Problem of the Week #5: April 5


Both sides have partial blockades. How do we handle these positions?



Cash game, center cube.

(a) Black to play 4-3.

(b) Black to play 5-1.

with the 4-3 i like making the 2 point. fills up our board and leaves the opposition with a fair few awkward numbers, they can't run easily either as we have the 15 covering the outfield.

with 5-1 i go 15-10 5-4. being hit on the 4-point really doesn't hurt us

A) Black to 4-3

The 3 likely choices are 6-2,5-2, 15-8, or 22-15.

I actually think the checker on the 15 point is the key to this position. It is in the perfect spot to try to catch white if he runs. It only gets hit with 6-6 which would be a disaster, but we can do nothing to defend against it and if he does roll 6-6, it will force us into a back game in which having an extra attacker in his home board isn't the worst thing that can happen. So that rules out 15-8.

Running to the 15 point is an attractive option since it will allow us to keep our prime intact longer, but even with the blot on the 23 point white has too many attackers in place making it easy for him to both hit and cover, leaving us dancing trying to come out on a 4 point board. This option might be better if our prime was blocking whites 6 rolls which would force him to break his anchor in an effort to get out.

i think 6-2,5-2 is good because it gives us a 4 point board in preparation for when we must break our prime and white runs, which will be soon.

B) white to play 5-1

I might be absolutely out of my mind, but i think actually breaking our prime might be the best play here. We want to encourage white to run. As it stands now white has plenty of attckers and lots of room to put them, either in front of, or behind our anchor. Unless we disrupt white somehow our prime is sure to collapse 1st anyway leaving white free and clear to play into the outer boards with any roll 4-4 or higher So why not encourage him to run by clearing the 7 point by playing 7-6,7-2. This way we still have an anchor 5 points away for white to clear as well as the attacker on the 15 point to hit with should white get past our 8 point. This creates at least one awkward roll of 6-4 in which white must then leave a shot on one side of the board or the other and many others which force him to take checkers out of play by moving them behind our anchor on the 22 point

I think 4-3 its quite simple we don’t give our anchor, don’t give the blocade, keep flexibility with spare on 15 and turn 3 point board to 4 point by playing 6-2,5-2

With 5-1 its more difficult but giving anchor is out of question so it can be 15-10 leaving white indirect shot and 5-4 slotting the point in case of hit we have anchor and 3 opened points in opponent board in case of no hit we can extend blocade to 5 point prime.

4-3: Time to leave, I think. I don't wanna use my spares to make a point behind his anchor, and I don't wanna give up control of the outfield by playing 15/8. It also looks like timing won't be in our favor if we elect to stay. Also the blot in whites board makes it a little less risky to make this play. I play 22/15.

5-1:15/10 is the only five (15/14 6/1 retains outfield control, but I can't stomach burying another checker on the acepoint here). Slotting the 4-point has to be better than slotting the 9-point. If white had covered the blot in his board 6/5 could be right, but here I'm not that scared of leaving a couple of shots to try and make a five prime. 15/10 5/4.

a) 4-3 22-15 to slither a back man out of there. Better than 6-2, 5-2 which makes an inner-board point but leaves 4 men out of play, and 15-8 which leaves both back men stranded by themselves.

b) Yuck. Can we roll again? 6-1, 15-14 I guess, to leave the 4-pt prime intact against 2 back men and if White jumps out with 6-1 to 6-4 the man on the 14 has a direct shot. 15-10, 6-5 leaves a big stack on the 5 and just doesn't feel right and 7-2, 7-6 breaks the prime.

A) 22-15. I'm in favor of delaying the break of the four point prime, as it is black's biggest asset. With the blot in white's inner board, I count only 6-6, 3-3, 1-1, 6-1, and 5-1 for hit and covers playing this way. It is more likely black will have to escape first, so why delay until white has a better board?

B) 15-9. Playing this way, white can't hit and cover without 6-6, and that roll is a disaster no matter what. I don't want to slot the four point and leave two blots, because if we are hit, there are too many bad rolls from the bar which will leave black facing a cube decision that will need to be declined.

That was my first choice too actually. But then I figured with 2 men back and the race about even (black down 5 I think, on roll), we'd want to make it harder for white to jump out at this point. Dunno

I think 6-1 and 5-1 leave a blot on White's 4 point, but 6-5 does hit and cover.

