Problem of the Week #72: August 15


Cash game, Black owns the cube.




Black to play 3-2


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.

18/13. Race for 5s.

18/15 13/11

I think 13/11 is a must. You want to make sure you get additional shots at white's checker if he happens to get in with the 5. The question is, what to do with the 3.
I like 18/15. It looks crazy, but in reality, there's hardly any added risk by doing this. You give black shots with 3 or 6. But, black can hit the blot on the 23 point with a 3 and he can hit on the 11 point with 5-6 (if black fails to cover his blot on the 11 point and makes a different set of moves instead).
Mostly, white will dance or he'll get in and then be in an awkward spot, giving black more opportunities to hit.

Answer - 13/11, 18/15

After discarding breaking the bar point, 11/6 and any board-breaking move, I have the following choices: 13/10 11/9 and 13/8.

13/10 11/9 leaves 5 shots (5-5, 5-4, 5-3) while 13/8 leaves 4 shots (6-5, 5-3). If White enters and possibly escapes, Black will be better with a checker on the 11-pt than on the 10-pt.

My pick: 13/8

Hmmm, lots of reasonable possibilities:

11/6: Get a checker safe and minimize the blot count
18/13: Switch one point for another closer to home, keep maximum coverage of the outfield, keep your army connected, and leave 5-6 duplicated
13/10 11/9: Create two builders for the 5-point
13/8: Same thing, but maximize your outer board coverage and minimize shots, and diversify your numbers because you'll want to use the 5 on the other side of the board
13/11 18/15: Switch assets, block Villain's runner, duplicate 3s (although 55 now hits, but that's a strong roll in any case)

I think I can narrow this down to either 18/13, because it leaves us with the most flexible position in most cases, or 13/8, which gives an extra builder when White enters unconstructively. This only happens with (5-1, 5-2, 5-4) but that's 1/6 of all rolls. So the question is whether the extra equity is worth it. All in all, I think so, because I don't think it really matters all that much what we do if we knew White was going to dance, so we might as well maximize equity when he enters.

So... 13/8.

I'm probably missing something here but I think 13-8 and it's not even close. We want to close out the 5 point and this play maximises that chance.

There is danger with any play of this roll, but this move gives us the best chance for a gammon.

But I'm a little worried that this seems so clear to me.

Well, personally I'm not going for a closeout here in general (unless I roll a gin number, of course) because it's not really necessary. It's the pick-and-pass equity that is the best argument for bringing another attacker down. We can win plenty of gammons with minimal risk by just bringing our checkers around and keeping Villain on the bar.

Hi,

the reward for a risky play is not so high, since the gammon chance by closing out the checker ,
is below 40%.
So 10 extra close-outs give you 4 extra gammons, so you may risk 2 losses.
For example a builder on 8 gives you 2 extra closeouts (63 and 36).
That is 0,4 extra gammons, so you may risk 0,2 losses!
Now it seems that 53 is losing anyway since there is a hit also with 20x23.
But this hit is only 25/36 effective because of the return from the bar, while the hit bar/5*8
has returns only with 23, so this hit is 34/36 effective.
So the risk ot the inboard hit is 2*25/36= 1,4 losses
and the risk of the outfield hit is 2*34/36 = 1,8 losses,

the extra risk is 0,4 losses, that is too much.

So what else can you do, the risk of 53 will be there, and right now there's a risk of 56 and 51.
You can lower the risk by 18/13, making use of the duplication of 56.
It also has good connectivity.


greetings k.

I think the game plan is to run home while you've got white on the bar. This isn't about trying to complete a closeout (you leave too many blots if you try to maintain flexibility, and white's board is very strong) and I don't see any other path to victory (a holding game should be your backup position if white gets off the bar in the next roll or two).

13/11 18/15

13/8 would be my reply. Bearing down on the 5 point , hoping to lock white on the bar.

