Problem of the Week #99: March 6


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

Three scenes from the same game.





(a) Cube action, both sides?




(b) Cube action, both sides?




(c) Cube action, both sides?


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.

Here is my guess, and my answer is based partly on having a set of symmetrical answers. In other words, if I was presented positions A or B as standalone positions I'm not sure I would come to the same answer. For me, I find position C the easiest. I'd say this one is a double/pass. To escape black's prime white will need to roll a 6 or 5-1, so two thirds of the time she will not escape and will instead likely provide a shot in her home board or at the very least start scrunching it up. Black also has a good chance of making that 2 point at some time. This will make escaping more difficult and more painful if hit in the outfield.

Position B is similar, but not quite as nice for black. I still think he has a double, but this game could easily turn around real quick. Therefore, I think white has a take in this position.

Position A is not quite so clear. This is the first position I tried to solve and had a real hard time deciding what to do. Black has a lot of men stuck on white's ace point, and could easily watch his game get much worse. However, he could also watch his game turn into something like position B, so I'd wait to see where I'm at before doubling.

Solution:
a) No double and take
b) Double and take
c) Double and pass

In all three positions, White has a big lead in the pip count. With three checkers back, however, he will have a hard time converting this game into a race. In Part (a), White leads 109 to 166. In Part (b), he leads 100 to 155. And in Part (c), White leads 109 to 146. This kind of lead must be worth something, but – at least initially – it is not clear just how much.

In Parts (a) and (c), White is positioned precariously. Unless he rolls a six or some combination of four and five on his next shake, he will have to open up another home board point. White’s board is deteriorating just as Black is improving. Perhaps Black has a double in both positions. Even in Part (a), where Black is on the bar, he has a good double. After all, he is favored to enter on the first shake, and when he doesn’t, White is favored to give up an inside point on his turn. If he is lucky, Black will enter immediately, and when he is unlucky, Black will often be on the bar with a double shot to send a fourth White checker to the rear.

The fact that Black is on the bar in Part (a), together with the racing advantage held by White, gives White a take. In Part (c), however, White should pass. With the immediate threat of cracking and with Black in complete control of the outfield, White has to let this one go.

Part (b) is an entirely different circumstance. Here, White has an outfield checker to play, so the anti-joker 3-3 is the only roll that will cause him to crash on his turn. Furthermore, White's outside checker is placed to threaten Black should he move into the outfield. Black should not double. White has an easy take, but not a beaver.

My Solutions
Part (a): Double, take.
Part (b): No double, take.
Part (c): Double, pass.

For the Record
I am so often wrong that I like to post my record in these messages. It's kind of a truth-in-advertising thing. Grunch: I have been answering these problems without the use of a bot, and before checking the excellent solutions of others, since Problem 28. My record at this writing is 54%.

Double, pass.
Double, pass.
No double, pass.

Well the easy part (for me at least) is they're all passes. I've studied these positions (with Snowie and GNUBG I haven't checked with XG) and here's an area humans still have an edge.
In the first position white is inflexible and in danger on exposing more checkers and black has much more of an easier time simply entering without any problems.

In the second position although white has escaped a checker he just won't be able to dodge all the black bullets coming his way. True also for the first position should he not expose another checker.

The third position white is worst of all and it this must be too good.
Imagine if white were on roll, what would be his best possible 2 roll sequence? 66 followed by 44? Even then white probably couldn't redouble. That's how bad it is for him.

IB

I don't want any part of the white position. It's too crunchy and too gammony, and black almost always has outfield control against 3 guys trying to come around. Good luck dealing with that without rolling 66 somewhere.

a double/drop.

b is even better. The 65 is a huge roll for black, and although the escape for white was good, this was a net bad sequence. Even bigger double/drop.

c is just godawful after getting the blot sent back. The only question IMO is playing on. Too good/drop.

Grunch

a) Seems a clearish double to me. White has huge problems if they fail to throw a six, and even if they do early, black may well get back in, grab control of the outfield and pose a very serious threat. Even if they don't get in quickly, black has a well timed ace point game regardless, so even very worst case black has OK outs. Seems a very bad mix for white considering how often they crunch and lose or get gammoned.

Double/pass.

b) Again, seems a relatively clear double to me. White has a checker out, But blacks anchor on 19 is a huge threat to this, we are in a great spot with any nine, and white still has their problems with their board crunching and a complete lack of likely out field control with all blacks men to come around. This might even be too good but I think I ship the cube here.

Double/pass

c) Evereything that is bad with white's position in the previous two is in full force here. Board about to crunch, zero outfield control, black in pretty much total control. This could also be double/pass, but I think I play on here for the gammon. Even double six is not a clear game winner for white in c), so in spots where even their best joker does not get them back in the game, it seems just too good to let them off the hook.

Too good/pass.

right now i'm not shipping the cube in any of them

right now i'm not shipping the cube in any of them

Great problems! These prime vs. prime positions always make my head hurt a bit so hopefully I will learn something here.

The only position I would be ready to answer now is the last which looks too good to double. I'll take a shot at the others when I have more energy.

In such positions, I don't bother to get an exact pip count, since White has some wastage in his board.
Edit: I will more focus on men back than an exact pip count, that's what I meant.

a) Black has 5 men back to 3 for White. On the other hand, Black needs 5s or 6s to run his back men, while White needs 6s (or 1-5+ combos), which favors Black. But Black still has a man on the bar and he needs a 1 or a 6 to enter in the first place. With all those men back, Black has somewhat better chances to make his barpoint and block White, but he isn't close to do this now. Since Black has the cube, I think he should wait.

No double / Take


b) Black has now 3 men back (behind the 4-prime) to 2 for White. It seems that Black owning the 6-pt is an asset (a rear guard waiting for White's runner), but since it's Black's turn he might have to break it if he doesn't roll a 5+ dice or a double. He could also wait if he rolls a small roll like 2-1 or 4-1 and play in his inner board. Instinctively, I think Black has made enough progress to warrant a double, but I would say that White has enough counterplay for a take.

Double / Take


c) Black has made more progress as he sent back White's runner. So it is still a double (it doesn't look like too good for me). Black will either escape a back man or move the checker on the 19-pt, increasing his chances to hit if White rolls a non-hitting 6. Plus, without any timing, White will probably have to crush even more his board. Which means Black could even scoop other checkers. Hmmm... if I'm Black, I wait, since I could always double later if thing don't go my way. As White, I drop this.

Too good to double / Drop

It sure looks like I overestimated White's position in a) and b)!

Id say double/take, double/pass and enormous too good on the last one. The last position is by far the easiest. I dont know anyone that will ever take this and as such I conclude its too good.

The first one is trickiest to me. There are sequences that are gross for black. I think I have a take as white. The second one I cash as black. Its also a good practical double I think. White has escaped a checker and is happy about it so he just might take this. Still think its a solid pass.

White is screwed in all 3 of these games. But it seems unlikely that he will get gammoned in any of them. So, that makes black's decision to double pretty easy.

a) Double/take. White may be able to escape without totally destroying his board. Also, black still has to get in and then get his checkers moving any 1 without a 5 or 6 is bad for black.

b) Double/drop. White has a checker out but black is a lot stronger now. Even if white succeeds in escaping his checker on the 10, he still has 2 more that are stuck

c) Double/drop. This one is even worse for white than b but I still think the double is warranted because I really don't see that many scenarios where black can get a gammon. But, maybe it is too good to double and black should wait a little.

My solutions:

Double/take
Double/drop
No double (too good to double)/drop

I am far from sure as I find this type of positions quite difficult.