Problem of the Week #76: September 12


Cash game, White owns the cube.




Black to play 3-1.


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.

I discard making the bar point right away. Then, it's either 10/6 (doesn't do anything constructive, only preserve the anchor but leaves 2 indirect shots), 20/16 (running while White's board is a mess) or 20/17 6/5 (running and duplicating 5s). The latter leaves the same number of shots but uses duplication, so it's my pick.

20/17 6/5

Black doesn't have a whole lot of good moves here.

He doesn't want to break the 8 point or 20 point, so he has to break the 10 point.
There seems to be little or no downside to slotting the bar point. White can hardly afford to hit. The only scenario where he hits is if he rolls a 5-5 (which anyway would be a disaster for black as his edge would be completely gone). Hitting with anything else is probably going to be too risky because he's breaking the anchor, his home board is weak and he'll have to leave 1 or more blots. With the cube already turned, white has to be careful about getting gammoned.

Answer - 10/7, 10/9

20 - 16

I'd rather have white break first, so I don't mind sitting on the anchor for one more roll (and hopefully rolling a better running number). 10/6 is nice and safe, but I think I like making the bar point here. If white rolls a 6, he's got a tough choice of abandoning his anchor (and increasing the chances of getting gammoned) or risk having two checkers stuck behind a 6-prime with poor timing (any 2 or 11 will complete the prime).

Tricky little problem here. Best ace seems to be 10/9 to me. After that I'm torn between 20/17 or 10/7. Running for it doesn't seem to be fatal and 5's are duplicated and indirectly 52 and 53 as well with either 3) My final vote would be the aggressive looking 10/7 and keep the anchor in case white hits a superjoker like double 5, 1 or 2's.

10/9 10/7

10/7 8/7. solid

When this is a followup of problem #75, i will remember, what the director of the fermilab of backgammon told us: “...The key idea is that Black isn't leaving the 20-point unless he throws a big double. ...”.
By the way, i would have lost my market. Lesson learned. Water is boiling hot. The golden point is now our fuse when we are cooking white’s stragglers. Therefore i would reject the breaking from behind plays. Also, every play which includes moving in our home board. That can not be right, because the home board would shift into a frontloaded position. By now, we have a broken six prime with a 5 point hole. We can slot the hole or we can convert in a broken prime with a 6 point hole, the 6 point also slotted. When we look at the anatomy of this primes, we have a difference in escaping numbers: 6-hole 11 numbers, 5-hole 9 numbers. If there would be only one straggler, this could be a difference. But there are two. So let us play the market. If white will hit us after a slot without a perfecta, a target will stay. Let us suppose an exchange of hit, where white enters on the ace-point. How about our firepower after making a broken 6-hole or a broken 5-hole prime? I think better after a broken 6-hole prime. If we are hit, the remaining structure for a future forward-moving of the prime will also be better with the broken 6-hole prime. A better connected position is better. And our prevent defence will reach with double sixes the hole of our broken 6-hole prime. Finally, tailoring the risk according to the requirements of the position. White is outboarded 4 : 2 with 2 blots. Now is the hour for a bold play. We have the buntline special ready for attack, backed up by Doc Holliday. No delay plays. So my solution: 10/7, 8/7.

In this week's problem, Black's advantage in the pip count -- he leads 118 to 127 -- translates into a disadvantage for him in timing.

White has six checkers, two each on his 6, 7 and 13 points, that he can move while he waits for Black to give up his anchor. Black, meanwhile, has only three: two on his 10 point, and the spare on his 6 point. Black can gain further delay, however, if he abandons his block on the 8 point. But dismantling his broken five-point prime is not an attractive option for Black.

By leaving two blots in his home board, White may have given Black an opportunity to run now. Should he take it?

The usual arguments revolve around timing. The pip-count leader often wants to run sooner rather than later. In this problem it is easy to guess that White's position is going to get stronger on each turn, while Black's will tend to decline. If Black is forced to run later, his risk of losing the game after a hit will be much greater than it is now.

Pay Now, ...
There is a good running play that uses duplication. White needs fives to escape, so by playing 20/17, 6/5, Black gives White a duplicated five to hit. Furthermore, Black's risk of being hit is the same whether he gives White fours or fives. There is no advantage on this score to moving 20/16.

