Problem of the Week #146: July 1


(a) Cash game, Black owns a 2-cube.




Should Black double? Should White take if doubled?


(b) Same position with the score tied 1-1 in a 5-point match. Cube in the middle. Should Black double? Should White take if doubled?

(c) Same position with the score tied 7-7 in a 15-point match. Black owns a 2-cube. Should Black double? Should White take if doubled?


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.

a. double/take. there have to be lots of market losers - but easy take
b. play for gammon no double/take.
c. double/drop too many gammons to take.

a) double/take
b) no double/take
c) double/drop

a) Double / Drop
b) Double / Drop
c) Double / Drop

Too dangerous for white to take, imho. Wait for a better chance.
But I'm a fish!

Hi

B. position/attack looks strong and white may be gammoned quite often.
4s 5s and 6s escape and attack also in the homefield but is this really duplication?!
I would'nt want to put the match on the line in this game - drop in b+c for me.
No recube power in b and gammons win the match for white in c.
In a Moneygame b may get some efficient recubes and maybe ... but i would`nt take this. Looks too expensive...
I'm a fish too

(a) Cash game, Black owns a 2-cube. Should Black double? Should White take if doubled?

Positing a double and a take, I put the cube on White’s side, and then played this position out 100 times. From this tiny sample, I conclude that Black is a favorite, but is not quite good enough to double. Black wins about 58% of the games, and wins a gammon in a whopping 26% of all games. White wins very few gammons. More often, White is able to offer an efficient redouble that Black must take. Combining these, we have White winning 42% of the games, with 10% of all games resulting in a gammon victory for White, or else culminating with White winning 4 points after a redouble has been accepted.

No double, take

(b) Same position with the score tied 1-1 in a 5-point match. Cube in the middle. Should Black double? Should White take if doubled?

Now the gammon threat is severe. If White takes, he may very well lose the match in this game. Black’s gammon threat increases his match winning chances (MWC) enough to offer a very efficient double. White’s decision to take or pass is close. When White drops, the Kazaross XG2 Match Equity Table (MET) for 4-away, 3-away sets his MWC at 43%. After a take, my data give him only about 40%.

Double, pass

(c) Same position with the score tied 7-7 in a 15-point match. Black owns a 2-cube. Should Black double? Should White take if doubled?

Now the score is 8-away, 8-away. Black still has a strong double, but this time the MET gives White only 38% MWC when he passes. My data for a take push that to around 41%.

Double, take

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%.

Challenge Question

Rolling this out by hand taught me quite a lot about checker play in this position.

For instance, how should Black play 53? Why?

What about 56?

(Assume that White owns the cube at 2.)

Even though Black seems to have a well-timed backgame, his big numbers are duplicated and his bar point is open. He might be a slight favorite in the game, but it doesn't seem to me that it's enough to double.

In all 3 situations, I go for No double/Take.

Note: Read last week's problem. Had a few too many drops as White!

Challenge Question Answer

Black does not yet have enough ammunition to launch an attack. So when he rolls a 53 or 65, he should not hit loose on the 1pt. Until he gets a modicum of outfield control, Black cannot sustain being hit in White’s inner board. In the case of 53, there is a second reason Black should not hit. Doing so would place him in the precarious position of needing to escape a runner on his very next toss, or else face the prospect of cracking. With both 53 and 65, Black should use the 5 to jump out with a runner.

But from which anchor?

Usually, it is automatic to keep the most advanced anchor. When Black rolls 53, however, keeping the higher anchor, the 22pt, while running from the 23pt, would provide an opportunity for White to attack when he rolls a 3. It is better for Black to break from the 22pt. Then, White’s hitting numbers are 1 and 2, the same numbers he needs to enter from the bar. Duplicating these numbers is the reason Black should abandon the 22pt. With 53, Black should run one checker all the way.

When he rolls 65, Black can keep the higher anchor, and still obtain the same duplication of 1s and 2s. He should run both checkers off the 23pt out to the 17pt and 18pt. Thereafter, White can hit only when he enters with 11, 21 or 22.

53R (Run) = 22/14
65R (Run) = 23/18, 23/17