Problem 1 shows Red in a situation that might look hopeless at first glance. Five checkers are stuck on the ace point behind a five-prime. Red’s home board is not ready to contain a checker, if Red should be lucky enough to hit one. There’s a very good chance that he will fail to roll an adequate amount of sixes quickly enough to avoid crashing his board. It looks like a gammon loss is on the way – perhaps even a backgammon. If Red jumps out with a six now, he is a favorite to get hit, and then every roll that he dances will make the dreaded triple-game loss more imminent.

So there is a great temptation to just give up on the possibility of actually winning the thing and play cautiously in the hope of minimizing the amount that will be lost. But this would be a big mistake. Red can win this game a full 22% of the time. He can also, if he so chooses, give away almost a third of his winning chances on this one move with a single pessimistic play.

Problem 1: Red to play 6-3.

The plan is as follows: Red will hit a blot at some point. Then either White will dance a few times or Red will have built a prime to imprison the hit checker. Red might have to resort to an attack – an attempt to keep the hit checker on the bar – but he would prefer to do the job with a prime. One reason for this is that he will likely still have some checkers to bring around from the far side of the board, so he will not want to leave himself with work to do on the near side Another reason is that with a prime he can permit White to keep moving destructively in his own home board, and perhaps pick up a second checker.

The plan absolutely dictates one play, which happens to be the right play. Red must avoid crashing, and he needs to make checkers available for prime-building: hence 24/18. For his prime he needs to make his five point: hence 8/5.

This particular play happens to have other advantages. Playing 24/15 would leave more shots and make it easier for White to get around Red’s outfield blot if he should happen to miss it. And by staying on the 18 point, Red might get to follow it up with another six and actually make the point before White gets home. But these are relatively unnecessary considerations. The systematic optimist sees how he is going to win and makes the plays that are needed to make it happen.

Something like 24/18, 9/6, by the way, would be just silly. Red would presumably be thinking that he would hate to get hit on the five if he happened to hit a lucky shot in the outfield. But this is a much more remote possibility than immediately getting hit on the 18.  If the first risk is worth taking then the second, which is far less likely to cost anything, must be worth taking too.

Is it justified to play this way, “against the odds”? Up to a point it is. As the underdog you have less to lose than your opponent, so risks are less serious than they look. Secondly, many players have an exaggerated fear of a gammon loss. The fact that losing a gammon is only half as bad as losing the game is hard to grasp intuitively, so to compensate it helps to focus more on the upside when playing from a weak position. Of course there are situations where the best policy is to pretty much give up on the game and try to save the gammon, but these are less common than the average player seems to think.

If Problem 1 was not quite desperate enough for you, you might enjoy Problem 2, which arose in a recent club tournament match of mine. It may look like Red has nothing, really, to think about or to do here, but I made a play which my opponent found more surprising than anything else I did in the entire match. (At any rate, it was the only one that he felt compelled to ask me to explain.)

Problem 2: Red to play 1-1.

At first I just pushed the point, 9/8*/7(2), but after looking at the result I took it back and played 9/8*(2) 4/3(2), which certainly has a more ragged look to it. Why make the alternative play?

Red hopes to roll some fours. If White stays on the bar then Red gains time for rolling fours, so Red would like to make more home board points. The problem with moving checkers to the seven is that sixes then send them to the ace, where they could never possibly contribute to making a new point. If sixes force me to blot after my play, that doesn’t bother me much. I would often rather have a blot on the deuce, where it might become part of a point, than a dead checker on the ace, which could never be constructively useful.

It is extremely optimistic for Red to think he can move all four of his back checkers out while White remains on the roof. That might actually happen, but Red can be satisfied with a less dramatic result. If he just gets one or two checkers out then he improves his chances of winning the race later on, when White is bearing in and off. Also he will crash more slowly, which will give him a better chance to benefit from hitting a fluke shot at some point.

The Snowie rollout (at the end of this article) shows the top two plays to be nearly equal, with a tiny edge to my 9/8*(2), 4/3(2), though it is really still too close to call after 2000 trials. It seems that by far the most important part of the plan is to roll fours while White fans, and it is up to the Dice Gods to carry out that part. I am satisfied to find that making the common-sense active play didn’t do any harm. Note that the top play gains wins and costs gammons, as is often the case with active winning plans. The still more active 9/8*/6, 5/4, which gains a builder for the three at the cost of a 3-6 shot, wins even more games, while losing more gammons. This might be correct at double match point (DMP). I had given the blotting plays little consideration over the board, thinking that it could not be right to take that much extra risk for a couple of point-making rolls when the resulting home board would probably just crash anyway. But #3 is much closer than I would have expected.

In Problem 3, Red had no particular cause for desperation before he rolled the dice. While 4-3 seems not to be worst, it is definitely in the bottom five. All reasonable plays leave either a double shot or a single shot (with extras) and two or three blots. Red is not well placed to attack, with only 8 men in or around his home board, three checkers back to two, and two home board points to four. Priming prospects don’t look so hot either, at least not in the short term. What to do?

Problem 3: Red to play 4-3.

The natural tendency is to look for a play that is not too passive, not too committal, and that preserves as many of Red’s assets as possible. We have all learned not to expect an attack to work under circumstances such as these. The right play probably hits one of White’s blots, because the alternatives are passive without being safe. One would rather not play 6/2*, because starting the deuce is impure. But after 6/3*, 13/9 and 11/7 are too risky, so it looks like 6/2*, 11/8...

Except that there is another play. Red can hit both of White’s blots with 6/2*, 6/3*. It is easy to overlook this, an apparent attacking play in what is not an attacking position. The attack will probably not succeed. On the other hand, it might. The double hit, though, happens to have a couple of things going for it in addition. First off, it holds all of Red’s points. Second, the double hit gains time. If Red’s blots are missed then he might be able to use the time gained to run his checker off the 23 point, going into a holding/racing game. But if one of Red’s blots is hit, he might have an extra half-roll (or more) in which to roll a deuce and get a playable back game.

Problem 4: Red to play 1-1.

In Problem 4 above, the beginner hits both blots, because he believes that hitting blots is always good. The more advanced player realizes that (a) attacking is useless (in fact a closeout is fatal) with something trapped behind a full prime; that (b) his home board looks ugly, and if he tries to counter-prime White the effort will probably fail; and that (c) timing for an ace-point game is good, but if he does a lot of hitting he could just end up with a hopelessly busted ace-point game. So he calmly plays 8/5, 3/2, preparing for the hit that he hopes will come later on when White is bearing off.

Did you spot the fallacy in that “advanced” reasoning? Red dismissed the priming plan for the wrong reason. The question is not whether it ought to work, but whether it ought to work better than the alternative. Ace-point games don’t work so well either. After hitting the two White blots Red will have 13 checkers to use for prime-building – enough for a full six-prime with one left over. White’s timing will be almost all tied up in his two back checkers, so if they get blocked a couple of times White might crash even before Red can build a substantial prime.

One of Red’s problems is that White has a five point board as well as a full prime. In building a prime of his own Red will have to take some risks – at least to the extent of leaving indirect shots in the outfield. The risks begin with White’s possible immediate 5-5, which would be devastating. A single hit could easily get Red gammoned. This could be reason enough to avoid the try for a counter-prime, except for one thing. Red is so far down in the race that he is more likely to be gammoned if he sticks with the ace-point plan. 15/14*, 13/10* is best for the win, best to avoid a gammon loss, and best for a gammon win.

Here are the rollouts for the positions above:

Problem 1: Red to play 6-3.

Problem 2: Red to play 1-1.

Problem 3: Red to play 4-3.

Problem 4: Red to play 1-1.