This backgammon position doesn’t look very hard, but a good player went very wrong at the table.
1) Match score: Black leads 4-1 and the cube is on 4. Gammons mean very little to Black. Leading 8-1 Crawford will make him 93.5% to win the match, so the gammon gains 6.5%. However, if he loses the game compared to winning, he goes from 93.5% to 42.7%, a drop of about 51%. Black can play for a gammon only if he wins 8 times as many gammons as he loses games.
2) This position is a sort of holding game. Black simply wants to come home safely against the gap on the 3pt. Black leads in the race, and may well lead by a lot if white stays out.
3) At the table, Black played 11-6.
4) As for the Snowie results, Black was way off:
What was Black thinking?
Black would surely have gone right if he had looked at the match score and thought about the position.
The five best plays all involve lifting or covering the blot. In fact, the five best plays are all the legal plays that do not leave a blot.
Even for money, Black misjudged. His play gains about 5% gammons while losing 7% more games. A play winning 7% fewer games needs to win 14% more gammons. But it might have been more understandable.
Black was seduced by the idea of “purity.” Purity refers to positions where all your checkers are in play, all working toward the eventual goal of an overwhelming positional advantage. Rather than bury a checker on the ace-point, Black kept the checker in position to make a useful point.
As far as the best play that does not leave a blot, there are two approaches: Player 3-1, or cover the 3pt. Opening the 5 or 6pts seems clearly bad. Black wants to bring his checkers home safely. Making White enter on the 3pt means that Black checkers on the 10pt and higher are safe. They also give Black the chance to put builders on the 4, 5 and 6points to pick and pass or maybe even make the 3pt.
If Black plays 3-1, he has to pick a 3 to play. 11-8 leaves only 53 as a hitting roll, while 18-15 leaves 31 and 32. However, Black will need to get the back checkers moving. It is much safer to do it now, while White is on the bar. Further, 18-15 does two more good things. It forces White to create two new blots to hit, and it keeps Black’s checkers connected. In this position, each side wants to make it difficult for the opponent to cross the outfield and get their checkers home. 18-15 helps Black take control of the outfield. I was a little surprised that it leads to only 0.5% more gammons for White, since White will have builders activated to make points in his board and Black will have several blots.
With gammons being so significant for White, I have to admit that over the board I would look long and hard at 11-8. But the time to take risks like this is when your opponent is most helpless to respond. White’s board is going to get better, and once he enters, every extra Black checker in the outfield will represent at least a 2-number fly shot. Giving one fly shot now to resolve the issue may be better than giving multiple fly shots later. Probably the roll out is seeing that Black can lose a gammon as easily from being hit with a fly shot later when he is vulnerable as he can now.