An 8 Cube From Chicago

by Gerry Tansey

Winner-Gerry Tansey

The championship division of the Chicago Open this past Memorial Day weekend was run using the “More Swiss” format.  In each round, the organizers try to pair players with the same record.  Players with four losses cannot cash and are eliminated, but players with two losses or fewer can still win the title.

My tournament started out well.  I managed to win my first four matches on Saturday, including one against the number two Giant of Backgammon, Michihito Kageyama, known to the world as “Michy”  (you can see this match on the USBGF channel on YouTube if you would like to see just how good my dice were at the start of the tournament).  My fifth round opponent was Paul Weaver, who has been named one of the top 32 Giants of Backgammon in every incarnation of the list since its 1993 inception.  Our 9-point match only lasted two games, but there was plenty of excitement.

In the first game, Paul rolled an unfortunate 66, and eventually we reached this position.  I am White and on roll, considering a double.  Scroll down slowly if you want to consider your own decision, as XG’s opinion immediately follows.

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Here I decided to “double on ugly.”  I figured that Paul’s position was dangerously awkward.  I can make another offensive point or attack the lone checker on the ace point.  If Paul cannot escape his back checker quickly, he may be forced to leave blots where he does not want to, since he does not have a great deal of flexibility in his position.

However, Paul is up in the race, and he often can make a three-point board, which is strong enough to fight back with in a blot-hitting contest.  The true “danger time” for Brown is often two or three rolls away, when I have more ammunition near my home board, and Brown has perhaps stripped his midpoint.  Basically, I need to improve my position a bit more in order for Paul to seriously consider passing.

I did not roll this position out to statistical significance in XG because it really isn’t necessary to get the practical verdict.  This position is on the border between a double and no double, and it is a trivially easy take.  Whether it is a technical double or not, I think I would cube this against anyone.  A lot of players on the Brown side will look at the state of their home board and just not feel like playing it out.  But, as someone once said, “Backgammon ain’t no beauty contest.”  Brown needs to take this, and Paul correctly did.

Well, I ended up having to attack Paul’s back checker, and it didn’t go very well.  Paul turned the game around, and we reached this position, with Brown on roll.

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Paul is leading by 10 pips in the raw pip count, but his racing advantage is not quite that large.  He has a few more checkers buried on low points, and those gaps on the 4 and 5 points will hurt him in the bearoff, since he will be forced to bury checkers when he rolls 4s and 5s rather than bearing checkers off.  But still, Paul is a solid favorite, and he will lose his market if he points on me, or if he rolls a lot of pips and I don’t respond well, so he redoubled now.  Facing this cube, I decided that I was not dead in the race, and I noticed that Paul leaves a direct shot when he rolls 63, 62, 53, 43, 44, 55, and 66, so I took.  If I had to rely solely on my racing chances, or solely on hitting a shot in order to win the game, I would be less thrilled about taking this cube, but my combined chances make this a huge take.

The game continued and turned into a race.  I was able to bear in my last checker relatively quickly, and then I rolled 22 in the bearoff, to reach this position, as White, holding a 4-cube:

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There is quite a bit going on here.  Most experienced players will know that the 5-roll vs. 5-roll position (where both players have 10 checkers on the ace point) is an initial double in a money game, but not quite a redouble, as seen in the XG diagram below.

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However, the main reason this is not a redouble for money is that by redoubling, White is giving Brown access to the cube that he did not have before. So if White redoubles and Brown takes, consider the sequence where White rolls a non-doublet, Brown rolls a doublet, and White rolls a non-doublet. Brown is now on roll, holding the cube, in a 3-roll vs 3-roll position, and so Brown will redouble, and White should pass. If White had held on to the cube, Brown would have had to play this game out to the end, giving White a chance to get lucky and win the game. It is the fear of Brown’s potential use of the cube that makes a redouble slightly wrong for White in a money game.

Now what should White do in that 5-roll vs. 5-roll position holding a 4-cube at 0-0 in a 9-point match? The first thing to note is that if Brown takes White’s 8-cube, White should not fear Brown’s 16 cube. White is never going to pass a meaningful 16-cube in this game. This is because if White passes a 16-cube, he will be trailing 8-0 Crawford, a score from which he wins only about 5.6% of the time. Thus the value of Brown’s cube ownership is reduced to almost nothing, so at 0-0 in a 9-point match, White should redouble the 5-roll vs. 5-roll position to 8.

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Now that we know what to do with the 5-roll vs 5-roll position at the score, we can return to the position that arose during the match. Both White and Brown have worse positions than in the 5-roll vs 5-roll position.

White can fail to bear off in 5 rolls or fewer if he “misses” (fails to bear off two checkers in one roll) twice. This will typically happen when he leaves a gap on the ace or deuce points, and then rolls an ace or deuce. Further, 11 and 22 do not save a roll for White, and while White will welcome rolling 33, this will leave a gap on the three-point, which will end up not saving White a roll if he rolls another 3.

Brown can fail to bear off in 5 rolls or fewer if he misses once. This will only happen if he rolls a single ace on two distinct rolls. As for Brown’s doublets, only 11 fails to save a roll.

The upshot of all this is that while both Brown and White are worse off than in the 5-roll vs 5-roll position, White is quite a bit *more* worse off than Brown is. So Brown has a trivially easy take.

I confess I did not analyze it quite this calmly over the board. I basically said to myself, “I’m favored. I don’t have to worry about his recube to 8. I’m playing Paul Weaver. I double!” It turns out I was right, by a razor-thin margin.

Paul thought about the take for quite a while, as is good practice when facing what is almost certainly the last and most important decision of the match, and then correctly took. I then rolled…21! This one roll dropped me from nearly a 2-to-1 favorite in the game to a 52-48 favorite. Fortunately, in spite of creating two gaps in my board, I only missed once in the bearoff, and Paul never rolled a set of doublets, so I won that game, and then later the match. Sometimes an 8-cube decides matches when neither player is crazy or otherwise out of line. Paul was very unlucky to lose this one, although he did get some measure of revenge against me in the After-Tournament Tournament. It’s hard to beat a Giant twice in a row.

As for the rest of my tournament, I became the only undefeated player in the field on Sunday afternoon at 6-0, and then won my next match to go to 7-0. Then, I crashed and burned, losing my next four matches to finish out of the money. My dice just ran out of magic, although I do believe that my last four opponents, Di Di, Neil Kazaross, Matt Cohn-Geier, and Carol Joy Cole, played very well in beating me. Dorn Bishop, a very strong player from California, was the deserving champion of the event.

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