Cube action?

Well, in the match White confidently cubed and after a bit of thought, I took and not very happily either.
Were we right? It's interesting to see what XG thought. At 4-ply it doubled confidently, at XG+ it revised its cube to marginal and a full rollout downgraded White's cube to a blunder! We can hardly criticise White for blundering when the world's most powerful bg program playing at 4-ply makes a mess of it. I nearly passed it too, but of course now that I know the answer I can see that it is a very easy take!
Even though this position is horribly gammonish, White doesn't get full value for her gammons, as she can only use three of the four points and of course her backgammons are no better than a gammon. Moreover Black can recube and cancel out White's gammons entirely if he can get to around 40% in the game.*I could fill a book with all the different directions this game could go. What actually happened is that White hoovered up almost everything, but was unable to make her 4pt. Black anchored there and gradually entered all his blots and we came down to Last Chance Saloon.

Some people cube this, reasoning that they are certain to lose a gammon if they miss. What this does is give up the equity that they would have if they hit and manage to save the gammon, but still lose the game.  Black should hit and then see where he has got too.A redouble is only a very small mistake though, because if Black can hit, he will immediately jump to around 40% in the game! This is a very useful figure to remember and it is surprisingly high given that he has yet to make a point anywhere.

Here's a typical position a couple of rolls down the line. Black is about 41% to win this game, so just in his window. He should double. I didn't.

 He should double this one as well, although rolling is only a minute mistake. I didn't cube, but I did find the right play for the 4-1. See if you can.
The point of showing you these positions is to make the point that you mustn't wait until you have made several points. Get that cube across and double your opponent in. Waiting until you have a cash is criminal!

*Some of you will, I hope, be asking, "How does he work out that Black needs a minimum of 40% to have a minimum recube?" It goes like this.
In all these problems, you need to figure out what you risk and what you hope to gain. If you divide your risk by your risk plus the gain, you arrive at the figure that you need to make it worthwhile.
Here, a redouble for Black risks the 16% Match Equity that he has at 5-away, Crawford in order to try and gain the difference between 3-away, 3-away (50%) and Crawford, 3-away (75%). He risks 16 to try and win 25 and the formula is Risk/Risk + Gain, 16/16+25 = 16/41 = 39%.
Until the next time, enjoy the game!