yogiman, you said to bleep69 to avoid beginner problems, and you reply with a problem like that? Come on man, you can do better than that!

Grunch.
OTB I would have played 11/8 3/2 or 11/7 and hoped to get a shot.

The QF makes me look toward a crazy-looking 16/12, forcing things and duplicating 3s. White should not be happy to hit if he can't cover. But a lot of rolls would hit at least 1 checker and clear the inner board blot for White (1-1, 2-2, 3-3, 2-1, 3-1, 3-2). That's 25% of the rolls and gammons are already activated, so that's too risky.

After the roll, we're 6 pips behind in the race, so no big deal.

I guess I'll stick with 11/8 3/2.

I'll post position numbers if I post another position. The problem with assessing the difficulty level of a problem that is above your current pay grade is another matter however!

In the problem posted by Mike, I would have great difficulty playing a move that splits the checkers on the 16 point. We get hit with a majority of rolls (22), and the position isn't great when we are on the bar.

I'd play 11/8 and then either 3/2 or 8/7

I am not here to do exam. And what is also important is the equity difference between the "obvious" move and the right move.

Another thing is that it is a bad idea to mix problems. After the rollout you have got half a day (12 hours) to show your view on the story, and 1 day to post a problem, and we just go on. If it is really important you can make a new topic.

And in order to get around the QF expectation issue I propose the following. If you intend to come up with a new problem, throw first a dice. If the number is 6, present a problem in which the obvious move is actually the right move. ??

I think Z and Yogiman are right. We need to slip in a few positions where the obvious play is also the right play. That should damp down some of the quiz factor.

In future, I'll be doing this. You are warned.

Mike

Black to Play 3-1
XGID=-BBDB-B--a-A----B-bbcab-d-:1:1:1:31:0:0:0:0:10
White - Pips 71

Black - Pips 81

Position 37 is an example of a rare class of plays that arises in the last stages of contact. Here are some of the characteristics:

• It is near the end of contact. If White does not break contact on this turn, he will likely do so on the following turn.
• Black trails in the race. He may have some race equity, but hitting also counts for a lot.
• White has defects in his board. If Black gets hit himself, it may not spell doom. This matters less if Black has little or no race equity.
• Black can place a checker 6 pips away from the last White straggler.

The key here is the distance. There is a surprising number of rolls that total less than 6 pips: 11, 21, 31, 32, 41. That’s 9 out of 36. When you station a blot 6 pips away from an opponent’s blot, 25% of the time he will roll 5 or less! A quarter of the time, you will get a direct shot. 5 pips away is a different story. There are only 5 rolls that total 4 or less.

As players, we are used to staying out of direct range. We like to keep our blots 7 pips or more away from the opponent. If we must come closer, we know that coming as close as possible reduces shots. 1 pip is better than 2. 2 pips are better than 3. And so on. In a position such as Problem 37, those are the tactics the race leader will be following.

In most cases, the race trailer will do the same, particularly if he has some race equity or being hit carries a significant cost. When, however, the criteria listed above are present, the trailer may have an opportunity for a bold alternative. Forcing contact will often be the way to go.

In Problem 37, Black can stay back if he wants. His blocking point is 7 pips away. White has 17 rolls large enough to pass (66, 65, 64, 63, 62, 55, 54, 53, 44, 33, and 22). The problem for Black is that White can play the other 19 rolls efficiently on his side of the board. Some of them will patch up White’s board. All of them allow White to stay safely out of direct range. Black will get only 6 fly shots, and when he misses, he may have difficulty playing safely himself. That could force Black to keep his outfield point, and hurt his race by moving more checkers to the lower points of his board.

Now look what happens when Black splits his outside point. If White does not hit, Black will have made the best move, both for racing and hitting. Here is a breakdown of White’s rolls:

• 9 rolls fail to hit or pass: 41, 32, 31, 21, 11
  These are very good for Black. He gets a direct shot, plus a few fly shots. Compared to not splitting, Black gains about 390 millipoints of equity on each of these. These 9 direct shots will turn out to be the difference.
  
  
• 9 rolls hit, but fail to cover inside: 52, 51, 43, 42, 22
  With 22, White would have passed without hitting, so Black gains about 250 millipoints by splitting and being hit. The others are a mixed bag. Black loses in the race, but gains 12 or 14 shots from the bar. Compared to not splitting, Black loses about 70 millipoints on each of these. Overall, this group cost Black only about 35 millipoints each.
  
