Problem of the Week #111: July 1


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




Black to play 5-4.



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.

The guidelines provided in the solution to Problem #110 notwithstanding, Problem of the Week #111 presents a case where breaking the prime is probably best. As things stand, Black's cubeless chances are only around 42% (see http://www.bkgm.com/rgb/rgb.cgi?view+1543), and they will be less if he cannot achieve an optimal close out. Yet, there they are: two juicy blots in White's home board, just waiting to be hit. If Black can get one of them, he will become the favorite.

Hitting gives Black two advantages. When White hits the return shot from the bar, Black may well get another direct shot at one or two blots. And when White misses, Black will have stolen a tempo from White, making it much less likely that White will be able to clean up his blots.

Also, note the duplication. The ones and twos that White needs to clean up his board are two of the three numbers he can use to enter from the bar. Unless he rolls 11, 22, 31 or 32, any other one or two that he rolls will not allow him to enter and simultaneously clean up his blots.

By playing bar/21, 8/3*, Black can preserve a four-point block. Playing bar/20, 7/3* is distinctly inferior.

My solution: bar/21, 8/3*

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 49%.

I think the rules given in the solution to 110 don't apply. If we move the prime home, we are going to need to bear off aggressively and probably are still underdogs.

We need to hit and get hit now - as soon as white rolls a 2, he will clean up his home. Even if white breaks through, we have two blacks waiting for him in the outfield to bring him back.

Solution: B/21 8/3*

Edit: Looks like I copied and pasted Mike's answer. Looks like I am making progress. 49% here I come!

Too bad, you scratched. Sure, we have to hit open. Despite the dust, i love my "Vision laughs about counting". But when we hit open, we transform a six-prime into a broken six-prime with a hole. Just for a five-finger exercise, count the numbers which will escape from a broken six-prime, if you are on the edge of this prime. A broken six-prime with a hole on six will give 11 escaping numbers. A hole on five will give 9 escaping numbers. A guess what a hole on 4 will give?
Let us look for some possible routes. We hit. White comes in, cleans the blots with a two. Or the ace with a one. Or nothing and we miss. Than we have to contain with a broken prime. I am just an old crock and contaminated. I want to fight with the best broken prime i can get. And i think, the best broken prime is the prime with the fewest escaping numbers. Just my opinion. That is for me reason enough, to play Bar/20, 7/3*. Thanks, Danny.

It ain't a guess to say 7!

This is an interesting consideration that I missed completely. One distinction between this problem and the one Danny Kleinman discussed is the fact that when Black is hit (anytime soon, that is), he will have direct return shots from the bar. And if Black can hit a second blot, he becomes the favorite.

With these ideas thrown in the balance, I'm not sure which of the hitting moves is best. I still have a bias, however, in favor of bar/21, 8/3*. When White misses, Black will ofen remake a five-prime on the next roll.

BTW: I failed to notice that 21 is a roll that will let White enter and clean up. Together with 11, 22, 31 and 32, White has 8 rolls from the bar that clean up his blots. And 28 rolls that don't!

My vision is often misleading, but i see here a broken six-prime and not a block. And the goal is a close out, not to make a five prime. Tied between a fourpointboard and a rebuild five-prime, i guess. If there is a semi-goal, then to rebuild the six-prime, as bill spelled out last problem. I bet double money, that the variants with getting not a second checker, containing the single checker then with a broken prime overall will favour Bar/20, 7/3*. And hitting here not will be rather a blunder then an error, i guess.

bar/21 8/3*

As we have both implied already, our primary goal is to be hit by White! We want to be hit before he can pick up his blots. Then, we plan a return hit from the bar. (If you are not planning to be hit, then you should just keep the six-prime, and roll it forward normally.)

In case our plan fails, and we cannot pick up a second White checker (either because White misses us, or we miss the return shot), we need the best postion possible to contain the White blot we already have behind our block. From that position, depending on the dice, the next step will be to continue the attack, or to rebuild a six-prime.

Both plays work well when we hit the second checker. The question is whether 7/3* beats 8/3* when we fail to hit the second checker.

Any thoughts?

Due to the board position our main priority should be maintaining the 6prime. By playing with the goal of recirculating we can almost guarantee maximum 2 points for villain. With that in mind my play maintains prime and looks to prepare a good move for 44.

bar/20 19/15

Well, both B/16 and B/20 19/15 will allow to slot the 3-pt after 4-4. But B/20 19/15 seems to play better after 5-5 (puts a builder on the 5-pt).

B/20 19/15

I find interesting the discussion between Tape_Mike and higonefive. However, if the plan fails badly and White somehow escapes quickly, White still has gammon threats.

If Taper_Mike's number of 42% is correct for Black winning chances, it isn't that bad. I prefer to first secure that we won't get gammoned (by bearing off a checker) and then take some risks, which might mean having to recirculate some checkers.

bar/20 7/3*. Gives a 2 to rehit on our bar point if needed. Definitely worthwhile to risk the gammon. Swing for the fences.

bar/21 8/3*

Hitting seems to be a must and this looks better than hitting from the bar. One reason is that if white enters with a one he is not threatening a direct hit with that checker, 8-3 just looks safer.

You can also look in my dropbox: http://db.tt/wcmL50J

Note the differences in equity. Note the best move. The broken prime with the hole on five comes in on second. And it is better to make the five-prime then trying to complete the six-prime again. That were my thoughts, when i first looked at the text position. I am contaminated. I will bet on the best broken prime. And that is not the broken prime with a hole on five. Just my opinion.

