Problem of the Week #101: March 27


Cash game, center cube. Black on roll.




Black to play 6-2.



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.

The 2 is forced: B/23.

22/16 seems better than 21/15 because of the return 6 that Black would have if he's hit on the 16-pt.

So I discard 21/15 and also 8/2 for obvious reasons.

So it would be between 22/16 and 13/7. The barpoint would be a very useful blocking (and priming) point for Black. If he's hit, no big deal, Black is already behind in the race anyway.

22/16 provoke some contact and is about the same if Black is hit. But if Black isn't hit, 13/7 is more constructive (and it doesn't even strip the midpoint!), so it's my pick.

B/23 13/7

Usually, I run a back man when I have to play an awkward six in the early game. In this position, however, it seems pointless to walk into a double shot. White might hit both outside and inside. Instead, I'll play 13/7. It leaves White the fewest number of outside shots at me. I might still get hit twice, but because I've left three checkers in the rear court, I'll have a better chance of anchoring, plus I get to unstack the midpoint.

My solution: bar/23, 13/7

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 52%.

Oops, return 5.

Slotting the 7-point is usually not so good early in the game and I don't see why it is good here.
Also, slotting a point while your backcheckers are split is also usually not such a good idea.
So in my opinion the right 6 is either 21/15 or 22/16.
Here I prefer 22/16 because it keeps my checkers better connected.

I like 22/16 a bit better as well

B/23 is a given.

My gut instinct is 22/16.

If we were not blotted on 21 and 22, I would have said 13/7 instead. On the one hand, it leaves me with a blot in a space that I'd rather not have one, but on the other hand, if it doesn't get hit, I have a good position to cripple whites pieces on 1 by setting up another block using my pieces on 6, 7, and 8.

Because of the blots on 21 and 22, I would be reluctant to do this as white can keep knocking me, preventing me the opportunity to set this up.

B/23 22/16

Running has some interesting possibilities. 22/16 leaves some nice return shots if White hits light.

Think otb I slot the seven as we have the start of a nice proto prime, although it's a higher risk move that could well see us getting the cube shipped pretty soon. Very tricky one.

Hmm. I like slotting the 7 in an attempt to build a prime, and I think getting hit is no concern this early - especially if making an advanced anchor is the result. But maybe 22/16 sets up the most return shots if the blot gets hit and improves our race. Ehhh.

I'll try Bar/23 13/7.

Bar/23 13/7 looks right to me, we're already behind, I want to get some structure ASAP, 13/7 seems like the best way to get there. if I'm hit back then I'm firmly behind in the pip count and my game plan needs to change.

B/23 13/7

B/23 13/7. If hit then can make an advanced anchor on the 4 or 5 point. If not hit then can make the bar point or another inner board point.

8/2 just looks stupid, and 13/7 activates some of his 6s to be much better. Also, do we really want a 4th blot when he has potential hits on about every roll? I like 22/16 a little better than 21/15. It duplicates 4s to a bigger degree, and we're fighting for a better anchor with a blot on his 4 than on his 3. We're actually about even in the race, ahead in home structure, and closer to making a good anchor than he is. We don't have to go crazy trying to get even further ahead in structure when there are normal moves. I think 22/16 is best, but I think both are better than 13/7 (and 8/2 is the worst).

Good observation. I hadn't done a pip count. OTB, it looked to me like Black was behind with one more back man, but the count is 168-168 with Black rolling!

Apparences are often deceptive. What lies beneath...

go to the 16 and keep the troops connected

I like 21-15. I think leaving the checker on the 15 point is bad because white would just love to attack us there whould he roll a number that allows him to hit twice. This is a very good reason not to play 13-7 and less reason (but reason still) to prefer 21-15 over 22-16.

JMHO.

I didn't consider the possibly of a double hit, so let's see if I can correctly count shots.

After 13/7, 66 65 64 63 62 33 22 11 (3 hits with a double direct return shot) leaves 12 shots.
After 22/16, 54 56 52 11 22 44 55 42 46 leaves 14 shots.
After 22/15, 44 43 46 45 11 33 36 35 leaves 13 shots.

So, I still vote for 13/7 unless I'm miss counted.

After Black Plays Bar/23, 13/7
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White can hit outside with any 6, plus 51, 42 and 33, for a total of 16 shots outside. Of these, 62, 63, 64, 65, 66 and 33 (10 shots) give White a double hit. Otherwise, 11, 22, 44, 55, 42 and 53 (66, 64 and 33 were already counted) hit and make an inside point. These give White an additional 8 shots. Of these, 22 and 44 can be used to double hit.

