Editor's Note: What's Your Game Plan? is the new book by Mary Hickey and Marty Storer and can be purchased through Carol Joy Cole's at: Backgammon Boutique.
This problem was part of the original series, but fell through the cyber-cracks on its way to publication here. But that loss is our gain, because it gave me the chance to update it with 4-ply rollouts using XG 1.21, the best and fastest backgammon bot now available to us. The XG program is also the one Marty and I are using for the book.
Ben Franklin said this about respect: “Reputations are like fine china. Both are easily broken and never well-mended.” In backgammon too, if you break up a vital asset, you may never have a chance to recover it.
Since you are behind in this race, your game plan has to involve hitting. Sometimes a hit can be a winner even if you have an upper point in your board open. Here, though, you sure don’t want to depend on him fanning indefinitely while you try to escape your two back men and get them all the way home around the board. That means you want to preserve your powerful, not to mention respectable, five point board at almost any cost.
If you understand before you roll that your game plan is hitting followed by strong containment, then before the dice have stopped spinning you will already have rejected the “safe” alternative of making your ace point. It’s cowardly in the extreme to give up so great an asset, your best possible five point board, if the danger you face elsewhere to avoid doing so is not excessive.
Your six point is like Franklin’s fine china and reputations: very valuable, but easily broken and difficult to remake once the deed is done. Fortunately, you have three plays that allow you to hang onto it.
One is to run a man all the way from the back to the midpoint. Another is to use your 6 to step up to the bar point with one back checker, then play from the bar point to the 2 point with the 5. A third way is to play 18/7, giving a direct 6 shot but completing a six-point prime.
The weakness of this last approach is obvious if you look at your opponent’s forthcoming rolls. Before you play, most of his 6s are terrible! But if you play 18/7, all of a sudden every one of them is great. You still leave him with bad 5s, but why settle for just those shots when you could have the 6s too? The rollout shows that 18/7 is so bad that it’s worse than breaking the six point to make the ace. Breaking your primary holding point is also giving up a key asset for insufficient gain.
The actual play of 24/18 7/2 is better, since it holds onto your position's key assets. But it has the flaw that it takes the man from your own bar point to a bad location. No matter how this game goes, you will be better off with that spare man higher up. For example, the loss of flexibility will cost you next time if he rolls a bad number, but you then roll something small yourself. You’ll face a similar choice again, to weaken your board or leave a direct shot. But that's not the main reason 24/13 is a better play.
There is a major strategic issue that makes it better to run all the way here. This is something I discovered in my earliest studies of backgammon: if you have only one way to win, try to concentrate maximum power into it, especially if you can correctly double him if your plan starts to work. For example, rather than trying to get two single shots on two separate turns, you’re often better off setting up to get a good double shot once, especially if you get a legitimate cube turn out of it. This “principle of concentration” frequently works well even when you don’t have access to the cube, or cube isn’t in use.
In this position, you’re interested in getting all you can from his immediate bad 6s and 5s, since if he rolls one and you miss, he’s going to double you out anyway. Fortunately, you’ve rolled a number that lets you do this taking on too much added risk.
In the 12th installment of this series, the problem was one where duplication might lead you astray. Here, though, duplication is what allows you to take this risk of being hit outside with an ace. Once you’ve made the mandatory play of 24/18 with the 6, you’re exposed to crushing 41, 31, and 11s anyway. This lessens the added danger of the outside ace shots you give him with the running play, but leaves you with the full value of the added shots you get if he rolls one of his bad 6s or 5s.
If you had a 6-4 to play instead, if you ran all the way with 24/14 you’d turn his otherwise bad 2s into great shots. You’d still step up, 24/18, but would play 7/3 with the 4 instead of continuing your run with 18/14. Strategically, you would still prefer to concentrate more power into whatever shot you might get in the outer board, but tactically it would be too dangerous. This is an example of the need to use the "principle of concentration" with caution, since it is often too dangerous to apply it even when its benefits will be substantial when it works.
Back to your cube decision if you get a shot after running with 24/13: You may own the cube, since the opponent may have doubled after your play. Rollouts indicate he probably has a center double if Jacoby is in use, but probably does not if it isn't. Even in the Jacoby case, his cube so skinny they probably wouldn’t allow it on the runway in Madrid. Should he send it over anyway? Sure, even without the Jacoby Rule, if he thinks there's any chance whatever of a pass - it wouldn't take much to push this close decision in the direction of doubling!
If your opponent rolls a brick (I used 63, played the forced 13/4 as the test case), then if the cube is still centered you have a good double whether or not the Jacoby rule is in use. Of course he still has a huge take. But if you own the cube, you have to consider that if you hold onto it this turn, he can't steal your remaining winning chances by redoubling you out if you miss. He also can't sneak back into the game by various means after you hit him.
It is hard to calculate these decisions over the board, but in this case a strong rollout shows that preserving those equity tailings is more important than getting more bang for your buck from your 24 immediate hits. The original problem is thus a case where that "principle of concentration" mentioned earlier leads to the right play even when you don't get to increase your equity by redoubling when your shots materialize.
Problem 1 with rollout:
What's Your Game Plan? is the new book by Mary Hickey and Marty Storer and can be purchased through Carol Joy Cole's at: Backgammon Boutique.