The next position is an interesting problem with a few non-standard elements. On the one hand, it’s a prime versus prime problem; both sides have 5-point primes, and both sides have some escaping to do. On the other hand, it’s an action play problem. White is on the bar shooting at a couple of blots, and a lot hinges on whether he hits or not next turn.
Money game, center cube, White on roll.
Should White double? What should Black do if White doubles?
So we have a blend of priming elements and action elements. Which elements are more important? That’s actually an easy question to answer. Take a look at Position A:
Position A: White on roll. Cube action?
Position A is just our original position with one Black checker moved from his 2-point back to his 14-point. White now has 27 shots from the bar at three blots, so the action aspect of the position is even stronger. (Look at how 1-1 now plays!) But – the checker on Black’s 14-point now gives Black more timing, so the priming aspect of the position is worse for White.
Compared to our original position, White has more action but less timing. Which is more important? If you said “timing”, good for you. Black’s extra timing dominates White’s extra action, and in fact White’s winning chances drop by almost 7% in going from the original position to position A. Fundamentally, this is a prime versus prime situation. The action element is secondary, although if White’s advantage is big enough, the action element will push White to double now rather than later, as a bigger than usual swing could happen on the next roll.
Now let’s take a closer look at the original position itself. Clearly White has the edge. His threat is to enter and hit a checker – then Black enters and breaks his prime – then White hops out and hits another checker – then Black enters and cracks some more – then the inevitable gammon. A grim scenario. White should double and Black should pass, right?
Well, let’s hold up a bit on the pass. In evaluating positions, we need to avoid a certain trap which is easy to walk into, especially (but not exclusively) in priming games. I call it the Trap of the Main Line, and it’s simply the tendency to find what appears to be the main line of a position and assume that it happens much more often than it actually does. In positions where neither side has an especially strong inner board, the game can slide off into a lot of different variations, most of which offer the defender more resources than the main line. Players who train themselves to supplement computer rollouts with the occasional manual rollout are more inoculated against this trap, but we all fall victim to it from time to time.
(If you’re a hold’em poker player, the ‘Trap of the Main Line’ has an exact analogy in the fallacy of “putting your opponent on a hand”, where you assume your opponent has a single hand and you play against that hand, instead of putting him on a range of hands and making the play that works the best against that whole range.)
While the main line in the original position is a disaster for Black, there are plenty of other variations where he does all right. In prime against prime games, I think it’s useful to look at the hard cold facts of the position as it now stands: White has three men behind Black’s 5-point prime. That’s a lot of men behind a big prime. White is only a slight favorite to hit a shot, and whether he hits it or not, he still has three checkers to extract. When Black’s prime does break, it breaks from a 5-prime down to a 4-prime, but plenty of games are won by a 4-point prime.
On the bright side, White has some timing left and Black has almost none, so there will be plenty of variations where White hits a checker and wiggles free. Those variations won’t necessarily lead to a gammon, because White only has a 3-point board right now. But there will be plenty of games where Black falls into a low-anchor game with a busted board, and those are easy for White to win.
Conclusion: White should double, and Black has an easy take.
How much timing would make this a pass for Black? Take a look at Position B:
Position B: White on roll, cube action?
Compared to our original position, White has seven more pips of timing. Each pip gave him about an extra half-percent in winning chances, so B is a strong double and just barely a pass. There’s no formula that I’m aware of that “solves” these priming games, but notice that in B, White can play at least two full rolls with his outside checkers (barring an awkward double) before he has to think about breaking his prime. That idea – how many rolls can I play without rolling a six and without breaking my prime – seems to be a useful parameter to keep in mind when judging these tricky situations.
