Wednesday, 14 March 2012
Learning To Love The Cube, part 6
At the end of the last post, we finished with a cube action question and here it is again.
Black on roll, White on the bar and the score is 3-away, 3-away. Cube action?
The "correct" answer is that this position is too good to double and White should pass. In round numbers Black wins 84% of these including 24 gammons. Black's equity according to a rollout is 1.121 if he doesn't double on this turn. Nevertheless, doubling here is a good practical play for Black, against any standard of player. Why, you may well ask, is he advocating that we make a cube blunder here?
Cubing now and getting a pass puts a point onto the scoresheet. Without any mental effort and without having to play skilfully, you get your point and it is a real point. The 1.121 points that are your expectation if you play on are theoretical and you have to play perfectly to get them. If you like, you can view that extra 0.121 as a cost that you pay to have your point delivered to your door. Is this price too high? I don't think that it is and here's why.
In order to grasp that extra 0.121 you have to play perfectly from here on, with cube and checkers. Studying this position and playing it a lot, I found that it was very easy to make mistakes that added up to or exceeded that 0.121, even in the first phase where Black is just running his checkers round and White is dancing. When White enters things get harder and if White can enter and hit, it turns into a very tough game indeed. If White's play was equally difficult in each of these phases that wouldn't matter, but it isn't. She can't make a mistake while dancing and if she can enter with a 2, then her play will be pretty easy too. In the "enter and hit" phase things get tougher but I found that it is still Black who is more likely to err, as it will be him who is facing the cube questions. In real life, the actual price is very much lower than the theoretical cost of 0.121 and there is often no cost at all. In a proportion of the games Black will play perfectly of course, usually those where he cashes later, but in some games he will make mistakes that add up to more than 0.121 as well.
Don't believe me? Here's a useful exercise. Set up this position in your bot, use play it from here and analyse each game in turn. If you are any standard below world class, then you will find yourself making errors here.
Some points on how to play this. Freeing those Black checkers in White's home board is top priority, much more important than arranging checkers to close the 2pt. Making the 8pt is nice of course, but if you can't you need to pick it up. When you get into the bearoff, you can play very aggressively because of White's weak board and blot. When she enters it's sometimes double and pass, sometimes you can still play on. it won't surprise you to know that I tend to cash these!
Here's some examples.
Black is on the bar. Cube action?
Black is on the bar. Cube action?
These are just five of the dozens of tough plays that I found. You can find a lot more yourself if you play this position. All of these can be avoided by just cashing in the first place, saving mental energy, avoiding tough decisions, avoiding the careless mistakes that we all make. Lastly right at the beginning, I said that you should double against anybody, weak or strong. The stronger the player, the better the cash as she will clearly outplay you. Double weak opponents to0. Their play will be simple or forced in a lot of the games anyway, although when it gets tough after a hit they may play badly, but if they are very weak, there has to be a good chance that they will take inj the first place! An 11% chance of a bad take makes the original position a correct double.
In the play-off semi for Fibsleague 55, BushSucks edged out stukatz in a tough and exciting match, so the final will be, ahem, BushSucks v. dorbel. I'll let you know when that is scheduled.
Until the next time, enjoy the game!