Problem of the Week #50: February 14


Cash game, center cube.




Black to play 4-3.


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.

8-1*.

The race is about even. Given white's very strong board, black's chief concern is not getting hit. The question is, which move will be safest for black in the long run?

The only move that doesn't expose any blots is 11/8, 6/2
Unfortunately, if you make that play, white can sit there for quite a few turns and maybe get multiple opportunities to hit. Black would have to get a whole bunch of doubles or other lucky rolls to avoid giving white shots.

I think black's best bet is to expose the blot now and play 11/4. If black is able to cover this checker on the next turn, white will start to feel some pressure to escape. I don't think the same can be said for 8/1*. 11/4 will give you a better board (if it succeeds) and it doesn't give white any extra opportunities on his next roll in comparison with playing 8/1*.

The cube position also favors taking a chance now. Black can always drop if he gets hit and avoid the doubled gammon. If white cubes before playing his next roll, that will create a lot more volatility. I think black will have to reluctantly take.

Answer - 11/4

Safe is no good with lots of long term trouble. The cube will be turning within a roll after either blot play. 8/1* seems safer but white is more likely to take incorrectly after 11/4 and a miss so that's my play.

Looks like a pay now/pay later dilemma. What are our options?

• The safe 11/8 6/2 leaves us with spares only on the 8-pt, not really great. But it is safe.
• Then we could play 11/4, preparing to clear the farthest point and leaving 11 shots.
• What about 8/1*, also leaving 11 shots? It leaves spares on the 3 far points and, if we're not hit, it moves his back checker forward.

The thing is, a hit right now is fatal, since White will double us out if he hits, so safety has to priority #1 I guess. On the other hand, we might want to provoke things now, otherwise White might have an efficient double. Ah, I go with the safe and ugly move and pray:

11/8 6/2

I'm going back and forth over this, but I'm inclined to make the ugly safe play. Getting hit here is pretty much a lost game. Could we end up giving more future shots by making this play? Possibly, but I'm not sure.

Even though 11/8 6/2 is very unflexible then there are some rolls that could smooth this out next turn and actually even with the very unflexible postion we are not favorite to leave a shot next roll and no roll leaves a double shot.

8/1* to get that straggler of the acepoint looks miles better than 11/4 if we do decide to leave a blot, though.

A 17 pip lead and on roll, not exactly even.

I didn't actually sit there and count the pips. Is that really a big lead at this point in the game?
We all agree that black's chief concern is not getting hit. The only question is what is the best way to accomplish that.

I understand your point. But the fact that Black has a noticeable lead highlight the importance of avoiding getting hit, because we know that if Black doesn't get hit, he will probably win because of that lead.

I would think that if the race was dead even, Black might want to play a little riskier now (to avoid shots later and maybe to optimize the bearoff), knowing that even if he doesn't get hit, he will have some other concerns (the race).

Is it a big lead at that point in the game? I would say that it's Black only leverage for now, so that's why he want to protect it so badly.

My first inclination is to play 8/1*, hoping to get White off my ace point, and making the bear-in a whole lot simpler, while keeping my position as flexible as possible. However, the backfire possibility looks bad. If I get hit, it isn't just the one checker sent back against a 5-pt board. White is still on my ace point, and I still have to bear in against it unless I roll a miracle 61. 11/4 looks worse to me, because if White can't hit, he's still on my ace point!

As ugly as it looks, I think 11/8, 6/2 is right. White will likely have to leave his 16-pt in another couple of rolls, if I can wait that long. And each roll I have 16%+ chance of rolling a joker double. This is a case of planning to pay later, and hoping that later never comes!

imo it's big enough that once we clear 11 point safely it instantly becomes a double/pass, so at this point we should protect it and live to see another roll, if the race was close then it's a no-brainer hit

I'm by now means a backgammon expert, but I'd be surprised if that were the case. Black still has the ugly stack on the 8 point to clear as well. Like Bill often does in his solutions, lets make a new position, call it 50a, and rearrange the checkers so that Black's 11 point is cleared. Let's move black's 3 checkers on the 11 point to the 2 point, and move white's 2 checkers from the 9 point to the 17 point (to balance things out in terms of the pip count). Would GNU now show that this is a double/pass?

well if you put them in the very worst possible spot (and it will take some creative playing for them to end up there in first place) it prob won't be a pass anymore but should still be a double I think (I'm definitely not an expert myself and those weird home boards - huge stacks on 2 and so on, come around not too often, so I'd have to run a sim once I get to my home PC)

Getting hit this turn (or next) looks like it results in an instant double-drop without a miracle re-entry. And, obviously, you're in great shape if you don't get hit (ever). 11/8 6/2 looks ugly, but you actually have a decent number of safe rolls next turn. 35, 25, 26, 34, and all doubles. There's a chance that if you roll safe, he has to give up his 6 or your 9, which is makes life easier. He'll probably get a single shot at some point, maybe even 2 eventually, but I don't want to give up my parlay of getting in safely, especially when 14 rolls are safe next turn too, including some very good doubles.

11/8 6/2

+ 32, 41, 42, 51.

