Problem of the Week #23: Solution


Cash game. Center cube. Black on roll.




Part (a): Black to play 4-4.




Part (b): Black to play 5-1.




Let’s start with Part (a). The first four is easy of course. Black will enter Bar/21, then look around for three more fours. With White’s two blots and so many checkers in the attacking zone, it looks at first like some sort of attacking play must be the right idea. But the various alternatives are underwhelming.

If Black plays 7/3*(2), he’s a little stuck for the last four. 6/2 and 8/4 are both silly, while 13/9 breaks the midpoint and leaves White two blots to shoot at. This play only works if White dances.

Black can try the aggressive 13/5* and 7/3*, good if it works, but also a play likely to shove Black into some sort of feeble back game.

Another approach is 13/9(2), coupled with either 8/4 or 6/2. This play builds a little structure, but leaves the back men disconnected from the front position. In addition, the follow-up is likely to be awkward.

Although 4-4 at first seemed like a very good roll (Black certainly wouldn’t roll over!), none of these ways of handling the roll seem especially effective. What’s wrong?

Black’s real problem lies on the other side of the board. With two men on the 21-point and two men on the 18-point, Black has 78 pips tied up in those two points. Not only is that a lot of pips, but Black is unlikely to be able to move those checkers anytime soon without rolling a fortuitous double (like the one he just rolled). The right idea for Black is to free two of those checkers with 18/14(2), then simply play 6/2 with the last four. Now he has a better balanced and more efficient position, with one anchor holding back White’s checkers while the rest of his men can maneuver more easily.

When players make two high anchors early in the game, like the 18-point and the 21-point, or the 18-point and the 20-point, they often have the impression that they are restraining the opponent. Actually, they are the ones being restrained! They have too much force tied up in a small area of the board, and as a result their front game becomes harder to develop. The key to playing efficiently is to have checkers working optimally all around the board.

[Two additional comments need to be made here. The 20-point and 21-point combination early in the game actually works fairly well. Although the points are high and close together, they prevent the opponent from building his board. And of course in the later game, after the opponent has escaped all the back men, a combination like the 18-point and the 21-point do offer some extra defensive chances.]

Now take a look at this Part (b) and see how this same idea applies.

The obvious play here for Black is 24/18, which seems to leave him in good shape to make the 18-point in the next couple of turns. But does he want the 18-point at all? As we just saw, the 18-point and the 20-point perform duplicate work in the early stages. The best way not to tie up too many checkers on the points is to ignore the 18-point once you have secured the 20-point.

The right idea for Black is 22/16! If Black can make the 16-point he will have achieved some real progress, as the 20-point and the 16-point are farther apart, and securing the 16-point will make up in part for Black’s loss of the midpoint. And since White’s 13-point and 10-point are both stripped, White can’t hit without giving up a point that he’d very much like to keep.


Solutions:

Part (a): Bar/21 18/14(2) 6/2

Part (b): 22/16

No disrespect to Bill, but I'm skeptical that problem A can be solved through pure reasoning alone.

GNUBG has no fewer than 44 reasonable moves on its list of hints. With so many options and so many tradeoffs in the position, a rollout seems mandatory.

I did a 2-ply rollout of the top 12 candidates, truncated at 10-ply, quasi-random dice, 216 trials, and b/21 13/9(2) 6/2 came out clearly ahead.

There were other interesting results, such as b/21 8/4(3) coming out ahead of any hitting roll.

So all we can really conclude IMO is that hitting is wrong, and it's debatable otherwise.

Rollout results:

A full 0-ply GNU rollout of bar/21 13/9(2) 6/2 and bar/21 18/14(2) 6/2 gives 13/9(2) as clearly better, with the other move -0.056 cubeful equity (SE of 0.013). Only -0.018 cubeless.

You could argue that GNU is misplaying one side or the other. However, the argument for 18/14(2) is that it will lead to more balanced positions where Black's men can manouevre more easily. If the position tends to play itself, one would expect GNU to make less mistakes playing these positions than more awkward positions, which means any advantage on a rollout would go to 18/14(2). So unless I've done something wrong, 13/9(2) looks better. The general point is well taken though.

Edit: I might do a full 2-ply rollout later, mostly because I'm curious to see if it changes the results much.

Naturally, I do rollouts of all the postions in our problem series as a matter of course. The days of solving BG problems by pure reasoning are long gone. (For me at least.)

The point of the explanation is to show how to think about positions of this type for the occasions when they arise over the board.

OK, makes sense of course.

So in your opinion, is this a Snowie vs. gnu discrepancy, or different rollout settings giving different results?