Problem of the Week #36: November 8


Cash game. Black owns the cube. Black on move.




Should Black redouble? If he redoubles, should White take or drop?

In this position I would apply Robertie's Rule:

"Give yourself an above average roll (but not your best). Then give your
opponent a below average roll (but not his/her worst). If the resulting
position is still a Take, then don't double, otherwise double."

For Black, I would consider an above average roll to be any roll that jumps out one of his back men and creates more timing for him; a below average roll for White would be one of the many that causes his home board to further weaken.

If this sequence were to occur, it would be a clear pass for White... therefore Black should redouble.

As for White's decision, I am not so certain. He does have a huge lead in the race but because his home board is so fragile and he has no real threats left, I am inclined to think he must pass.

Because I find Robertie's Rule to be so useful for Black in these situations, I cannot help but wonder if the Rule has a corollary for assessing White's decision. Anyone have any insights? Thanks in advance

With White about to crunch, the redouble seems clear.

As far as the take, the problem is that Black has very few bad rolls. The large numbers that often play poorly in these types of positions are mostly fine in this case. 5-4 is really the only awkward toss. With two gaps in White's prime, I think he has to let this go.

This looks like a straight-forward redouble/drop. Black's escape is very probable (two open points to escape through plus decent distribution of spares for some timing). White needs two perfect numbers to escape so he's basically crunched if he doesn't hit the 61 joker. White needs to worry about leaving a blot and getting a second or third checker sent back, and possibly getting gammoned from here.

Black is trailing in the race 126-79 before the roll, but that means that he has the timing on his side. Plus, he has a nice 5-prime that he can extend/roll forward to contain White's back man.

On White's side, his spares are a bit deep (3 and 4 points) and, even if Black splits/escapes one back man and White points on Black, White will have a hard time escaping his own straggler. White is not in great danger of being gammoned, but does his winning chances are high enough to justify a take? I say no.

My take: Redouble and a close Drop

Black should not redouble. There's not enough scenarios where black can maintain his prime while white will be forced to crunch his board.
White can escape with a 6-1 unless black manages to make the 3 point.
If black slots the 3 point, white may be able to hit and then escape next turn.

Black is ahead but I think there is too much that can go wrong at this stage.

If black does redouble, I think white has to take because his chances are too high to pass.

redouble - pass

double/pass

I'm not sure why you think black can't maintain his prime. Can you elaborate a bit?

Also, white's board crunches if he rolls a 4 or 5. I think you should take another look at the position.

1 in 18 shot counts as a big joker to me. I would be focusing on the 17 in 18 at this point.

It may happen, but it doesn't happen quite as often as I think you think it happens.

What rolls do you count for bad rolls for black?

redouble seems pretty clear, maybe its just toogood to ... white need a joker to escape and not crush , and not to lose another 1/2 cheker. in this case i go with the feeling i have with my opponent: uf white is a taker i double, if white is "tight" i try to gammon .

The problem with playing on is that when things go wrong, they usually go horribly wrong, and quite quickly, so you become a dog and are then nowhere close to being able to use the cube effectively.

This is the moment when you have very good cube leverage, and I think you should spin it. White is far from cooked and you should be perfectly content to take the immediate win if he drops.

Plus a whole bunch of things have to go right for you to win a gammon anyway. If things don't go well for White, usually he just crunches and accepts the loss, and even if you pick up another checker, he will still run off the gammon a whole bunch of the time.

Plus it's a deceptive position, and even a very good player may hallucinate and take, making a double even more attractive. (This assumes most of us are right and it's a drop.)

In Problem 36, White has a tougher decision than Black. White’s board is crashing, and he has a man trapped behind a five-prime. Still, he is heavily favored in the pip count, 79 to 126, if only he can get his backman into the outfield. If doubled, should White take? Should he pass? At first glance, the answer is not obvious.

Kit Woolsey provides a doubling rule for these circumstances, a simplified version of which goes like this: If you’re considering a double, and you aren’t sure whether your opponent should take or drop, then certainly you should double. This presumes, of course, that you’re not too good to double.

So, Black should double, especially considering the number of two-roll sequences that will cost him his market. Depending how you count it, Black has eleven rolls that either make the two point on White’s head (such as 64), or else are out-and-out market losers for Black (such as 53). Even if Black rolls a more neutral number, White has many disaster shots on his turn. Almost any large roll is bad for White, but his fives are horrible, many forcing him to break his six point. Black should double now, to lock in his advantage.