Even if White does hit, he will likely be forced to leave a return shot in his home board. Of the rolls that hit with a five, only 51 and 55 button up everywhere. The other fives all leave one blot inside. But don't forget, many hits will also force White to leave one or two loose blots outside.

White's better rolls are the ones that hit inside. Doubles 1, 2 and 4 play very well for White. Together with the 55 and 51 mentioned above, White will have six rolls that hit and cover all his inside blots.

... or Pay Later
The safe play -- for this turn -- is 10/6. It leaves only a fly shot outside. This move could succeed if White's back men remain trapped, and White subsequently loses outfield control.

Admittedly, it's a close call. Black's racing lead is not that great. His timing disadvantage is not monumental. And modern theory almost always favors paying later. Nevertheless, my tendency here is to be proactive. In this case, I favor the run.

My solution: 20/17, 6/5

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 51%.

It's always the plays I didn't even see! Those are the biggest mistakes! Every time!

After reading the posts from Ferrengi and Aaron, my eyes were opened to other possibilities...

I generally don't like the slot when I have only one cover. If I miss -- as I'm favored to here -- will I end up picking up the blot next time? And afterward, will I slide into a badly timed holding position?

Still, making a six-point prime is a plan with real prospects for winning. The threats are immediate. The path to victory is direct.

And, right or wrong, I didn't even see it!

This might be not a pay me now or pay me later position. Kit Woolsey wrote in his groundbreaking work “New Ideas in Backgammon” a whole chapter about this topic. I remember that even Jake Jakobs found it difficult, to generate general advice for over the board playing out of this. For me, if I remember it correct (i have not my library at hand), this topic means, that you sacrifie a little amount of equity now, usually to volunteer a shot, before a bigger accident happens later. That means that the position, we will reach after giving freely the shot, when we are not hit, will almost lock the win. Our insurance must pay dividends. Here we are in good shape, but there are a ton of winning ways for white even after breaking from behind:

1. Attacking with the freakboard. We will unfortunatly fumble, the board will close in, white scrambles home.
2. White will fly out his rear position with a freak double and win the race.
3. White will hit in the outfield, when we are coming in.
4. White will hit when we are bearing in against the leaden point, which generates surprisingly often a shot.

This is far from “almost lock up the win”. So “pay me now or pay me later” is a very delicate concept and can be misleading.

The 10 is clearly the most useless of the 20, 10, and 8. So after 10/7, would I rather have the 7 or the 8? The 8 since it's 6 away. So 10/9 or 6/5? 10/9 leaves more flexibility, so 10/7 10/9. I'm not afraid enough to play 10/6- if he goes 55, nhwp (but this roll sucks anyway), but on anything else, a hit isn't that bad, and the benefit of locking up the 6-prime is pretty good.

Driving yesterday 20 kilometers home with my bike, thinking about the position.
First, looking at home for the “pay me now or pay me later” criteria. Woolsey said:
1. If you pay now and get away with it, will the position be a near claim or will there still a lot of work to do?
2. Is your opponent’s position improving or is it likely to get worse in the next few rolls?
3. Is your own position deteriorating quickly, or do you still have some flexibility?
Generally at least two of these conditions have to point forwards paying now-otherwise it is usually correct to pay later.

Second. The broken prime with the 5-hole can be only completed with 2’s. 11 numbers. The broken prime with the 6-hole can be completed with 3’s and double sixes and double-aces. 13 numbers. My brother is financal trader, and he said, 5.6% rising is a big gain on volatility in the stock market.
But then i made a little experiment. I remembered, that backgammon is about trying to make your next numbers good and trying to make your opponents numbers bad. Suppose you are going for the gut. Suppose, your opponent throws his Hail-Mary-Pass. What is with your Prevent Defense? After double 5’s he stops at the midpoint, giving only indirect shots when he can not clear later the midpoint with doubles. After double 6’s he will stop in six point range to our Prevent Defense, giving a direct shot, if he can not clear later with doubles. So i think, the Hail-Mary-Pass is much more dangerous with double-5’s, and double 6’s are much more in favour for our Prevent Defense. John Madden once said, all a prevent defense does is prevent you from winning. But here, it can save a lot of equity, if we play for the right Hail-Mairy-Pass to prevent. Never die easy. So, absolutely no doubt anymore, that 10/7 8/7 is clearcut.