Not really sure if we wanna play 6/3 6/2 with 43, though.

white timing is very good. black flex is poor. very ... said that, i think black plan is to hit : if white miss next hit , then it's a clear double ( pass i guess ) , if white hits , then it's lost.
I don' t like the safer play: it changes nothing , reduce even more black flexibility, and next roll is a nightmare .
8/1*

As ugly as it looks, I play safe. You're risking a lot for a small gain by hitting loose. Return shots are essentially fatal and it's not as if you take yourself to a gin position by hitting loose, even if he dances. You'll still have to get the ace point covered and deal with two high open points on your home board. I'll hold out for doubles or point-clearing roll.

I wonder what your thoughts are about the following rationale...

After 8/1*, white dances on 9 rolls...efficient double/take for black. White enters without hitting on 21 or 20...efficient double/take for black (except for double 5 and double 4 where black's lead is cut). White enters and hits on 11 rolls...inefficient double/drop for white. This gives black 23 efficient doubles and white 11 inefficient doubles after 8/1*. I'm not too sure about all the doubles but even if I'm a few out would this make the hit correct ??

ok,first of all i was wondering why the cube is still in the middle,the lead in the race is surely big enough for a double and the contact does not really favour any side,so i would have doubled before this roll but i guess it is close.
11-4 leaves the same hitting numbers as 8-1* but i think it does ot achieve as much as the hitting play.You dont want to have the checker on your 1 point because it is far easier to bring your man home if he enters on a higher point,plus he might not come in at all.
The 'safe' play is of course an option,and usually when your opponent has such a strong board it is right most of the time no matter how awkward it looks.But in this case i think to get the man off your 1 point adds enough for the hitting play to be right.
So,i think it is 8-1*.
After the roll we double on every non hitting number and 55 and maybe 44.

Force Him Away
Paul Magriel has a subsection in his masterwork entitled Force Him Away that may be applicable in Problem 50. His idea is that when you must leave a blot anyway, hitting your opponent off the one point might force him to reenter high in your board. Although Magriel's text recomments this move during the bear off, when you can force your opponent to pass you, the concept may be relevant here. If Black plays 8/1*, and White misses him, Black will be left with an optimal distribution of builders. He could cover with any 1, 5, 7 or 10 (26 shots in all). If White enters without hitting, Black may not need to cover. He'll have thirteen rolls that make either his four or five point, plus a few hit-and-cover numbers that make the one point. Eleven rolls (24, 26, 33, 36, 44, 45 and 66) would leave a blot somewhere, either inside or out.

Slot the Four Point
Alternatively, Black could slot his four point, playing 11/4. This move follows the maxim put your checkers where they belong. White has plenty of timing in this position, and the double gap on Black's four and five points is almost guaranteed to present White with one or more opportunities for a winning hit. If Black slots the four point, and White misses, Black could safely cover with twenty-one rolls, thus reducing the gap. Another six rolls would safety the blot without covering. Only nine rolls (33, 55, 66, 23, 36 and 56) would leave him exposed after his next turn.

Play Safe
Finally, Black could play safe with 11/8, 6/2, a move that has a lot going for it. Modern backgammon theory has largely repudiated the old idea that leaving a voluntary shot early is often better than leaving potentially many shots later. More often, it is a mistake to voluntarily expose any blot during the bear in.

Is Problem 50 an exception? After Black plays safely, he'll have a brittle position, stripped everywhere except the two and eight points. To make his four or five point safely on the next turn would require doubles (22, 33, 44 or 66); 63 would make the five point, but leave an outside blot. Ten rolls would force him to leave a blot (13, 34, 36, 45 and 46).

Pay Now or Pay Later
At the table, Black should simplify the analysis by assuming that if he is hit, he will lose. After all, he'd have to roll a joker to prevent White from doubling him after a hit. That done, Black can reduce this to a pay-now-or-pay-later situation. All three of the candidate moves above give White between nine and eleven chances to hit on the next turn. White will hit something like one third of those shots, giving him about a 10% chance to win on his second turn after this. But in addition, the first two candidate plays offer White an immediate 30% chance. Only the safe play removes these immediate chances. Of course, the safe play also leaves Black with a very inflexible situation downstream, and he will probably face serious risks on the third and subsequent turns after this. He should trade those risks, however, for the immediate 30% advantage he gets with safe play now.

My solution: Pay later, 11/8, 6/2.

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. I have been answering these problems without the use of a bot, and before checking the excellent solutions of others, since Problem 28. Including the 39(a) tossup, my record at this writing is 55% correct.
16 Correct: 28a, 29, 30, 32, 35, 36, 38, 39a, 39b, 42b, 43, 44, 45, 47, 48a, 48b. 13 Incorrect: 28b, 31, 33a, 33b, 34, 37, 40a, 40b, 41, 42a, 46, 48c, 49.

I would like to applaud this poster for his honesty. He could not put in an answer before the solution was published (for what reason I do not know) but put in a thought out answer nevertheless.

You are a decent human being Taper_Mike.

Yeah, I was wrong again!

Thanks for the kind words, though. I had this written up late Saturday, but saw that the solution had already been published by the time I went to post on Sunday. As always, I submitted my solution before checking the answer (or the posts of others).