“A Quarky Match Cube” first appeared in The Chicago Point in 1995. The reprint here includes the introduction from A Funny Thing Happened on the Way to the Four-Point!
“A Quarky Match Cube”
Kurt S., boy scientist, has proved to be one of my most popular characters. Not so surprising, since in real life he is one of our most popular players. Kurt is one of two players to come out of Fermilab. The other is Tom Fahland, who also shows great promise (though he has some peculiar ideas about football).
The proper handling of the cube at this score is so tricky that I screwed it up. Fortunately, an alert reader caught the error, and I include his corrections.
This is the case history of Kurt
S., a brilliant young computer scientist, and rising star of
Last night, during a match, Kurt S. misplayed a 2 in this position:
Match to 7. White (Kurt S.) leads 4-3. White to play a 2?
Kurt S. noticed that if he bore off, a set of double-ones would then bear off only three checkers, and so played 3/1.
It is difficult at first to see what difference the two plays make. At Fermilab they bombard things with tiny particles to see what sort of sub-atomic critters they can flush out. Borrowing their technique, I have bombarded the positions with tiny doubles -- double-ones, followed by double-twos. After Kurt S.’s play we have:
After bombarding Kurt’s play.
known in the trade as the “atomic pile.” After bearing off the 2, we have:
After bombarding the alternate play.
the “split atom”. We need release no further energy to see that failure to bear off may blow up in our face. That a talented player like Kurt S. got this wrong may be attributed to some personality quark.
After the spectators gasped over his misplay (I was the only spectator, and so may speak for all of us) his opponent rolled double-twos, bringing us to the nucleus of this article. What is the proper cube action here:
Match to 7. White (Kurt S.) leads 4-3. White on roll. Cube action?
This is what may be called an “everyone knows” situation. Everyone knows that the proper time to double in the bearoff is when both sides need four rolls. What everyone knows is wrong, which is why some of us win slightly more than our fair share. In this particular case, the score is the central feature to be considered. Three-away, four-away is tricky because the leader’s take is lower than normal, and the trailer’s is quite a bit higher. We’ll use the numbers: 83%; 68%: and 60% for the relevant scores: one-away, four-away; two-away, four-away; and two-away, three-away. The scores three-away, three-away; zero-away, three-away; and zero-away, four-away are relevant too, but if I need to supply those match equities I suspect this article may not be for you. Just look at the pictures.
If White doubles, and Black passes, Black has 32% match equity. Can she do better by taking? If Black’s strategy is to take, and immediately redouble, her match equity is equal to her cubeless probability of winning this position: 30.5%. Recent articles have discussed the great recube leverage Black enjoys at this score (She has little else to enjoy!). Can Black do better by waiting to redouble? Can she move the world with her powerful cube leverage, or is that too simple a machine to use on this physicist?
Sort of, no, and yes. The real leverage occurs only when one arrives at a position wherein White’s cubeless probability of winning is greater than 25%, his “money take,” but less than 40%, his takepoint of a recube at this score. If Black waits to roll a double before recubing, White will always have less than 25%, a pass both at this score, and for money. Black can cash the position 33.8%. Her match equity then is the sum of 60% of 33.8% and 17% of 66.2%. When I was figuring that out in the shower this morning I came up with 31.694%. This is better than 30.5%, but still less than the 32% available by passing. So, next time Kurt, avoid confusion, and bomb her with the cube.
A Reader Replies:
read “A Quarky Match Cube.” In the
words of Queen
1. Jokes about Fermilab. Once you accept physical humor, it’s a short and slippery slope down to pratfalls and other debased forms of humor.
2. “Kurt S.” Despite the attempt to disguise the name, any fool can figure out this is a personal attack on Newt Gingrich. (I did.)
3. Mr. Jacobs clearly has no concept of how to handle the cube at this match score. Black, the taker, has a redoubling window that opens at 30%. If White rolls a double after doubling, Black must hold the cube, otherwise she properly redoubles (as an underdog).
Following this strategy, Black’s match equity after taking White’s double is equal to 100% x 55.5%(White rolls a non-double not including an ace) x 34.3%(Black’s cubeless winning chances) + 100% x 27.8%(White rolls a non-double including an ace) x 35.9%(Black’s cubeless winning chances) + 13.9%(White rolls a double other than 1-1) x 5.3%(Black’s chances of winning owning the cube) x 60%(Black’s match equity at 2 away, 3 away) + 2.8%(White rolls 1-1) x 27.3%(Black’s chance of winning owning the cube) x 60%(Black’s match equity at 2 away, 3 away) + 13.9%(White rolls a double other than 1-1) x 94.7%(Black loses) x 17%(Black’s match equity at 4 away, Crawford) = (I’m sure all loyal readers of the Point are already screaming out the answer) 32.5%. This is greater than 32%, so Black should take.
Since I can’t imagine anyone failing to work this out at the table, I can only conclude that Mr. Jacobs’ article was pointless, as well as being unfunny. Next time, instead of being in such a hurry to fly off to Seoul or Manila or Bloomington, Illinois, or some other glamorous place, he should take more time to get it right!