Wow! Nice job. You may have said final word on this.
Even when White cannot cover, we have ...

except...

What about the first way to fail? What if White enters on the one or two point? Or White fans?

The rollouts you posted focus on a relatively small space of outcomes where we hit White, and he then rolls 32. What about the other cases? From the bar, White's rolls fall into these groups:

• Group A - 2 rolls (32): White enters, hits, and cleans up both blots
• Group B - 2 rolls (31): White enters and hits, but cleans up only one of his blots
• Group C - 7 rolls (33, 34, 35, 36): White enters and hits once or twice, but leaves both blots
• Group D - 4 rolls (11, 22, 12): White enters, misses, and cleans up both blots
• Group E - 6 rolls (24, 25, 26): White enters on the two point, misses, and leaves both blots
• Group F - 6 rolls (14, 15, 16): White enters on the one point, misses, and leaves both blots
• Group G - 9 rolls (44, 55, 66, 45, 46, 56): White fans

You have made the case that for Group A and, perhaps, Groups B and C, 7/3* is best when Black misses the return shot. NetWorth suggests that 7/3* is slightly better for Group C, as well. (Perhaps Group C should be subdivided based on how many times White hits.) When Black hits the return in Groups B and C, there may be a small advantage for 8/3*, but more likely, it's a wash. In Groups D and E, Black should continue the attack in most variations. I suspect 8/3* is at least a little better than 7/3* in those cases. LoveInVain argues that in Group F, 8/3* is clearly best. In Group G, we should just call it a toss-up.

So, you have convinced me of one thing at least: 7/3* is not "distinctly inferior." In fact, it may the correct play.

Either way, I want to thank you for explaining your thought process. You have exposed a way thinking about this problem that I hadn't been aware of.

What are the odds our outfield blots hit him back, assuming they are on separate points? I assume they are pretty high. THis is assuming he takes advantage of his ability to bust through our broken prime

These positions are so different from the problem position that this doesn't prove anything IMO as there are many things to consider when considering your play.

In the second diagram, playing 9-7 looks to be wrong as there doesn't seem to be a good reason to give black a 6-6 joker to win the game.

In the first diagram, either a hit with 5-5 or 6-6 wins for black so may as well play 9-8 completing the 5 prime.

4-4 almost wins the game as well, unless Black hits back from the bar.

"Almost wins" is overstating it as black has 17 numbers to hit from the bar.

Looks like it's 16 numbers (for White, not Black), but I get your point. I thought initially that it was more 13-14 numbers.

Nonetheless, Black has 20/36 numbers that give him a gammon and, even if he gets hit, he can still win. So 4-4 is still a joker imo, but "almost wins" was clearly an overstatement from my part.

I don't want to prove anything. But just writing down "Playing bar/20, 7/3* is distinctly inferior" also doesn't prove anything. When we come to conclusion, that hitting is right, because 9 men out is heavy, and a double shot is juicy with cube access, then it boils down how to hit. A broken prime with the hole on 4 seems to be better for containment. If you look on the second diagram, it is better to move then to shift the hole. It is only an example for the gut feelings i had. But the better structure of the broken prime with the hole on 4 must show a difference in the rollout of the text position, given that the other items of the position are equal.

I'm not understanding you very well here.

Firstly, I never said that hitting with 7-3 was "distinctly inferior", or did I? I do think that intuitively keeping the longer block (hitting from the 8) seems better unless there is some tactical consideration that makes another play better. And in both cases we are hitting leaving a broken prime. I am far from sure though that hitting with 7-3 is not correct as the "obvious" play is often not correct in these problems. All I'm saying is that I don't yet see why hitting from the 7 would be better.

As far as looking for a reason to hit from the 7 instead of the 8 leaving a shorter block, for me personally, your diagrams if anything argue the opposite as in the first position, lengthening the block from 4 to 5 is correct according to the rollout. This makes a lot of sense to me and seems to confirm my theory - when there are no tactical reasons to do otherwise, may as well lengthen the block. When choosing between 2 broken primes, may as well pick the one that includes the longest block. In the second position, there is a tactical reason to not lengthen the block (6-6 game winning joker) and IMO, that is why rollouts show that NOT lengthening the block is the better play.

I admit I can't prove that hitting from the 8 is the best play. I have offered no evidence at all except my instincts tell me it is best because the longer block "seems better". I have no more proof to offer, and I admit I could be way off. I am looking forward to learning why hitting from the 7 is better should that be the case, but so far I am not seeing it.

16 hits is correct - oops.

Agree with all this. 4-4 still a joker, just not an immediately game winning joker.

I finally figured it out, least I think that maybe I have LOL.

Over the board, I would hit from the 8 for reasons I already explained. Since this is a problem though, and as I said earlier in these problems the "obvious" play is often wrong, I gave this one a bit more thought. Again, as I said earlier, for 7-3 to be the better way to hit, there needs to be some tactical consideration.

In this position, the main thing to consider is that black wants to hit another checker, this is by far his number one priority. For this he needs to be hit and white will try to avoid hitting while he still has blots. White has two blots and every roll that goes by without black not getting hit, white is threatening to safety one or more blots. Therefore, the time is now.

Hitting with 7-3 leaves more numbers that force white to hit!

3's are a wash either way. However, after hitting with 7-3, white is also forced to hit back with 6-1 and 5-2, after hitting with 8-3, white has only 6-2 as an additional number which forces him to hit.

This the immediate tactical consideration that overrides by a considerable margin the value of a slighty longer block and IMO makes hitting with 7-3 clearly the best play.

But, you're still not buying the containment argument?