Problem of the Week #100: Solution


Cash game, White owns the cube. Black on roll.




Black to play 5-1.



Note: All ‘cash game’ problems assume the Jacoby Rule is in effect. That is, you can’t win a gammon unless the cube has been turned.


Problem 100 shows White playing a well-timed holding game while Black is struggling to clear his points and get his men home. Black leads in the race by just over 60 pips, so it’s always been highly likely that he’s would have to leave a shot or two unless he rolled a useful set of doubles. Now Black has reached his first key decision point. Out of spares, he can still play safe, but he may not want to.

With the 5-1, Black has just three reasonable plays. Let’s take a look at them.

Play #1 is simple and safe: 6/1 6/5. Black avoids leaving a shot, but his board gets weaker and he still has two outside points to clear. Unless he rolls a double next turn, he’ll leave a shot somewhere with all his big numbers except 6-3 and 5-3.

Play #2 is 13/8 and 3/2. Black volunteers a double shot, but keeps his board and clears the most difficult point. White has a lot of shots: all fours, all ones, plus 2-2, 3-3, and 6-3, a total of 24. If Black doesn’t get hit, he’s got a reasonable chance of getting his blot on the 13-point home, after which he’s a solid favorite to clear his remaining points. If he does get hit, he’s got some chance of getting in and getting out, since White isn’t positioned to make his 3-point quickly. Clearing the midpoint now is the high-risk, high reward play.

Play #3 is the in-between play: 8/3 8/7. Black leaves only 11 shots, but loses his landing spot and leaves the midpoint checkers a bit stranded. Black takes a small risk to keep his inner board, and gives himself another turn or two of timing (if he’s missed) before he has to make the tough decision regarding his midpoint.

What we have is what’s generally called a “pay now versus pay later” problem. Black can take a chance now to reach a playable position, or wait, see if he rolls a double, and pay later if he has to. Before we try to balance Black’s plays against one another, let’s step back, think about the different features of the position, and see how they affect the play we want to make.


Guidelines for Pay Now/Pay Later Problems

Pay now/pay later problems are rarely easy. A lot of different features of the position affect the decision-making, and balancing them against one another can be very hard. Let’s start by making a list of the features we really care about, and see if they favor one play or the other.

(1) How many shots? A play that pays now and volunteers a shot is better if it doesn’t leave much more than a single direct shot. Here 13/8 3/2 leaves 24 shots. While 8/3 8/7 leaves only 11 now, the ultimate cost of that play is some much higher number, since the midpoint remains to be cleared. Leaving 24 shots is a lot, so this feature favors playing safe.

(2) What about White’s board? The weaker White’s board, the more inclined you are to pay now. This is the feature that beginners tend to overlook. They see getting hit as a disaster in itself, whereas it’s only really bad if White can easily contain the checker. If White’s board has a blot, or a high open point, Black should often volunteer the shot. Here White’s board is pretty good – not perfect, but he has no blots and he’s made the 4, 5, and 6-points. This feature also favors playing safe.

(3) Is White’s position improving or deteriorating? If White’s game is improving, you’d rather pay now, before his structure gets even more dangerous. If his game is likely to deteriorate, you’d rather wait and play safe. Here White has a fine position, but if he has to move, he’ll give up something. Rolls containing an ace are especially hard for him to play. This feature favors playing safe.

(4) Is playing safe constructive or destructive? A safe play which actually improves your position will almost always dominate any play that leaves a blot. Here playing safe is destructive, but that’s the usual case in interesting problems.

(5) Do you have real gammon chances? In any normal pay now/pay later problem, Black will be well ahead in the race. If Black is so far ahead that winning a gammon is a real possibility, then playing safe and destroying the home board will decrease gammon chances simply by wasting pips and allowing White to pick up crossovers. This is a minor point which might serve as a tiebreaker in some unusual positions. It’s not relevant in Problem 100, where Black’s gammon chances are in the 12% to 15% range, which is a sort of normal background reading.

The most important features to weigh are (1), (2), and (3), and here they all point toward playing safe. The right play, by a solid margin, is 6/1 6/5.

