Problem of the Week #147: July 15


Cash game, Black owns a 2-cube.




Black to play 2-1.



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.

10/7 seems right, you want to get hit back and try to get a second checker. Closed out white is still a big favorite with only one check back.

I would play 10/7, trying to hit another White checker. Sure, I expose myself to 6-1, but without going through the calculations, my instinct tells me that it is to close to close the board right now.

10/7

10 off tells me to not play for the close out.

10/7

Grunch.

Good old fashioned perm/equity problem imo.

Can't win very often by covering. 4/1 does very little - saves some gammons, but we don't lose very many when hit anyway so not a huge consideration. White has beared off way to many for us to have much equity playing safe here.

What does do something? Good possible situation is a made 6 prime, where you don't mind being hit and get a counter shot at the loose checker on the opponent's 2 point and we get back in the game - possibly even closing our board with White having two in the air. What's the easiest way to do that? Get a man on the bar and try and make it ASAP.

What's the downside of that play? Double hit with 6 1/possible further shots on the other loose checker after this is obviously not great, but its rare we dont get a hit/decent number of counter shouts in the outfield later, and I can't see many backgammon combos here, so our equity is not hopeless even on their worst roll.

The big joker shot we are not out of it much more than we were before, rest of the time we are often back in the game. Looks a no brainer to me.

10/7

10/7 hoping for a 6 prime and hitting the 2 checker if white rolls back in.

10/7 and not 4/1 for the obvious reasons. We have to try for the second man.

No need to make the one point even if we start bearing off here. But prime not great and wont hold so 4/2, 10/9 to rehit with 1s if he enters..

I have reference positions. For 1 man closed out 14 men off against closed board 8%. A second man raises to 68%. And 2 men/10 off are a bare pass, 79%. So if we can get a second man the game is virtually won.
Closing only one man out leaves us as the underdog, whereas hitting pushes us in the driver seat. So i will not make the ace, that is for sure. But will i play 10/7 OtB, for the classic squeeze? OtB, i will think as follows: He must hit us, we must hit him, 121 out of 1296, 9,3%. The joker 16 5,6%. I will neglect any other calculations. This rough calculation will show me, that it is difficult, to win with the big play more then twice games to compensate for the rised gammons (supposing an additional win and gammon loss for the variants).
So i will look for a quiet middling play. I will not touch the checkers in the house. Putting the spares down will rise their dillyness. So i will play 10/8, diversifying the hitting numbers, will the joker arise, and then 12/11, to complete the move.

10/8 12/11.

Btw, look at www.mindgamescenter.com. There i got my reference positions. Also stuff from Bill for small money.

If Black wants, he can save the gammon right now. When he closes his board with this 21, he is guaranteed to get off the gammon. The problem is that he is also buying a place as a distinct underdog to win the game. According to Stick’s rollouts, when White has 10 checkers off, Black has about a 32% chance to win (assuming also that he has a 1 White checker closed out, and spares arranged ideally on the 4pt, 5pt and 6pt).

Can Black do better by trying to pick up a second checker?

If that is his plan, it looks like the best way to accomplish it is to slot the bar point with this 21. Black will need to complete a prime if he is going to play to get the second checker, and slotting is really the only practical way to do it. He is not very likely to roll a perfect number otherwise.

Then he needs White to enter with something other than 11 or 16. The worst is 11. After White plays that roll, Black can never pick up a second checker, and he will have missed the opportunity to close his board. The 61 might also be disasterous. While Black is distracted entering 2 checkers, White might hit again, and run home in the melee. Black could wind up losing a gammon, and sometimes even a backgammon.

Even in the good variations, where White enters with 12, 13, 14 or 15, Black will be under pressure to perform immediately. He will need to enter, and either hit back, or complete his prime, pretty much right away. When he cannot do either of these, White will have a 9 rolls that escape, 9 rolls that pick up his blot, and 2 rolls that do both.

Notice that Black’s 5s are duplicated. After slotting the bar point, he will need a 5 to cover, and also needs a 5 to hit on the 1pt. As well, from the bar, Black cannot hit when he rolls 51 or 31. Therefore, he only has 23 hitting numbers from the bar. Of course, when he rolls a 2, Black will be in the driver’s seat.

Nevertheless, these are not the kinds of odds I like when I play to pick up a second checker.

My solution: 4/1

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%.

[...According to Stick’s rollouts, when White has 11 checkers off, Black will has about a 32% chance to win (assuming also that he has a 1 White checker closed board, and spares arranged ideally on the 4pt, 5pt and 6pt)...

Can Black do better by trying to pick up a second checker?

If that is his plan, it looks like the best way to accomplish it is to slot the bar point with this 21. Black will need to complete a prime if he is going to play to get the second checker, and slotting is really the only practical way to do it. He is not very likely to roll a perfect number otherwise.

Then he needs White to enter with something other than 11 or 16. The worst is 11. After White plays that roll, Black can never pick up a second checker, and he will have missed the opportunity to close his board. The 61 might also be disasterous. While Black is distracted entering 2 checkers, White might hit again, and run home in the melee. Black could wind up losing a gammon, and sometimes even a backgammon.

Even in the good variations, where White enters with 12, 13, 14 or 15, Black will be under pressure to perform immediately. ...]

Very good. I missed it. So this lowers the equity to 88/1296=6,8%. Even more urgence to adress the joker 16. But getting the second checker rockets the winning chances from 32 to nearly a pass. I would stay at the middling play.

I would reject 10/7 as a 61 by my opponent would be devastating. If your opponent rolls 61 you want multiple shots not to have 2 men on the bar.

After that you need to diversify so that you are not hitting with 2's (as you already do from the bar) so it has to be 12/11 10/8.

4/1 is just a little too conservative for me but if a good player like Taper_Mike suggests it (as he has) it would cause me to stop and really think about it but white has too weak a board to let me do it.

After posting, I realized that Black will have better odds from the bar that I reported. My mind's eye failed to see the checker that would be on the bar point after Black plays 10/7. If White then enters with 12, 13, 14 or 15, Black would have 2, 3, 5 and 6 as hitting numbers. Many 1s would still miss (11 13 14 15 16), so Black would have 26 ways to hit on the 23pt or else to hit loose on the 1pt. With a roll of 44, he would switch points, hitting on the 1pt, so that is a 27th hitting roll.

If Black makes your play instead, and White enters with 12, 13, 14 or 15, then Black gets only 23 shots from the bar.

After making the play suggested by NetWorth, 10/9 4/2, Black will have solved his ace problem, but he will not have 6 as a hitting number. From the bar, and with White blots on Black's 1pt and 23pt, Black can hit with any 1 (except 11), 2 or 5. The doublets 33 and 44 hit as well, although hitting with the former entails switching points. That's 28 shots in all, plus there is no danger of the double hit when White rolls 61. Of course, there also is no chance that Black will ever complete his prime.

I am not sure which play is correct, but with so many saying that closing the board is definitely wrong, I would have to withdraw it in a consulting chouette. That play must surely be wrong!

At the risk of stealing some of Robertie's thunder, here's an article I found very helpful for these situations:

http://www.gammonlife.com/writers/07tardieuart1.htm

Newbie question, but does hitting a second checker really improve our equity that substantially? 4/1 seems automatic... if White succeeds in hitting us we only hit back like 30% of the time, right? Please explain why I'm wrong