I am mad. Double aces will make also the broken prime with the 5-hole complete. so only 2.8% gain. That makes me what i am: an intern and Bill Robertie the leading authoraty of high energy backgammon. But nevertheless, 10/7 8/7. I will mortgage my house.

Mad man II. With Hail-Mary-Pass double fives, white will stop at the bar-point, threatening our blot at the 8-point and close the 3-point. Even more catastrophic. One or two fumbles again, and white can think about a juicy 4-cube. So, the Prevent Defense has to play against Hail-Mary-Pass double sixes. If we play against double fives, John Madden may be right.

Grunch: 20-16.

Thanks for this. Especially number 1, which I seem to have ignored.

The clear answers here are 1 (no) and 2 (yes, it's improving). Question 3 is not so clear cut. Black can buy a couple of moves, but after White cleans up his board, may find he is trapped into surrendering the 8 point. Let's answer 3 with "sort of deteriorating."

Remember everyone White owns the cube

So 1 vote yes, one vote no, one vote sort of not clearcut. Doubts. I would pay later. Nevertheless, going for the gut pays also now. But with the Prevent Defense as insurance. I showed a friend the position. He voted for the broken prime with the 5-hole. Then i suggested a proposition. I played white, 31: 10/7 10/9 with double fives 23/18(2) 13/3 against 31 10/7 8/7 doublesixes 24/11(2). Hail-Mary-Pass double fives unfolds as follows: very difficult checker plays for both sides, with several recubes, one lost gammon!, -7 on the scoresheet after 20 games for black (yes, white owns the cube, big asset here!). He played white with Hail-Mary-Pass double sixes: easy going, often hit a blot, even after entering without a shot easy play and despite the racing lead problems for white to get the position home. +3 on the scoresheet for black. He then turned the move into 23/17(2) 13/7(2) and after 20 games +5 on the scoresheet for black. If black hits a blot from the bar, and this blot enters the ace, the blot first has to scramble to the edge of the prime. The 17-point isn’t really a lifeline. This was not aequivalent to a rollout, but we learned that you even have to ponder, which joker you permit.

Reread in the principia of backgammon “The Aesthetic of Shade and Shadow”. There, our Isaac Newton of backgammon, Danny Kleinman, writes:”... your judgement of a position must be incorporated in your perception of it. You must not only see a move, but “see it as” good or bad, beautiful or ugly. You must have an aesthetic of backgammon. ...”
Compare the two possibilities of slotting. Try to view the “shade” of the prime after a hit of the slot with one man from white.
After slotting the barpoint and hit there with one man from white, i will view the shade of the prime going from point 8 to point 3. Only one builder left for the bar point, one builder killed. Okay, new shade. Point 7 to point 2. Suddenly we have only four points made. And only one builder for the ace.
After slotting the 8 point and hit there with one man from white, i will view the shade of the prime going from point 7 to point 2. 5 points made within the shade. And i will have 3 builders for the next point to made, the 2 point. And 3 builders for the ace. No man killed.
Slotting the barpoint leaves you with two loose ends after a tackle. Slotting the 8 point leaves you after a tackle with a strong block at the line of scrimmage and one tight end. My bet is for shure. Even the bots can’t go behind the principia of backgammon.

To stress it a last time. Making the barpoint plays not only against the playable shotgun formation, it leaves also the offense in better shape. John Madden would have said (remember, the man who threw the prevent defense under the bus): good block, offense well balanced, almost a two tight end position, quarterback sack likely possible. What? You have heard right. Football Teams also sometimes put two wide receivers in the outfield of a prevent defense. And so here. This is perhaps a perfect example for the janusheadedness of backgammon. In every single down you have defense and offense in place and it depends of our point of view to identify them. But you have only 15 men to play. So they have to work as hard as possible.

Black has a good position: He is ahead in the race. He has a 4-prime against 2 white men and the golden point. White has no real structure at that very moment and 2 blots in his inner board.

With a very good return shot (2 white blots in white's inner board), Black can play bold: He can improve his position by a solid blocking game or by a running game.
Black rolls 3-1: Black should play 10/7 8/7 making a solid 5-prime.

My solution: 10/7 8/7

My move is:

10/7 8/7.