Problem of the Week #126: November 6


Black on roll, center cube.




(a) Cash game. Should Black double? If Black doubles, what should White do?

(b) Match, score tied 1 to 1 to 5 points. Same question.

(c) Match, Black leads 2 to 1 to 5 points. Same question.

(d) Match, Black leads 3 to 1 to 5 points. Same question.



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
b) double/pass
c) nodouble/take
d) nodouble/take

Well done.

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

I can't drop here even 4away

As White, I would take in all variations. I don't think it's nowhere near a drop.

I would probably double in a cash game, although it might be a thin double. In the other 3 scenarios, I would hold the cube. If Black's attack succeeds, I can then play for the gammon. If it turns bad, I'll be glad I still have the cube and its leverage in such a short match.

(a) Double / Take
(b) No Double / Take
(c) No Double / Take
(d) No Double / Take

a) Double/take seems easy. Race lead and some blitzing gammon chances, but nothing absurd enough to drop.

b) Double/drop. Losing the doubled gammon here is brutal. Losing 1 is about -7%, 2 about -17%, and 4 -50%. So a doubled game is 2.5x bad instead of 2x bad, and losing a 4 is 7 times as bad as losing a 1. Since you're clearly behind, and the gammon chances are real, this works strongly against you taking.

c) This is the tough one. I don't know how anybody could do this math OTB with all the possible scores in play. Gammons are discounted and my singles are better than his (+10 for me, +7 for him from above) as we speak, both of which lean towards not doubling. It's a pretty easy take though as dropping is 33% to win while insta-shipping has to be at least around that, plus there's some leverage left in holding the cube to just lose a single and go down 4-1 instead of playing for the match. ND/take

d) Doubling here is godawful since he reships and plays for the match. It completely nullifies your gammon advantage and your singles play for 2 and his play for 4. ND/take/reship/fistpump.

I dont need to make a reply cos its this +1000.

Hi,

How good is black's position?

Pure positionally white's position is better:
No checkers out of play
A good prime potential

But on the other hand the black position is very good for a blitz.
If there were a white checker on the bar (as in a normal blitz), it would be a clear Double/Pass.

Here with only one checker back and not on the bar, it's a handicapped threat double.
Due to the high diversification of hit numbers (34 out of 36) it's still a double, but a take (certainly in a cash game where gammons have to be activated, but also at the score 1-1)

Ats 3-1 the doubling window is on [81-82] and I estimate black below 80%, so No Double.

The score 2-1 is the most interesting here. Although the doubling window here is [52-74], suggesting a double, there is more to it.

As soon as black has doubled and white has taken, suddenly gammons aren't as valuable for black, but they have a lot of value for white.

So black has to play careful with a position that is positionally unsound. Every direct shot will probably put white in his redoubling window [31-60].

Which, if taken, would make it virtually DMP, where white has the better hand.

So:

DT/DT/nD/nD

p.s.

Our manual rollout so far gives white 4 out of 5 wins. But with only 5 games played, it should be luck.

This is my answer as well. I suck at match, but even I know that doubling at d) is just insanely ******ed.

Left to my own devices I'd say D/T, D/T, ND/T, ND/T but based on some of the replies it looks like (b) is up in the air. if (b) is indeed D/P then I need to be walked though why since over the board I'd have taken as white. I kinda follow what Tom said but could use a better understanding of it. All the other answers looked clear to me.

Hi,

here an update on the manual rollouts so far:

After 10 rollouts black is on 61% (black won the last 5 games, after losing 4 of the first 5).

So, according to the rollout so far, only a) looks like a DT, b) a tossup, the rest nD.

Grunch: Although the solution for this has already been posted, I thought I would take a stab at this before checking it.

Background
Black likely rolled 55 at some point, and began an attack that has, up to this point, been inconclusive. Evidently, it was never good enough to get a double in before this turn.

Although Black has a substantial lead in the pip count, 112 to 140, this game is far from a race. After Black escapes his last back man, we can talk about the race. White has the better structure for a priming game, so Black should be thinking about attacking or escaping. Left unmolested, White will have many point-making rolls on his turn, so hitting is likely on the menu for Black. The fact that he has White out boarded, 3 points to 2, also indicates hitting.

In the second backgammon seminar presented by the US Backgammon Federation, Phil Simborg gave a very useful decision tree for doubles. It is based on considering the take, before examining the double:

1. Obvious pass — Unless you are too good, it's a sure double.
2. Close take/pass — By Woolsey's Law, it's a sure double.
3. Easy take, close double — Apply John O'Hagen's Law of Market Losers. If at least 25% of the subsequent two-roll sequences (your turn followed by your opponent's) are market losers, you should probably double. Don’t be dogmatic: it matters how much you lose the market by, and it matters what happens when you roll a bad roll.

Part (a) Money Game
For money, this looks like an easy take. Does Black have enough market losers to justify a double? After a hit and dance, White won't have much stomach for taking. POH (point on head), followed by a dance, is a clear pass (11 rolls: 11, 33, 44, 55, 66, 45, 46, 56, although 56 my best be played by running). Outside hit/dance looks like a pass (3 rolls: 62, 22, and 44 as well, but 44 was counted above). Loose hit inside/dance doesn't look too good for White either. And simply escaping with a 30+ pip advantage might change White's attitude about taking.

All in all, it seems pretty close, but when you throw in the fact that much of Black's equity in an attack comes from the gammons he can win, doubling seems mandatory. Otherwise, the Jacoby Rule prevents Black from collecting an undoubled gammon.

My solution in Part (a): Double, take

Part (b) Match Play, Tied at 4-away
At this score, Black's gammons play very efficiently for him, both before and after a double.

My solution in Part (b): Double, take

Part (c) Match Play, Black leads, 3-away to 4-away
At this score, Black's gammons are only efficient if he does not double. After a double, Black effectively gets only three points for winning a gammon. As stated above, a significant chunk of Black's equity in an attack comes from his gammon wins. Doubling here would only dilute them.

My solution in Part (c): No double, take

Part (d) Match Play, Black leads, 2-away to 4-away
A double here is "gammicidal" (a term coined by Danny Kleinman), completely killing Black's gammons.

My solution in Part (d): No 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 50%.