Can White take? Probably not. As Bill Robertie teaches, a crashing board is often weaker than it looks. Even though Black will often be forced to switch from a priming game to an attacking game, his chances will continue to improve, while White’s continue to worsen.

My solution: Double/Pass.

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. My record at this writing is 50% correct.
Correct: 28(a), 29, 30, 32, 35
Incorrect: 28(b), 31, 33(a), 33(b), 34

Judging by all the responses, it looks like I got this one wrong, but I'll elaborate anyway.

Just about any roll that black gets will force him to hit on the 2 point or expose a blot on his home board. The only really good rolls I see are 5/3 and 6/6 and 3/3. There's a few other rolls where black can just move his spares around but not that many.

So, I count any 6 besides the 6/6 as bad for black. If black hits, he may eventually have to crunch if white is stuck on the bar. If he doesn't hit and instead moves from the 23 point, white may be able to put him on the bar and escape.

The 5/3 is good. 5/5 looks OK but may cause black to crunch. With the other 5s, black will have to slot the 3 point or move a checker to the 1 point.
Maybe having to move a checker to the 1 point is not so bad in this position.

So, right now, white will have to crunch on a lot of rolls. However, because black has to roll first, I think it will create some opportunities for white

I think you're far too afraid of leaving that anchor. If you have the time, you should give black a 65 and run the back checker, and then roll out the position as white by hand a few times, up the point where either white escapes his one checker, or black gets both of his checkers into the outfield. I think you might be surprised at how hard it is for white to get out before he crunches.

Are Sixes Bad? Should Black Hold His Anchor?
In working out my solution to Problem 36, I determined how I would play each of Black's twenty-one rolls. As White is so close to crashing, I concluded I would be reluctant to break Black's anchor.

If Black moves off the twenty-three point, White has ten shots that allow him to make the point, plus a handful of rolls where he will hit loose if he can. I felt that these tactical opportunities represent most of White's equity, so I tended to hold the anchor.

Even with this strategy, I found to my surprise that sixes don't play that badly for Black. Here's what I would do:

66 - 23/17, 23/5
65 - 8/2*, 7/2
64 - 8/2*, 6/2
63 - 23/17, 23/20
62 - 8/2*, 6/4
61 - 8/7/1 (no hit)

I'm happy to defend my choices with all of these except 61 and 62. What do you think? Are those running dice?

I just run with any six. With the 5-point open, I'm not afraid of getting attacked. White still needs to close the 2-point, then roll a one specifically, then a six specifically, and even then I'm not cooked.

Meanwhile I'm not much of a fan of attacking the runner when I want my opponent moving.

This is a spot where I think I might not point on his head. I'd really like to send a second checker back, and the only way that happens if I allow him to crunch. And he can't crunch if he's on the bar. With two holes to escape through and a good amount of time, I don't think you have to worry so much about accidentally crunching yourself.

When your opponent crunches, I think you can play a little more aggressively for gammons because your chances of getting gammoned go way down. This means that your opponent must literally win two games for every one gammon you pick up, and not something a little smaller.

If white holds the cube, most of his equity comes from the fact that he can recube you out when he escapes if he does it quickly. This would really be the only reason I might hold onto the cube.

I'm honestly more afraid of white rolling something to leave me a shot without advancing his checker, which is then probably a spot where it's a clear drop. I don't want to miss my market, so I want to double now and take my chances with his escape.

No--if you are TG then you are certain about whether your opponent should take or drop (he should definitely drop). If you are really unsure about whether it is a take or drop but it is actually TG (rare case) then maybe your opponent will take. When you are wrong and it is TG it will be a small error when opp passes but you gain hugely when he takes.

Thanks, Atrifix, for the correction. As you say, a complete description of Woolsey's Law analyzes the costs and benefits of the kinds of errors you and your opponent might make in applying his basic rule. I still think, however, I've got his basic rule right: If you’re considering a double, and you aren’t sure whether your opponent should take or drop, then certainly you should double.

As you point out, if you think you are too good, then you are sure that your opponent should drop. My bad.

What do you think of think of description given by Phil Simborg at http://www.simborgbackgammonlessons....for-the-gammon? Even more than we have in this discussion, he describes the pros and cons when you or your opponent make a mistake in the application of Woolsey's Law.

Can you point me towards any other good online descriptions?

Yes, right.

Seems fine to me.

http://www.bkgm.com/articles/GOL/Aug02/rule.htm