Problem of the Week #53: March 7


Cash game, Black 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.

Obv I'm a complete amateur but I think 15/12 13/12 is better than going for the hit on 9. The hit leaves a lot of return shots and blacks home board is not great. Although quite far behind in the race black should get some shots later in the game (especially if we make a point on 12) and I would play 15/12 13/12 with the intention of building the home board up a bit and hoping for a later hit.

White is ahead in the race so black is going to want to hit.
The only other move that makes sense is 15/12, 13/12 but that doesn't appear to be so useful.

Answer - 13/9*

Also if we go for the hit and white does hit back, black is in very serious trouble. White has a very strong board and black could easily end up with two in the sky against a four or even five point board which is clearly a disaster. Def think I err towards making the point instead of hitting.

Too much risk not enough reward with hit. 15/12 13/12. Make a home board point or two before hitting.

We're behind so we want to keep as much contact as we can I guess. The only safe play would be 15/12 13/12. Yest it cleans 2 blots and yes it re-establish a midpoint, but it looks like it doesn't hinder White at all.

We could hit with 13/9*. After that, White would have 12 return shots, which leaves the least number of shots aside from the safe play.

What else do we have? What about 21/18 6/5? Forcing maximum contact and building our board. But White has the better board right now, so is it wise to try starting a blot hitting slug fest? On the other hand, we can't be doubled out and White has 4 checkers out of play for now, so that might favor a long and complex game where we can take advantage of all our active checkers.

We're so behind in the race that hitting wouldn't gain much (a tempo at least), so I discard the hitting play. If we go with 21/18 6/5, we pretty much force White to hit and we commit ourselves in a defensive game (back or holding game). After a second thought, I would re-establish a midpoint with 15/12 13/12. It is safe, bridges our checkers together and keeps a little control in the outfield. White's bearin is not gin at all and with the 12 pt made, it would make his escape more difficult if we hit him. Plus, the safe play probably loses less gammons (now that the cube is turned).

15/12 13/12

This looks miserable. If you lose much more time (losing pips getting hit and possibly whiffing or getting hit again after a 3), your chances of getting gammoned are going to get ugly. Hitting gets a few pips, but you're in no position to contain, so I don't see it as worth the risk. Play safe, try to make some home points, and look for a safer shot off the 12 or in the outfield off your anchor. Even if you don't get one, you're just losing a single instead of a gammon most of the time.

15/12 13/12

If this position had not been presented as a problem, I would undoubtedly make the twelve point, 15/12, 13/12, saving both outside blots. As things stand, the only roll White has that fails to hit one or both of them is 21. Any four, five, six or seven will hit. The real danger for Black is that he could end up with two blots up, while White cruises home unopposed. The pip count is 149 to 108, with gammon chances that are low, but still significant.

In the context of a problem, that answer seems a bit too obvious. Is this some kind of a trap? Unstacking the six point, 6/5, 6/3, would certainly be nice, but can Black afford the risk? I think not. So, what about hitting White, 13/9*, offering a return hit with 11, 12, 13, 15, 36, 45 and 55 (12 shots)? This seems premature, leaving the six point badly stacked, and offering little chance to contain White.

All things considered, I'll stick with the small play. Let's make the twelve point, save the gammon and resign ourselves to limited, late-game chances for a hit.

My solution: 15/12, 13/12

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.
18 Correct: 28a, 29, 30, 32, 35, 36, 38, 39a, 39b, 42b, 43, 44, 45, 47, 48a, 48b, 50, 52b. 15 Incorrect: 28b, 31, 33a, 33b, 34, 37, 40a, 40b, 41, 42a, 46, 48c, 49, 51, 52a.[/I][/B]

Hitting seems far too desperate. Even in the best cases, white is going to have plenty of time to escape before you build up a formidable board. You also greatly increase your chances of losing a gammon by playing loose.

Make the 12 point and hope to roll some small numbers to unstack that 6 point and put those checkers to work.

Grunch: 13-10-9*.

Okay, lets try to analyze this position.

Black is far behind, has two blots and an enormous stack on 6.
Whites innerboard is 2 points better.
White has 4 checkers out of play on the 1 and 2 point.

Possible plays:

a) 6/5 6/3
b) 13x9
c) 21/18 6/5
d) 15/12 13/12

the safest is d)
the most unstacking is a)
the most contact gives c)
the most pip-gaining is b)

First i'll look at c)

all throws hit one blot, and 41 51 61 42 52 45 55 22 33 hit double.
So 15/36 chance on a double-hit. This gives white a lot of time to come home safely without black improving his reception commitee.
It will most probably result in a 4-pt holding game with 10-25 % gammon chances.

Lets say black wins 20%, loses 70% :singles and 10% gammons:

equity is: 0,2-0,7-2x0,1 = -0,7

Now a)

again all throws hit one blot, and the chance on a double hit is 42 52 22 65 = 7/36.
The double hits will be losing again, the single hits give some return hit chance: for example if blot 13 is hit the return chance is
32 42 = 1/9 So in 1/9 * 29/36 is about 10% of the games black will get some blot hitting-contest chances in which he is the underdog
so lets say he will win maximum 4% more than in c) and has 8% gammon losing chances so...

Black wins 21%, loses 72% singles and 7% gammons:

equity is: 0,21-0,72-2x0,07 = -0,65

d)

In his first following move the crossing of the white 9 checker will leave no, a direct or an indirect shot
(of which the 13 blot will only leave a 1/9 shot instead of the 1/6 shot on the 14 point.)
Lets say the medium shot is 1/6. And later on the crossover of the 8 point checkers will probably leave a direct 1/3 shot.
So the chance of black hitting is totally 50%. But since the difference in inner-boards black is still the underdog here.

Say he wins 20% of the holding games and 40% of the hitting games, and there are no gammons here.

Equity is: 0,30 - 0,70 = -0,40


b)

And now, the hit 13x9.
White has a return hit on: 11 21 31 51 36 54 = 11/36 (31%). Lets for simplicity-sake say that the return hit will conclude in a holding game and the
rest in a hitting game with some more chances for black (compared to a) c) and d)) because of the white blot on the bar giving some chances to make another inner-board point.

Say he wins 20% of the holding games and 50% of the hitting games:

equity = 0,2x0,69 + 0,5x 0,31 - 0,8x0,69 - 0,5x0,31 = -0,41.

Conclusion: My answer is 15/12 13/12.

hit because we own the cube. we dont have to fear a double if he hits us with one of his 11 return shots. if our opponent held the cube or the cube was in the middle id make the safe play of 15/12 13/12.