  
• 6 rolls hit, and cover inside: 66, 63, 61, 33
  Of these, only 61 would have been blocked if Black had not split. That costs Black 750 millipoints of equity. Perhaps surprisingly, Black gains about 70 millipoints by splitting when White rolls 66. That is explained by the awkward stack White must leave on his ace point. The others, 63 and 33, cost Black about 325 each. Compared to not splitting, the plays in this group cost Black around 415 millipoints on average.
  
  
• 12 rolls pass: 65, 64, 62, 55, 54, 53, 44
  There is not much difference here either way. Because splitting will diversify Black’s race, he picks up an average of 13 millipoints on these.

The totals tell the story: 9 rolls gain about 400 millipoints each, while 6 rolls lose about the same. 12 rolls gain about 15 millipoints each, while 9 rolls lose round 35. On balance, Black gains when he splits.

My 15k rollout follows. Overall, it has splitting (16/15, 11/8) ahead of safe play (11/7) by 22 millipoints.

Mike


15k XG2 Rollout – Unlimited Game, No Jacoby, No Beavers

Black to Play 6-3
XGID=-BDB-CC-a----------aAcbdd-:1:-1:1:63:0:0:0:0:10
White - Pips 53

Black - Pips 69

What and why?

Mike

I don't know what the obvious or correct play is. If you run all the way, small numbers hit for white and big numbers are good for the race. If you stop at the 14pt. 3 more numbers hit, but small numbers are really bad as in your previous post. It probably matters where you stand in the race, and I'm not too good at figuring that out when the pip count is an inaccurate assessment. I guess I'll run all the way thinking our racing chance are pretty good. I think we get more return shots when we are hit on the 11pt -11, 21, 31, 63 (should white even hit with 63?) vs 15, 24, 61. I don't know if that has any bearing on the right play.

Well, if it has anything to do with the previous theme...

Ok, the 6 is easy because it's forced: 20/14

Now for the 3, 3 choices: 14/11, 6/3 or 5/2. I would eliminate 5/2 because it is inferior to 6/3. I'd play 6/3 and hope White rolls small or has to hit us. With the 2 high points open in White's house (do not confuse with the White House) including a blot, I'll happily go with 6/3 for the 3.

20/14 6/3

All I meant is that it's not always "obvious" to determine if the solution to a problem is... obvious or not. The seemingly obvious problem posted by bleep69 generated different answers and a small discussion. The one you posted right after had a unanimous answer and little place for debate.

Mike, thanks for the detailed breakdown of the previous problem. It raised a question in my mind though - are expert players breaking down the move like this OTB? Or is a more general assessment done based on past experience and knowledge of percentages? I find it takes me forever to work out the number of good rolls versus poor rolls, so to go into that level of detail would be a game killer at the moment!

As to the current problem, the 6 is forced, 20/14. The 3 seems irrelevant, as after the roll we will be 7/60 = 11.6% behind, with a chance of being hit, and so will have to drop the cube, surely? Assuming I've made an error there, likely considering my abysmal cube play, I would move 6/3, based on the fact you revealed in your previous post, that 25% of his numbers leave us with a hit when he rolls less than 6 total. Getting hit in this case is not so bad, as we then have another return hit as he tried to come through completely.

So after that somewhat garbled analysis, 20/14 6/3

Black to Play 6-3
XGID=-BDB-CC-a----------aAcbdd-:1:-1:1:63:0:0:0:0:10
White - Pips 53

Black - Pips 69

In the problem before this one, Problem 37, I identified four criteria that might motivate you to volunteer a direct shot during the last vestiges of contact.

1. It is near the end of contact. If White does not break contact on this turn, he will likely do so on the following turn.
2. Black trails in the race. He may have some race equity, but hitting also counts for a lot.
3. White has defects in his board. If Black gets hit himself, it may not spell doom.
4. Black can place a checker 6 pips away from the last White straggler.

When your blot is 6 pips away from an opponent’s blot, there is a 25% chance he will roll low, and fail to pass. The shots you pick up on those variations may be enough to tip the balance in favor of moving within direct range. Getting hit, however, carries a price. That’s why this sort of play requires that your opponent have some defects in his board. The return shots you get from the bar mitigate the damage, but that does not mean you want to be hit. Quite the opposite.

In the last problem, the decision is close. Only 22 millipoints of equity separate the top two plays. In this position, failing to put a blot 6 pips away is a clear error. In fact, it’s a whopper with cheese! 20/14 6/3 beats 20/11 by 140 millipoints.

It may be instructive to pause for a moment, and try to identify why the margin is so much larger in this position. For reference, here is the previous position, Problem 37:

Black to Play 3-1
XGID=-BBDB-B--a-A----B-bbcab-d-:1:1:1:31:0:0:0:0:10
White - Pips 71

Black - Pips 81

I see two differences. First, In Problem 37, there is a respectable alternative that does not require leaving a direct shot. In Problem 38, some sort of direct shot is forced. The only question is which one. Second, White’s board is weaker in Problem 38.