18/13 gets hit by 5-6, 5-3.
13/8 gets hit by 5-6, 5-3.
18/15, 13/11 gets hit by 5-3, 5-6, 5-5 and just generally creates a bit of a mess in blacks outfield. Black will have to scramble to clear his blots, and if he re-anchors on the 15, he is abandoning his blot on the 23 pt.

I dont think 13-8 really adds enough to our game. When white enters, he will hit immediately 2/6 times and leap over us 1/6 times. While we gain the other 3 times, we also lose connectivity, making life hard for our back 3 checkers.

18/13

I also prefer 18/13. This leaves only 5-3, 5-6 (duplicated) as shots where white can hit. Even if white does hit us, 5-3 leaves us a direct hit in return. Further, we are still retaining connectivity between checkers.

In the event that white does roll 5-3, I would rather force white to hit us on his 2-point with no builders than on his 17-point (if we played 13/8). However, 5-6 is less damaging after 13/8.

doesnt affect much, but obv shoulda said 4/11 and 1/11 respecitvely

Grunch. 18-15-13.

Double six would have closed his five point, but instead Black must play this 32. There are many choices, so it is worthwhile to identify some of the key features of the position before focusing any specific play.

First, the big swings in equity will occur when White enters from the bar on his next roll. If he dances, almost any move now will work for Black. In evaluating potential plays, Black should check closely how a subsequent five by White will affect him.

Second, Black should keep his anchor. Connectivity is the reason. As things stand, Black's back man on the twenty-three point has good support from Black's anchor. If Black abandons his anchor, however, the straggler could be stranded. Black should try to hold onto White's bar point until his back man escapes. Furthermore, the anchor gives Black a holding game as a fall-back in the event White enters safely next time.

Third, safety matters. White has a five-point board, and the cube has been turned. Gammons count. Several plays that Black may be tempted to try will leave three blots. Just a few leave only two. Duplication may also be important.

Finally, Black should try to cover all boards. It is probably a mistake to give White a safe landing spot for his blot. Black's most direct pathway to victory is to scamper home while White is on the bar. When White enters, Black wants to be in a position to hit. Another consideration is the race. Before this move, Black trails in the pip count, 107 to 115, so he needs White to be floating.

If Black will follow these guidelines, his choice of plays in Problem 72 is much easier. Plays like 18/13 or 18/15, 13/11 -- which might look good superficially -- can be discarded. They abandon Black's holding game a bit too soon, and both leave three blots.

So what's Black left with? Perhaps only two choices: 13/8 and 11/6. The former leaves three blots, and gives White a hit with 53 and 56. White can enter safely with 55, but would leave a single shot with 54. White leaves a double shot when he enters with 51 or 52. If Black is hit on the eight point, he can hit back with 23, but after he is hit on the eleven point, Black has no return shots.

Black does better with 11/6. He then leaves only two blots, giving White a hit with 51 and 53. White can enter safely with 55, but leaves a single shot with other fives. After he is hit on the twenty-three point, Black gets to hit back with any two, and even when he is hit on his midpoint, Black has a return shot with 52. This last return shot demonstrates more connectivity: Black's midpoint blot connects with his anchor.

My solution: 11/6.

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 48% correct: 25 right answers and 27 wrong.

I like the play that gives us the most return shots after those sequences where white enters from tha bar and hits and it also looks easier to bring round the remaining checkers.

The plays that force White to hit inside when he rolls 53 give the most returns: 18/13 and 11/6. Do you have a preference?

Maybe I miscounted ? My play is 18/15 13/11. I think of those hits not inside, we get the most returns here. After 18/13 where does white hit with the 6 in a 6-5 ?

When White hits on the 23 point, Black has 11 return shots (any 2 from the bar), plus whatever vigorish he gets outside. After Black plays 18/15, 13/11, if White rolls 53, White will hit outside 12/15* with the three. Black would then have only 4 return shots (23 and 26) even though White would still have two blots.

To answer your question, however, after Black spilts off his anchor, White can hit with a six by playing 12/18*.