Primes Versus Blots

Primes Versus Blots
by Walter Trice – 1 August 2006

Positions in which both sides are trying to contain a single blot with a prime, constitute the simplest prime-vs.-prime pattern. They deserve study because they illuminate the general problem of prime-vs.-prime strategy.

Of course they also come up in practical play from time to time. When they do, they pose checker-play problems that an uninitiated player is likely to get wrong. Even fairly strong players are sometimes prone to making huge blunders in these positions.
When both sides have 14 free checkers to play with, there’s a very good chance that both will be able to build a full six point prime. Once both have the full prime, the only way to win is to have yours last longer than the other player’s.

Rolling big numbers is bad, and rolling small numbers is good. Aside from luck, there are not many different ways to improve your chances. One way is to start out with more “timing” than your opponent – that is, spare pips that you can move without breaking your prime. Another is to get a blot hit and then dance!

Problem 1 is here for the novices. It illustrates the disaster that results (for the White side, in this case) when you lose the battle in the type of position under consideration.

Problem 1: Red on roll, cube action?

Red is too good to redouble. No matter what happens, he will always be able to redouble his opponent out as long as he has his prime. Red should hold off on the cube because he cannot lose by doing so, and because he might win a gammon. As long as Red stays on the bar his prime stands still and White cannot escape. White must keep moving, so he must eventually break his home board down and let Red in, perhaps exposing a second blot in the process.

Once Red brings his blot in, he should be able to roll his prime forward and close White out very easily. In a pinch he can almost always turn the cube and collect two points if the process does not go smoothly.

Problem 2: Red to play 4-2.

In Problem 2, White just improved his chances by dancing. Red would prefer not to move his checkers at all, but the rules compel him to play the 4-2.

If Red is going to be forced to make an additional point in his home board then he definitely wants that point to be the deuce rather than the ace. With the deuce made he may still be able to hold six consecutive points and keep White trapped, since the deuce is the next point ahead of his existing prime. Actually it is not a close choice – making the ace-point first in these positions almost always loses the game. That is one argument for 8/2 with the 4-2 roll.

But the main reason to slot the point is that Red might get hit! He might then roll an ace and enter right away, which would be bad, but the odds are against it. Only 11 rolls out of 36 enter, so Red, if hit, rates to stay take 36/11 (=3.27) rolls, on the average before he can enter. Imagine the damage to White’s position if he has to play 3, 4, or even more rolls while Red stands still!

Note that the smooth, very normal looking 9/5, 8/6 is an enormous blunder that gives away almost half a point.

Problem 3: Red to play 6-1.

White danced and now Red has rolled a 6-1. Meanwhile I have changed the context from money play to double match point, just because I was curious about whether 8/1 might turn out to be right if gammons did not matter. And it almost does! (But not quite.)

If you’re not going to play 8/1 it is still important not to blunder by making a home board point. Red’s chances are not good, but if White dances again they start to look really dismal. With 9/3, 2/1 (easily overlooked) Red can keep the 6-prime and leave two points open for White to come in on. If White rolls an ace (other than 2-1) Red’s prospects can improve drastically.

Problem 4: Red to play 6-3.

With Problem 2 to warm up on, I hope you considered the double-blot play 8/2, 6/3*. Not only is it a classy-looking move, but anything else is a blunder! This came up in a fairly important match of mine last year in Las Vegas, and I don’t recall even considering the right play.

In my defense, the downside is pretty drastic. If White hits with a three and Red enters right away with an ace, doom is imminent because Red must break his prime on the same roll. Even so, it seems that the potential for a whole series of dancing rolls outweighs the immediate anti-joker sequence.

Problem 5: Red to play 6-5.

We’re in the groove now, and 8/2, with the five played 9/4 (diversifying) was an absolute snap, right?

Red only has a five point prime, which might seem to call for a bit of caution. But the thing is that rolling an ace is so strong for White anyway, that Red might as well have a blot there. If White steps up with an ace then Red is going to have to hit. If he hits he’ll either have a blot there afterward, or he’ll have a point made, which could also be very bad, because White would then probably dance and Red would continue the big crash.

Red is in bad shape to start with, which entitles him to incorporate some “long shot” scenarios into his game plan. In one of these, White hits and then fails to jump the 5-prime for a few rolls, with Red dancing and hence not breaking the prime. In another, White hits and then Red anchors on the 23 point, which makes White crash faster.

It is also possible for the slot to work out constructively, with White missing, and Red then covering to get a six-prime that (against the odds) outlasts White’s.

 

Here are the rollouts for the positions above:

 

Problem 1: Red on roll, cube action?

Problem 2: Red to play 4-2.

Problem 3: Red to play 6-1.

Problem 4: Red to play 6-3.

Problem 5: Red to play 6-5.