After an outside hit, Black will have 3 points slotted as potential anchors when he rolls from the bar. His chance of making an anchor on the first try will be 75% or better (when he rolls certain combinations). After a double hit, Black will have 2 points slotted as potential anchors when he rolls from the bar. His chance of making an anchor on the first try will be 56% or better (when he rolls certain doubles).

Total: 24 hits with P(anchor) = 66% (12 single hits with P(anchor) = 75%, 12 double hits with P(anchor) = 56%)


After Black Plays Bar/23, 22/16
----------------------------------
White can hit outside with any 4 or 5, plus 22, 31 and 32, for a total of 25 outside shots. Of these, 24, 25, 44, 45, 64, 65, 55 and 22 (13 shots) give White a double hit. Otherwise, 11, 33 and 66 (22, 44, 24 and 64 were already counted) hit and make an inside point. These give White an additional 3 shots. Of these, none can be used to double hit.

After an outside hit, Black will have 2 points slotted as potential anchors when he rolls from the bar. His chance of making an anchor on the first try will be 56% or better (when he rolls certain combinations). After a double hit, Black will have 1 point slotted as a potential anchor when he rolls from the bar. His chance of making an anchor on the first try will be 30% or better (when he rolls certain doubles).

Total: 28 hits with P(anchor) = 44% (15 single hits with P(anchor) = 56%, 13 double hits with P(anchor) = 30%)


After Black Plays Bar/23, 21/15
----------------------------------
White can hit outside with any 3 or 4, plus 21 and 22 for a total of 23 outside shots. Of these, 33, 34, 35, 36, 44, 45, 46 and 22 (13 shots) give White a double hit. Otherwise, 55 and 66 (22, 33, 44, 35 and 46 were already counted) hit and make an inside point. These give White an additional 2 shots. Of these, none can be used to double hit.

After an outside hit, Black will have 2 points slotted as potential anchors when he rolls from the bar. His chance of making an anchor on the first try will be 56% or better (when he rolls certain combinations). After a double hit, Black will have 1 point slotted as a potential anchor when he rolls from the bar. His chance of making an anchor on the first try will be 30% or better (when he rolls certain doubles).

Total: 25 hits with P(anchor) = 42% (12 single hits with P(anchor) = 56%, 13 double hits with P(anchor) = 30%)

I'm kinda favoring the stupid move:
8/2.

The only number he can hit it with is an ace. If he does hit it, his checker may not advance very far and could be vulnerable to being hit back. And if the black checker gets hit on the 2 point, so what? It's early in the game, white hasn't had a chance to build a strong board and that checker could help build a good anchor over there. It has two over there to work with it. If it doesn't get hit, black just might build a point on the 2 spot on the next move.

Meanwhile, on the other side of the board:
If one of those guys is going to get hit, I'd like it to get hit right there where it's sittin' 'cuz white may not be able to cover (if he can and chooses to hit) and may get hit back when black enters.

wow 4 sixes to chose from! the cube is in the middle i'm going to to slot the 7 point.

Correction
Here is an improved breakdown of the odds of being hit and thereafter making an anchor. Rather than count the moves that allow a double hit, I have counted only the moves where the double hit is White's best play. As you can see, this reveals that White is twice as likely to have a double hit after Black moves 13/7 than with either of the other plays.

As a simplification, combination shots from the bar have been ignored. Only those direct numbers that enter and cover an existing blot were counted. The chance of making an anchor is actually higher in all three circumstances. Hopefully, the results are still meaningful for the purposes of comparison with each other.

As for return hits from the bar, I leave the calculation to another! My guess is that there are plenty of return hits after 13/7 and 22/16, and fewer after 21/15.

You shouldn't volunteer a 4th blot here. 21/15 may be a little better than 22/16 because it duplicates 31 and 42, instead of 42 and 53.

I missed the pip count on this one as well. I just assumed black was behind (probably one of the reasons Bill chose this problem). With even pips before you roll it's probably best to jump in to the outfield.

So, look what popped up in a cash game against GNUBG today!





I usually don't roll out the Problems of the Week until their solutions have been published, but considering the serendipitous appearance of this position, I thought it fair to roll it out. Note that by running to the outfied, Black will offer a triple shot.

Black has already made a point. The offense is started. By now, white has nothing. With three men back, we have to care for the defense. The natural way is to play one man into the outfield. Now the white blot has to declare. If white plays with the blot, he can not improve his offense. Now is the question: halfback or fullback? I would play the halfback with 21/15. So White is duplicated on 3 and 4, 31 and 42 plays anyway good and if he attacks in his board, he has to attack deep points. If he plays not the outfield blot, we have a return shot on this with the additional option to bring with a hit also a man into the zone.

21/15 for me, and it is for me not really close.

I dunno. I don't like bringing a checker out into the outfield just to get hit again. White's board is very weak and I don't mind taking a chance here. So...

bar/23, 13/7