Problem of the Week #71: August 8


Cash game, Black owns the cube.




Black to play 5-1


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 think this move depends on the race.

White: 126
Black: 111 (before moving)

So I like 18/13 6/5 to try to break contact as much as possible and get another runner closer to safety. Then I can hope to leap home from the 13-point later on, or keep leaping with the back runner until (with any luck) I can scramble him to safety.

White doesn't have very good attacking/priming prospects especially with Black's strong home board, so I'm fine with leaving the runner in White's home board for now. This also has the benefit of making various White rolls awkward to play.

The alternative 23/18 6/5 leaves Black inflexible and he will risk falling apart after his next roll.

Looks like 2 choices, 23/18 6/5 and 18/13 6/5. Everything else just looks awful (6/1 18/17??!?!). 18/13 6/5 just looks way better in every way. You have a bunch of awful rolls after 23/18, but you have plenty of reasonably safe/productive ones with the 3rd checker on the midpoint. You keep some coverage of the whole board, which makes it tougher for white to get around. You're closer to bringing a 12th checker around (safely) for a potential closeout or to just complete your board. The only upside of 23/18 is that there isn't an immediate shot, but given your structure, the fact that white can't make a 5th point on your head with any roll, and the fact that white has 5 checkers on the wrong side of the board, leaving a shot there isn't so scary IMO.

18/13 6/5

The super obvious play of 23/18 6/5 leaves black with a position that will fall apart fast. White doesn't have a lot of builders by his home board so playing 18/13 6/5 looks better.

18/13 6/5.

If this one had been in "Modern Backgammon", it should be in the chapter "Robustness" or maybe, being too easy, in the introduction as an example of robustness

With a fifteen pip lead before playing the roll, we need to be thinking about breaking contact and trying to get home. In addition, with our blot on the 23 point relatively unthreatened by builders we are free to make a play that doesn't focus entirely on locking up that blot. I believe 18/13 6/5 will be correct by a wife margin over the tempting, knee jerk 23/18 6/5.

The 1 seems pretty automatic, 6/5. Now for the 5, I see 2 plausible alternatives: 23/18 or 18/13. At first glance, I was to pick 23/18. Why stay back, when you lead 105-126 in the pip count after the roll? Very solid lead if it was to be a race, but after 23/28, it would become a mutual holding game (bar vs bar) and Black's lead would transpose into a timing disadvantage. If instead Black plays 18/13, it gives him a spare on the midpoint and the back man can still control some part of the outfield without being in real danger (White wouldn't hit loose with Black's strong board).

18/13 6/5

I must be missing something here. I don't see another good play besides 18/13, 6/5
There is no need to move the blot off the 23 point as there is no roll that white can point on its head. The blot is an asset right now as we're still hoping to hit white and maybe close him out.

Answer - 18/13, 6/5

Hi,

Everyone is answering 18/13 6/5 as a solution , that's why it makes me look to the other reasonable option:

23/18 6/5

right now white has two blots, is he able to safe them both next move?

Safety is an issue here since blacks board is strong.

It is not only black thats having a lack-of-spares problem, white has it too.

After 23/18 6/5 the only moves that solve whites problem are 53,54,D5 and 56 = 7/36.

The other 29/36 moves give a minimum 11/36 shot, let's give black 10 out of 36.
And after hitting there is a rather high gammon chance of about 50%.
The other moves will not all be winners for white, black can play small crumbling numbers,still keeping a threatening board, and with white still rather stripped he will have some more hitchances then.

White might also crumble, or black may leave a later shot that is not hit.
All later not hitting variations will serve black since he is ahead in the race.

If black plays the most suggested move the black force will be somewhat disconnected, and white has a lot of outfield control.

All in all, I dare y'all by suggesting

23/18 6/5

IDK, it DID occur to me that Black's strong home board could mean that he'd want to try to maintain contact instead of breaking it.

Plus metagame suggests that because 18/13 6/5 looks completely obvious once you examine the race, it therefore can't be right.

But if Black wants to maximize gammon chances, it's far from clear how to go about that. I could just as well argue that he wants to get another builder for his home board ASAP, and that 18/13 6/5 makes progress towards that goal with minimal risk.

But who knows. It could well be the case that with 3-play lookahead, there's some weird aspect of the position that makes 23/18 6/5 better. If so, whatever, the exception proves the rule I guess.

I think I blundered yesterday. Not that it is the deciding factor, but I completely forgot that gammons were already activeated and we own the cube. Nice problem

18/13, 6/5

Ignoring the the gammon-hungry desperados who might hit 23/18, 3/2*, there are only two choices in Problem 71: play safe with 23/18, 6/5, or run with 18/13, 6/5.

With the safe play, Black's plan is two-fold. Hit a blot if White leaves one, or roll doubles. Black is out of time, however, and if he can't execute his plan on the next roll, he'll probably be forced to break one of his outside points. Planning to roll doubles on the next shake is not much of a plan.

A more flexible approach is to run now. By putting a third man on the midpoint, Black buys time. White will take a big risk to hit loose on the twenty-three point. White has no cover, and if he is hit in return, he'll be facing a five-point block. If White had any real threat to attack on the twenty-three point, or if Black were trailing in the race, safe play would be preferred.

My solution: 18/13, 6/5.

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 47% correct.

White will have the same difficulty saving his blots regardless of the move Black makes. All the gammons you seek are available whether Black runs or plays safe.

Of course, White might hit with doubles when Black leaves a blot on the twenty-three point, so perhaps safe play will give Black slightly more gammons. On the other hand, the increased coverage of White's board provided by a blot on the twenty-three point should make it easier for Black to hit and win a few gammons that way.

18/13 6/5 is the computer choice , the disciplined human and the rollout choice too. By far the best actually. Safe margin.


Of course my human aggressive choice is the obviously risky 23/18 3/2 that comes 3rd in rollouts . I still however wonder if rollouts are done including cube decisions properly (even if they claim so) during those games (ie the effect of actually at some point doubling the opponent and he drops etc). He has 44.4% chance to not re-enter on first roll and then its party time usually. Of course if he hits we have only one back and he cannot any time soon cover a 5th blot inside his home so we will get out anyway at some point . But apparently what happens there is that we increase in doing so our gammons but we reduce a bit our wins and improve also his gammons . So assuming the simulations take into account properly the cube later on each trajectory studied then i suppose i have to abort this idea and accept the original safe choice i had which is the running choice not the locally safe choice because the locally safe becomes later risky .

Still funny how if i was playing live i would give it a try to play the risky hit choice unless i was on a disciplined day. What is for sure though is that i either play the best or the third but almost never the totally obvious to all people 23/18 6/5. No for me its either the run or the hit one not the second. Too bad its actually quite a bit inferior to the prime choice and not even close actually. Ah to be human and imaginative...and mortal.

An obvious question arises from all this by the way. In rollouts it is assumed the games are played between 2 computers . In reality of course you are playing vs a human opponent. Which begs the question now. Since a human opponent is more likely to make some kind of future errors (even in cube usage) is it still ok to argue that one move is better than the other if one of the moves for example is more likely to induce more errors for the opponent than the other "safer" choices? I wonder if there is some kind of stability argument that makes it impossible to argue along these lines convinvingly that ultimately an inferior rollout from computer vs computer choice proves better in a human real life problem because it leads to more hot waters so to speak lol. Maybe the effect is very minimal.