--------------------------------

Having solved the main problem, let’s get a little more experience in pay now/pay later situations by taking a look at a few riffs on the main theme.




Problem 100a: Black to play 5-1.

We’ve made one tiny change here, changing White’s spare checker from a builder on the 4-point to a blot on the 3-point with no cover numbers nearby. That change, however, is enough to swing the position completely, and paying now with 13/8 3/2 is massively correct. If Black gets hit he now has a 13-number shot at the blot on the 3-point. Combine the inner-board blot with Black’s 5-point board and White’s resulting outfield blots, and suddenly getting hit doesn’t look quite so costly for Black.




Problem 100b: Black to play 5-1.

Here we’ve taken away the blot but moved White’s open point to the 5-point. Paying now with 13/8 3/2 is now about equivalent to playing safe. Black will have a lot of chances to come in on the 5-point if he’s hit, but White will be careful about leaving blots, so Black won’t pick up quite so many loose gammons.




Problem 100c: Black to play 5-1.

Here we’ve broken White’s midpoint and given him a couple of builders for the 3-point. This is a more common sort of structure in actual play, and the changes all favor paying now. Playing 13/8 13/12 leaves only 16 shots, compared to 24 in the original problem, and White’s position is now improving, as he’s getting ready to make his 3-point. Breaking the midpoint now dominates playing safe by a wide margin.




Problem 100d: Black to play 5-1.

Here we’ve made several changes to the original position, many of which favor paying now.

> White has a blot on the 3-point (strongly favors paying now.)

> White gets only 16 shots after 13/8 13/12 (slightly favors paying now.)

> White has a dead checker on the 2-point (slightly favors paying now.)

That’s a lot of reasons to pay now, but there’s one item on the other side of the ledger: Black has a constructive use of his 5-1. (He can make his ace-point.) Being able to make a useful play is so important that 6/1 2/1 is about equivalent to 13/8 13/12.

One last comment before we call it a wrap. Notice that in none of these examples was breaking the 8-point the best play. (It was sometimes the second-best play.) That’s because breaking the 8-point is really a pay now and pay later play. Once you lose the 8-point, you’re likely to have to leave another shot breaking the midpoint, and you’ve only bought yourself perhaps one extra turn to roll a double.


Solution: 6/1 6/5

Thanks for another great lesson! This is a common circumstance where I'm afraid I still make more errors that correct plays.

What advise can you give in regard to the questions I posed in the problem thread? To wit: after you break the six point, what comes next in Problem 100? (One answer, of course, is to apply the criteria given above to each position as it arises.)

1. What is your plan? Will you continue to crash your board until absolutely forced to leave a shot? After breaking my board, I often feel forced into this strategy.
2. If you are forced to leave a shot, will you tend to leave the fewest shots, or might you then decide to "pay now," and break from the rear? (This you may have already answered in your remarks advising against both "paying now AND paying later.")
3. What happens if you are hit after breaking your board? If you fail to enter, would you accept a cube in Problem 100?

Thanks.

1) Depends on the position. Each position is a new decision.

2) If I'm breaking, I'm pretty much always breaking from the rear. I actually tried to construct a variant of Problem 100 where breaking the 8-point was correct, but couldn't. Doesn't mean there isn't one out there, but they're not common.

3) Depends on the race and what point is open in White's board. You're talking about the variation where I clear the 6-point, then White moves (let's say he clears the midpoint), then I volunteer a shot (let's say with 6-5), then he hits, then I dance. Typically I'm up 40-45 pips still in those variations, White's 3-point is open, and he has a couple of builders plus good outfield control. In the abstract, that looks like an easy take with a 40-pip lead. The redouble might be in question.

In position 100d, wouldn't you prefer 6/1 2/1 because it further constructs our homeboard?

"(4) Is playing safe constructive or destructive? A safe play which actually improves your position will almost always dominate any play that leaves a blot."

Sorry, missed these comments upon first glance... "Being able to make a useful play is so important that 6/1 2/1 is about equivalent to 13/8 13/12."