Problem of the Week #81: October 24


Cash game, center cube. Black on roll.




(a) Black to play 5-1.




(b) Black to play 5-1.



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.

Grunch.

At first, i had to ground my eyes. Similiar positions, mutual holding games, black with the better anchor. 51, a mediocre throw. How to handle it?

Position a) is really a mutual holding game. If we leave blots, there is the chance, that white with his balanced structure will get away with hitting. So i would lift the blot like a levanter, starting the third point in my board, jockeying for position.

a) 9/3.

In position b) i couldn't resist to play this pure. White is in the ropes with a 1 point board, a blot within, a stacked 6 point (that's a loud killer!) and a stripped 8 point. Despite it is an advanced anchor, i would attack it and therefore the position with 13/7. Watch how my prime will grow or eat a blot, giving up your sole asset. Must be the winner.

b) 13/7.

(a) Black to play 5-1. = slot the 7

(b) Black to play 5-1. = slot the 7

im gonna slot on both boards
cube is in the center and its early
i like the (b) slot a little better than the (a)

a) 13/8, 9/8.
b) 13/7

In (a) I am content to button up and play the holding game. Id rather keep my checkers in play than dump one in behind his prime here.

In (b), white's homeboard is a mess with a spare and a big tower. I think we can get aggressive here. Many of white's hits are not as good as they appear, leaving him wide open for a strong counter-attack. Also 3's and 5's are duplicated making it harder to hit and cover.

in the first case I just play the simple 9/3. slotting the bar is too much risk without a second blot to shoot at if hit. in the second casehowever, with whites blot on his three point, we can safely play 13/7 duplicating whites threes with a big upside if he misses.

Put me in the camp that goes with these plays.

a) Hard to find anything good to do with 5-1 here. I'm not too worried about leaving the blot on the 9 point but I see no reason to leave the blot. Breaking the anchor on the 20 point is out. 13/8, 9/8 isn't going to do any good. So, I go with 9/3

b) In this case, white's home board is so weak that it favors running. So, I play 20/15, 9/8.

I read the other replies and I agree that 13/7 is best in position b. Slotting is a better way to take advantage of white's home board and there is duplication of 3s as well.

a) I'm going with 9/3. Just makes sense over all the other choices

b) is a little trickier but 13/7 gives you duplicated 3's and starts some great points but I hate exposing an extra blot. I could still see playing 9/3 here too though.

I wouldn't want to stack the 8 in either case, that's for sure.

A) 9/3

B) 13/7

In part a), the race is nearly even, as are the respective positions. Black trails 153 to 148. He should be wary of leaving any voluntary shots. I would just button up, 13/8, 9/8.

In Part b), however, White's open position is begging for a slot on the bar point! The race is still close (Black 153, White 149), so the double slot seems risky, but notice that White's threes and fives are both duplicated. White has only a few rolls that would both hit and cover after slotting the bar: 3-3, 3-5, and 5-5. Furthermore, if White decides to hit, he must abandon his anchor.

My solutions:

Part a) 13/8, 9/8.
Part b) 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 53%.

I'm intrigued that part a) seems to be the hard part in Problem of the Week #81!

When I posted my solution above, my instinct to keep the checkers in front of White was so strong that I did not even consider playing 9/3. As always, the biggest mistakes are the plays you don't even see.

On reflection, I think 9/3 might be the better play.

A. 9/3
B. 13/7

I was relieved to see others agreed with this.

Hi Bill,

a nice problem again.
I think the theme of this problem-duo is:
How much risk can you take in a holding game to create extra landing points.

My first feeling says a) 13/8 9/8 b) 13/7

Of course because of the blot on 22 and the duplication of the 3 and the 5.

Another way to profit from the blot on 22 is 20/15 9/8, using the duplication of the 3.

But are these risks necessary?

What if i play safe?

How big, for example is the chance in a) to come home safe?

With only one landing point after 13/8 9/8 we are hoping for doubles.
With 38 pips to waste (about 5 moves) we hope for a double in 6 moves.
However since the 11-point is only attacked indirectly,also 52 is a relatively safe move.
and the double-1 wont help. So there are 7/36 good throws.
The chance of not throwing a goodie in 6 moves is (29/36)^6.
Before taking your calculator, you might see that this is between
(3/4)^6 and (5/6)^6 (closer to the second)
(3/4)^2 = 9/16, (5/6)^2 = 25/36, oh it was closer to the second, so lets take 2/3.
(2/3)^3 = 8/27, so the chance of not throwing a goodie in 6 moves is about 30%.

So not taking a risk, like in a) will give lets say a 1/3 shot in 30%, so thats 10% hits.
Taking the risk of 13/7 (like in b) gives a risk of white throwing 53 D5 or D3, about 11%.

The problem here is that after paying the 11% now, there might also be a price (though somewhat smaller than 10%) to pay later.
How big is this extra price?
Lets say there is an extra landing point on the 7-point. Now also 65 and 62 are good numbers.
The chance of not throwing a goodie in 6 moves now becomes (25/36)^6,
which is between (1/2)^6 and (3/4)^6, closer to the first.
(1/2)^2 = 1/4, (3/4)^2 = 9/16, lets say its a 1/3.
(1/3)^3 = 1/9 = 11%, so the hitchance = 4%.

So the total price of plan b) will be 15%.

My solution: In both a) and b) i would play 13/8 9/8.

Hi,

on second sight i do prefer 20/15 9/8 as an answer in b), when black throws a 5 or 61 next a lot has been achieved, and the situation will only get risky when white throws a 3 next move, and the only big risk comes with D3.

In both cases, the race is practically even. The lone difference being that White has a better distribution and a stronger board in (a).

5-1 looks like a very poor roll.

In (a) I would play 9/3 quietly and wait for a better roll. In (b), while White has a blot in his home board, I would keep the blot/builder on the 9-pt, trying to make the bar point as soon as possible and I would play 13/8 6/5.

(a) 9/3
(b) 13/8 6/5