Problem of the Week #68: July 18


Cash game, center 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.

Hi,

because this is a problem, i first try to discover what the theme is of the problem. Which dilemma is it that we will be discussing?

Here the rule under investigation is:

A staggler is a take when you're 10 or less pips behind.

And the underlying question is:

Is the staggler in this situation more or less vulnerable?

The analysis should be as follows: Every + move for black (for instance making the bar or pointing on white, or making another inner board point) will steer towards a pass. Every - move for black (for instance dumping a blot or leaving the bar-point or leaving a shot) will steer towards a take. We will have to take eventual gammons in account.

More follows...

greetings k.

Well, i have looked at the moves,

all 6's 51,42,D3,D2,D4,32,43,54 = 24 moves make it a better situation for black, meaning a point on, or a 4-prime, 9 of these moves point on white, and of these there will be, I guess, 2 gammons.

The other 12 moves are not constructive, though not leaving a shot.

So 24 (+ 2 gammons) moves steer towards a pass, and only 12 moves steer towards a take, so it's a pass.

In a match game or a money game without Jacoby (where too good to double makes sense), this position might be too good to double, since there are only few losing risks for black (D5 and D6 in the non-hitting variations) and 9 moves that are really worth of giving it a try (the points on).

greetings k.

ps: great that you're back from holiday Bill

White down 10 i believe, 1/4 of the deck points on white and 3/4 hits loose I believe, however Black being ahead won't hit loose with a lot of those. I've got double/take.

In Problem 68, Black leads by just 10 pips, 122 to 132. If this were a straight race, he wouldn't have enough to double. Here, however, Black has a couple of immediate attacking threats that might push him over the doubling threshold. He can make the four point on White's head with 10 shots (11, 22, 33, 44, 23, 24, and 34). He can also cover the bar point with any six (13 shots, not counting 22, 33 and 24).

Although it would solve most of Black's bear-in problems, making the bar probably would not give Black enough to double. He would have a four-point block, but White would be slotted right in front, ready to escape with fives and sixes. Of the twenty numbers that jump out, only half (51, 52, 54, 61 and 63) would force White to leave an outfield shot. All the rest would put White into a straight race. Even when White is forced to leave a shot, Black will only have a single shot, with hitting chances around one in three.

Pointing on White's head is another matter entirely. Of the ten rolls that make Black's four point, nine add a new inner-board point to his prime. (With the tenth, the roll 11, Black will switch points to hit.) Up in the air against a four-point board, White will be pressured to respond immediately with a good roll.

Together with Black's race equity, these other chances combine to give Black a double. Based on his racing equity, of course, White can take. After all, Black had to stretch to get his double in the first place.

My solution: 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. Including the tossups 39a and 62, my record at this writing is 48% correct.
23 Correct: 28a, 29, 30, 32, 35, 36, 38, 39a, 39b, 42b, 43, 44, 45, 47, 48a, 48b, 50, 52b, 53, 57, 62, 66, 67. 25 Incorrect: 28b, 31, 33a, 33b, 34, 37, 40a, 40b, 41, 42a, 46, 48c, 49, 51, 52a, 54, 55, 56, 58, 59, 60, 61, 63, 64, 65.

Yeah I agree with Mike here. It might be a no-double/take without the Jacoby rule but it seems too good a spot to not double here.

Double/take.

Seems like a pass to me. Down ten pips would be a comfortable take in a straight race (and probably just shy of a double), but contact clearly favors black. The point on head threat, with some gammon potential as well and the possibility of getting stuck behind a four prime, makes this a relatively clear pass to me.

Wow. No double/take

The double seems pretty clear to me. If you point and he dances, you've lost your market. If you point and he can't get out of your home board, you've lost your market. If you don't point, you've got a good racing lead (not huge, but close to a double). So the market swings should tip the scales into doubling territory.

I think white should be dropping this. While his home board is relatively strong, white doesn't have many opportunities to hit. He's not likely to hit from the midpoint, which means he's going to have to hit with the lone straggler. But blacks structure is pretty solid and white's shots are probably going to be indirect at best. If white held the bar point and could be more of a nuisance to black bringing his checkers home, I think it might swing into a take.