Let’s make it clear that I am no expert! There are many regular posters here, such as Z, Grant Hoffman, 911, Tom Cowley, Aaron W., and dozens of others to whom I apologize for not listing your names, who are much better players than I am. My PR is currently around 7.75. My checker play is decent, near 6.5, but my cube decisions are abysmal, averaging between 10 and 12. Perhaps a true expert such as Bill Robertie might comment on the OTB thought process of a top player.

Having said that, I think the answer is a qualified yes and no. Bill has often described taking a cross-section of 36 rolls, dividing them into groups as I did for Problem 37, and trying to put rough estimates on how many wins and gammons each group generates.

There is a limit to how far you can take this OTB. To reach the precision given in the solution for Problem 37 requires using a bot and tabulating equities in a spreadsheet. I selected the top two plays in GnuBg, and then clicked TM (for Temperature Map). For each of the 21 different rolls, I subtracted the equity of the 2nd-best play from the that of the top play. Weighting non-doublets twice as much as doublets, I was then able to find the average equities for each of the categories I was interested in. You can do a similar thing using Analyze > Dice Distribution in XG, but the GnuBg Temperature Map may be easier to use when making side-by-side comparisons.

So this is the homework I had to do in order to really learn what is going on is these sorts of positions. Before I added Problems 37 and 38 to my flashcard set, I had seen a similar thing before. While rare, these positions come up with a predictable frequency, often at the tail end of a holding game. I did all the calculation in order to test out my hypotheses about what was important in the positions. At the end of my exploration, I formulated the guidelines given at the top of this post. They may be flawed, but they are what I now use OTB. They are also completely original.

Mike

Thanks again for a great answer Mike.

Position ID: mLeHAgibeQgMSA Match ID: UYkJAAAAAAAE

Obvious is not always right...

Despite the caveat, I can't see a reason not to play B/23 6/3. I'm trying to justify hitting on the 13 point, but that allows white the chance to anchor in our home, and that surely is bad?

Great, Bleep69 suddenly gets a brainwave, and decides to give the answer away. I requested in an earlier post that one is not allowed to peek into the hint box. I wouldn't be surprised if this behaviour is related to some nationality issue. And maybe there is more to it, for even the bot is undermining my status quo here, who at the least I would expect to be neutral.


When I reduce black's stack on the 6-point by moving a checker to the 10-point 6/3* will be a doubtful move:
It shows that the extra builder on the 6-point as a direct cover for the blot on the 3-point is of big weight.

Surprisingly, creating a 9-point instead of a 10-point makes both moves even money:
This result diminishes the importance of a direct cover, downplays the value of an inner board point for white and adds to the relevance of a stronghold for black outside white's inner board. I will explain in more detail.
If black plays 16/13* and white succeeds in making a defensive point, he will still be very disconnected, which will give problems sooner or later, not in the least if he has no spare checker behind.
If black plays 6/3* and white hits and enters, black likes to have a stronghold to contain this checker, and doesn't appreciate any further vulnerabilities with a checker on the bar. If white enters with a 5 (without an additional hit), black will like to improve the flexibility of those two semi-stuck hind checkers, and again doesn't want any hassle with loose blots.

So my conclusion is that there are 4 reasons for 16/13*'s double whopper status, and maybe in the following order of importance:

• there is a direct cover in case black hits loose

• loose blots are a liability

• black likes a stronghold to contain white's checker(s)

• double 5 would be a joker for white, getting two black checkers on the bar

I don't see a 2nd checker getting hit...

It would be if black plays 16/13*, but that would be in favour of the move. You are right, it does not belong in the list.

Even if Black plays B/23 16/13*, there is no double hit for White on 5-5.

Just try it.

You're right, my bad.

I thought the whole point was to try and guess the move Yogi? Quite how this relates to my nationality is beyond me, but let's continue with the thread, shall we?

Position ID: mLfBISBme4EBAw Match ID: QYkNAAAACAAE

I'm playing to make the prime, 13/7 6/3 (2). Only 31 or 11 on our next throw are grim.

On second thoughts, we have great gammon chances if we play 7/1 6/3 (2), although we are a fair way off from covering. If I make this play, I do it because of the exposed blot on the 8 point, and white is stuck with the cube looking to get gammoned if he doesn't throw a 1 in the next couple of moves.

Torn between the 2 now... Take the risk, final answer is 7/1 6/3 (2)