The Joy of Sets
by Phil Simborg, 2008
Phil Simborg
The two things that excite me most about backgammon are: (1) watching my opponent reach into his wallet, and (2) rolling a set of doubles.

Whoever came up with the idea that you get to move twice as much when you roll doubles was a genius: he added great excitement to the game. And it happens about one of out every six rolls (more often than that if you are playing against the computer!).

But there is a downside to rolling doubles: if you don't happen to be one of the best players in the world, every time you roll a set, you double the chances of your making an error! Also, there are many times when doubles is not a welcome sight. Take, for example, the 2 positions below that both happened to me in real money games.

Position 1
Black to play 1-1.

Position 2
Black to play 4-4.

So not only can a set be great fun for the roller, as you can see, it can bring joy to the opponent as well. I mentioned that doubles give you twice as big a chance to make an error. Years ago I was told by the great Howard Ring that one of the toughest rolls to play correctly is double 2. Below are some double two's that I have rolled and misplayed over the years. Let's see if you can play them any better.

Position 3
Everyone loves getting
doubles on the bear-off,
particularly when it
doesn't leave a shot.
But do you know how
to play them?
White to play 2-2.

The right play here is to take 4 off. You win more games and more gammons that way. Taking 3 off is the second best play (-.027), but if you just moved 4 checkers to the 2 point, it's a huge blunder (.212)

Position 4
Money game.
Black to play 2-2.

Here we have a simple choice: should we make our 4 point, which is a 6-point prime, or make our opponent's 5 point? Play offense or defense? John O'Hagan was kind enough to explain to me why it's best to make your opponent's 5 point. It's a lot harder to make that point than your 4 point, and that's a pretty good rule of thumb to use when you have a choice to make. If you do make the prime, you had better roll well on the very next roll or you are in trouble, and even if you roll well, your opponent has the potential to counter-prime you and win that way. (It's a .127 error to make your 4 point, by the way.)

Position 5
Double match point.
Black to play 2-2.

Here you have basically 3 choices: (1) hit loose; (2) switch from the 3 point and hit with 2, leaving the 3 point open; (3) don't hit at all and hope White doesn't roll a 6 and cracks.

The best play, by far, is to hit loose. It's better to make him have to roll a 1 and a 6 than just a 6, and far better than hoping he doesn't roll a 3. So the best play is 7/5(2), 5/1*. A lot of people make the error of not hitting at all, afraid to take the risk that your opponent will roll a 1. The legendary Oswald Jacoby once told me a saying that I have thought of many times in positions like this: "Sometimes the greatest risk is to take no risk at all."

Position 6
Double match point.
Black to play 2-2.

This one appears to be pretty obvious. Just move the checkers from your opponent's 5 point to his 9 point, hitting along the way. That is Snowie's play. But the interesting thing about this play is I was watching one of the best players in the world, Petko Kostadinov, and he played 20/18*, 7/1*!!! It blew my mind: it was a play I didn't even consider—and that's why Petko is considered one of the best in the world. He's 29 on the current Giant 32 list, and I suspect he would be higher if he traveled to more tournaments around the world.

It's not hard to see Petko's reasoning. If he makes Snowie's play of just hitting one, White has a pretty decent chance to anchor, and that could give him around 15% winning chances or more. If Petko's is able to execute a successful blitz of White's checkers on the bar and a closed board—White's chances go down to around 3%.

Is Snowie wrong and Petko right here? For the answer, I went to another authority: GnuBG, and after a 1296 rollout there it was pretty much a tie. I think the great lesson here is that what is obvious to a normal player might not be so obvious to a great player. I can show you many positions that most people play pretty much automatically that are quite wrong if you truly understand all the factors involved.

Position 7
Double match point.
Black to play 2-2.

There are two reasonable choices here: 10/8(2), 4/2(2) or 4/2(2), 3/1(2). The second play, hitting White off the ace point, has the advantage of getting that checker off the ace point, and was so attractive to me that I made that play. The first play is better by about .03 according to a rollout on Snowie. Keeping your points in order and not leaving gaps takes priority over the hit. If you move from the 3 point to the ace point, that gap on your 3 point could cause problems later. By the way, for money it's right to make the ace point as you win enough additional gammons to make up for a few losses. This is a good position that illustrates the difference between playing match and money games.

So my parting wish to you is that you always have great sets (and that you know what to do with them when they come).

Phil Simborg is a fulltime backgammon player and teacher.
You can contact Phil at: psimborg@sbcglobal.net or visit his
web site: http://www.thebackgammonlearningcenter.com

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