10 pips + roll is a nice lead. Black shouldn't have too much trouble clearing the midpoint safely, since it's pretty much a disaster if white's blot gets hit in the outfield- he can't risk a gammon to stay back to luckbox a shot. And 22/23/24/32/34/43/42/44 point on his head, and 11 annoys him, which is a quarter of the rolls. This seems considerably stronger than the average 10-pip straggler position, which is a bare take.

Double/Drop.

Grunch. Doulbe/Drop.

No double/Take

Granted, volatility at this point seems pretty low but it is still hard to believe that black would be more than a 55% favorite here.

Very easy double, with an obvious advantage (both racing and attacking) and volatility through the roof.

The only question is the take... IMO there just isn't enough there for White. Without doing a detailed analysis, White's struggling in almost every scenario. Things have to go well for White to end up 50-50, and that's a bad sign. Because when things DON'T go well, he's usually crushed.

Just like in poker, flipping or crushed is no way to go through life.

Um... um... what????

Seems like clear double and probably a drop. 1/4 of blacks rolls hit and cover white's blot. When black doesnt hit, I dont see it being extremely difficult for black to either outrace white or get home past his blot.

Since you only need to have a 25% chance of winning to take (and actually, more like 22%), this is not a good analogy. In a volatile position like what you describe, it's often correct to take.

Because it's a cash game with the jacoby rule I think it's a double/take. if it was match play I think it would be no double/take but would depend on the score.

no promises on being right, doubling is the weakest part of my game

Not saying I'm right, especially since everyone else thinks this is a double. My reasoning is that black is not a big enough favorite to warrant passing control of the cube to white. Black has to be concerned that white may roll a couple of good numbers to run away and take the lead.
I'd be interested to know how big a favorite black is here. Apparently, he is a bigger favorite than I thought. If someone wants to put it into a spoiler tag, that would be fine.

The clearer part of this question is the double. There is so much chance of turning this from a one point win to a four point win that you must double now. And if white were to drop, black can't feel too bad about that either, as she books a win with only an 8% racing lead.

White's decision is much closer. This would be a clear drop for me if the cube has alreeady been turned because your chance of being gammoned is quite high right now. With the Jacoby Rule switched to "on" you would love to just get out here and move on (but I may be a nit).

I think its close but I say take. Getting pointed on are the only true disaster rolls. If black makes the bar point I'm unhappy, but my chances of rolling a five or a six are good enough for me. And the fact is if I'm white, I could care less if black makes another inside point on this roll. It should make running my straggler that much easier.

DOUBLE/TAKE

Black leads 122 to 132. In a pure race, that would be very close to a double, with Black a about 70% favorite, way more than your 55%.

Now look at who benefits from the contact. A reference position could be the relatively common squeezed bar point holding game : you have the midpoint, he has your bar point and he had to break first, leaving a blot there. It is generally a clear double/clear take with the boards and pipcounts about equal.

Compared to this reference position, Black hits are a little less easy but White is less likely to break contact and most importantly all these men in the outfield mean gammons for whoever strikes quickly, mostly Black.

Race, contact, gammons, everything helps Black.

Um, yeah, I kinda knew that.

What's 50%*(50%) + (50%)*0? Just as an example.

Volatility has very little to do with the take/drop decision, except to the extent that it creates efficient recube opportunities, which might get you another percent or two.

If anything, a LESS volatile position is better for recube equity because you are less likely to zoom into a huge lead, at which point the cube loses most of its value.

25% and an automatic take (ignoring gammons). There are explicit calculations you can do to figure out your take point when you consider the value of gammons (assuming you can estimate the frequency).

But you would basically never snap-call an all-in knowing you were drawing dead half the time and only a coin flip the other half of the time. (The exception being that there was already a lot of money in the pot and your opponent's push was a small amount.)

Volatility describes the situation where your equity will change dramatically depending on the next sequence of rolls.

My comment was that there are many situations where you take knowing full well that things can go horrendously bad for you in the next couple rolls, and even when things go well for you, you've still got work to do. What matters is the *frequency* in which those bad things happen relative to the *frequency* in which things go well.

Most of the time, you're facing cube decisions where you win 10-15% of the time when things go poorly, and 30-35% of the time when things go well. And many of those situations are takes, even though you will never be anywhere *close* to a favorite after the next couple rolls.

Double/ No take

Thanks