Problem of the Week #149: August 12


Cash game, White owns a 2-cube.




Black to play 4-1.



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.

I guess I'm missing something this time since 5/off is the only play I can see.

Good lead = safety first.

5/0 I guess. Bears off a checker and doesn't leave a shot after 4-4 next turn.

With white this cruched and with the dual blot/man in the outfield I think I'm playing for blood here. Getting hit could even be a bonus in some permutations, and our eyes should nearly always be firmly rested on playing as hard as possible winning gammons whenever we have such low risks in the worst case scenarios.

Sure we have a few extra long(ish) tail perms where we get in some kind of trouble compared to playing safe, but this is not a game for the meek - especially when white is in such a torrid state.

4/off 1/off

Two off seems like the right play, partly because of the question format. if I was on autopilot I could see playing 5/off or clear the 4 but White's in tough shape here and our risks are so low...go for the gammon.

4/off 1/off

for white 40 points to get the backman in the homeboard, 10 to get the other checker = 50.
average throw=8.6 divided by 2 = 4.3 per dice
50/4.3 is about 12 dices
with the 2-point occupied and 4 checkers on the 6point, black needs maybe 20 dices to get his men out, so playing this safe is no recipe for a gammon. if white hits, which in this state is not advisable, blacks board is much stronger than whites, so nothing to loose. only 2-1 and 2-2 could give white maybe a glimmer of hope to win.

When Black plays safely in this position, it is pretty easy to narrow his options to just two. That is because Black cannot play a 4 from his 6pt. His only choices for the 4 are to play from his 4pt or 5pt. The only two safe plays are 5/off and [4/3 4/off].

Between the two, my first instinct is to lift the 4pt. It begins the bear off, and also leaves a flexible arrangement of checkers for the future. Black will be completely safe on the next turn, and probably for the turn after as well. By the time he has to leave a shot, if ever, he should have five or six checkers off. Even if he is hit, against White’s crashed board, he will be a big favorite.

The other safe alternative leaves a much more brittle position, both stripped and stacked. On the following turn, a roll of 64 will force a blot, and eight others (65 62 53 42) fail to bear off any checkers. 44 opens up a double gap.

If those were his only choices, it is an easy call. Clearing the 4pt is much the better of the two.

What about leaving a shot? Can Black increase the rate at which he wins gammons when he rips off two checkers now? If he does pull two, he will have 13 crossovers remaining. White will need 8 to beat the gammon. By itself, this does not seem to give any motive for taking a risk. On the other hand, there is little reason not to. The 2 that White would use to hit is duplicated. White also needs a 2 (or 1) to safety the exposed blot in his home board. Furthermore, unless White hits with a roll of 22, he will leave many return shots.

Let’s count the return shots when White hits with each of his 2s. Although hitting may not be best, here are the best plays for White when does hit:

• 21E (Each) = 23/21*, 3/2 — Black has 32 return shots (any entering roll)
• 22R (Run) .= 23/21*(2), 12/10, 3/1 — Black has 1 return shot (55)
• 23U (Up) .x= 23/21*/18 — Black has 23 return shots (any 1, 3 or 4 except 11 12 24, plus 66)
• 24R (Run) .= 23/21*/17 — Black has 22 return shots (any 1, 3 or 4 except 11 12 24)
• 25R (Run) .= 23/21*/16 — Black has 22 return shots (any 1, 3 or 4 except 11 12 24)
• 26R (Run) .= 23/21*/15 — Black has 23 return shots (any 1, 3 or 4 except 11 12 24, plus 55)

Once the hitting begins, Black has a chance to suck up all of White’s blots, and coast home to a gammon victory.

My solution: 4/off, 1/off.

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 54%.

4/off,4/3

He could play 6/1 and it would be a safe play for this turn.

65 and 62 don't fail to bear off a checker, at least one, don't they?

Right on both counts! Thanks for pointing these out.

Adding them into the mix, however, does not change my conclusions.

4-1 4-off for me

Do you mean 4/3 4/off or 4/off 1/off ?

the latter sry

Hm, im sure i would play 5/off otb and this seems to be wrong.
Taking 2 checkers off looks safe and gives us much better gammon chances.
4/off 1/off

The cube has been turned and White is in a pretty bad shape. If all goes wrong there is still alot of life after death for Black. Go for the gammon.

4/off 1/off