After black's 22-15, white has 17-22*, 22-23 available with 5-1, and similarly 16-22*, 22-23 with 6-1. White can not avoid leaving a blot somewhere in the inner board with 6-5 if black gets hit.

Ah missed that one. Thanks.

a) 4-3 I play 22/15. The reason we can run is because of the open blot in whites home, this play gives us control of the outer board, gives us plenty of flexibility, allows us to attack whites checker if he decides to run. I don't like 6/2 5/2 as it buries our attackers, nor do i like 15/8 as gives up control of the outer board.

b) 5-1 We are forced to leave a shot, playing safe here is not an option for me with whites home board rather non threatening. I play 15/10 5/4......if i am going to leave a shot we may as well slot the 4, as well this play gives us many more return shots if we do get hit. I would have to think that 15/9 is very good as well, being that you are duplicating the 6s. I think the edge goes to slotting the 4, white is forced to roll a 1 now. Keep the pressure on.

Let's look at what happens when black chooses 15-10, 5-4 and white does roll a one. Keep in mind that black will have serious timing issues for a backgame, and should refuse the cube coming soon from white in this case.

With 1-1 white can make the bar point while hitting. With 6-1 white hits twice. With 2-1, 3-1, 4-1, and 5-1 white can hit and position an extra attacker on either the six or four points. Unless black rolls well off the bar, the cube is coming and needs to be declined. The critical aspect of this position is that black is too well advanced for a decent backgame, and shouldn't risk two blots at the same time. Furthermore, if black doesn't slot the four point, white has more difficulty getting to a doubling position if he rolls a one.

The more i look at it..... the more i like the slot. When white misses either hit, you are in a much better position having the 4 point slotted. You are a big favorite to make another inner point.you now have white behind a 5 point prime, as well your 6s play a lot less awkwardly. After you play 15/9 and are missed... take a look at any roll with a 6 in it. 6-1 is bad....6-2 is meh....6-3 leaves a shot....6-4 leaves a shot....6-5 leaves a shot ....6-6 leaves a shot.

How about if we are hit ....first off, with either play white will not be able to hit and cover,so with either play we will always have a direct shot after being hit, barring the 6-6 or a misplayed 6-1.

If black is hit after15/9....whites checker is now safe and sound homeward bound, this happens with all hits.

If black is hit after5/4 with 1-2, 1-3, 1-4 ...white is still trapped, black has more double hit opportunities, and more winning chances.

No debate about leaving the subsequent bad sixes when you don't slot the four. However, there are also bad rolls which don't make the point safely when white misses. 5-4, 5-3, and 4-3 are quite ugly. I just don't want to turn my opponents poor rolls of 3-1, 4-1 and 5-1 into good rolls plus leave follow up shots at the second blot. Slotting the four would be much easier to play if that was the only blot, but here we will be bringing the other checker into immediate re-hitting range of 6-x or 5-1. One other thing the slot play has going for it, is that you may be able to offer the cube if white misses. The threat of the five point prime could be too much for white to accept. Maybe that outweighs the risk of leaving both blots.

If black doesn't come in from the bar even though white still has two checkers behind the four point prime, can black accept a double? I think I would have to decline when I have the other blot open, but can justify a take if there isn't a re-hit available for white. It sure is an interesting position with the initial 5-1 roll, and both plays have merit.

(a) 43

There are three candidates:

• 22/15
• 6/2 5/2
• 15/8

I think that all three have some merit.

22/15 tries to exploit the blot in White's board. White will only have four rolls that are really trouble for Black: 61, 51, 65
and 66. But except for 66, which makes two points, I'll reenter with 20 out of 36 rolls. The major problem that I have with giving up the anchor is that I'm not guaranteed to escape the next roll. Also, the threat of escaping isn't strong enough to let me double next roll if White misses.

6/2 5/2 makes a point a the expense of my builders. If White breaks his anchor, I don't have much ammunition (but 54, 44 and 55 crush). However, I still have a checker in the outfield to pick off an escaping checker. The outfield checker does a very good job where it is. It would put the onus on White now, who would have to leave a shot with 62 and 64. Rolls like 65 and 63 strip him of his builders and 44 and 55 also suck for him. If he rolls a good roll though, like 61, I might be in big trouble.

So this leaves 15/8 for maximum builders at the expense of my outfield control. It will be more difficult for him to leave the anchor now, but if he rolls something good now, like 61, I might have the same problems as with 6/2 5/2. I'll have to use some builders for moving pips so that my anchor keeps intact. Then there is exactly one builder left, and White's next roll is going to decide it.

It seems to me that the outcomes of 6/2 5/2 and 15/8 are similar if we look two rolls ahead. The only bad issue with 6/2 5/2 is that if I then roll something like 51, I would either have to break the prime or leave a direct shot. So let's stick with 15/8.

(b) 51

I guess here we don't have much choice. I really don't want to break my prime so I would play 15/9 with the same ideas as with playing (a) 15/8. He can't really hit and cover except with 66 (but 66 would crush anyway, no matter how I play). His sixes are duplicated and the blot in his homeboard gives me a chance to play along the lines of my suggestion for (a).

(a) Black to play 4-3.

The obvious play is 15-8. It brings a builder for either making the four point or to hit on the three point if white runs. The downside is it concedes control of the outfield and leaves blacks so-so anchor on the 22 point isolated. This is a real problem because white could easily be stronger in a roll or two. Somehow it seems his timing is better than blacks

Not so obvious is 22-15. This takes control of the outfield (important if white runs with one checker off the three point) but leaves a blot open to attack on the 22 point. But this blot is only vulnerable to two builders (on the 17 and 16 points) and white would have a hard time hitting and covering his blot on the 23 point. If hit the 20 point is open and the outfield anchor within reach.

I'll go with 22-15. It's the sort of play Barcley Cooke might have advocated in "Paradox and Probabilities", a book I loved for it's fluid style (and despite the many problem positions that were later proven to be mistaken).


(b) Black to play 5-1.

I'd play 15-10 and 5-4. If white misses the blot on the four point can either be safetied or covered next turn. If white hits black has return hits on the 23 point and an open 20 point (along with his 22 point anchor). It's not a disaster now but will likely be later when white can make an additional point inside.

As an aside white is really hurt by having the extra man buried on the 23 point. In effect black has 13 useful men in play while white only has 12. In positions where there will often be a combination of hitting and blocking this is a significant advantage for black.

~ Rick

a) I'd make the 2 point
b) 15-10 5-4 i think, not sure tho

a) 22/15. Giving up control of the outfield is too much of a negative for me to consider 15/8, and 6/2 5/2 doesn't look as good because what do we do next roll? 22/15 leaves us flexible and in a good position.

b) What an ugly roll. 15/10 6/5 was my first thought but scrolling over some of the responses it seems like slotting the 4 is preferred by most people.

a) I think it is too dangerous to break the anchor here as white has 3 inner points and started on 2 point, if white hit and we fail to enter, it's over. On the other hand, the timing looks better for us than it for white, so we try to build our board and wait for our opponent to break first. 6/2 5/2 seems fine to me, also it saves 5s and 6s for the next roll.

b) 15/10 is a no brainer, and we look for the best 1. It could be either 10/9 or 5/4. I vote for 5/4. The reason is that we will never make the 9 point cos we have no builder behind and being hit here isn't too bad at all.

a) 6/2 5/2
b) 15/10, 5/4

I would agree that with the re-hit available in white's inner board, slotting the four would ordinarily be sensible. It also appears that a hitting contest at this point would be in favor of black's four point prime. The problem with 15-10, 5-4 is leaving white the return shot at the second blot if this does indeed become a hitting contest. With the second blot in range, a hitting contest now favors white. Neither side can afford to resort to a backgame since both positions are too advanced. The loser of a hitting contest here is going to get cubed, and probably won't have a correct take. Black can't be too conservative and play 15-10, 6-5 because that turns half of the subsequent good rolls into poor ones. I don't think black can offer the cube with most of the rolls where white misses hitting next either. Obviously a white 5-5 is going to get cubed, but otherwise we really have to see who's going to break down uglier first. I prefer the blot on the nine point which also takes away the covering sixes from white, instead of the more aggressive play leaving two blots. Making the four point for black would be ideal if white doesn't hit, but 3-4, 3-5, 4-5 and 5-5 don't cover while 3-1 and 6-6 are ugly. So it's far from guaranteed that black will fill the four point on the next roll. This is a semi-closed and well advanced position which calls for a balance of caution and aggression with the horrible 5-1 for black.