The Sharp End Answers

If you haven't seen the previous post, entitled The Sharp End, go there first for the problems.

Let's take a look at them.

Position One


Black (me) trails 3-away, 2-away. Sometimes position are much simpler than they appear. Black trails in the race 72-104 before the roll and although White's count is not as good as it looks, with the gap on the 4pt and the stack on the 1pt, that's still a substantial lead. When I first started playing tournaments, which was within a few weeks of playing my first ever game, I felt very intimidated. My opponents would sometimes study a position for an age before making their play. Often on my turn I had no idea what the best play was and no idea how to figure it out either, so I used to do the one thing that I could do in order to look as if I was actually a deep thinker like them. I counted the pips. After a while, I began to realise that the pipcount often indicated the right play! It does here too. Black trails in the race and must stay back as far as possible and block as many rolls as possible. 9/2 is the play, although in the match I actually cleared the 8pt. I was worried about having two blots in board if I got a shot and hit it, but that is jumping at shadows. If I don't get a shot, or I do and miss it, I have two points slotted. If I do hit a shot only 6-4 is enough of a lemon to fail to cover one of them. Stay back, block points, build a board as fast as you can, all point to the best play, 9/2. 2/3 for the panel.

Position 2


Position 1 wasn't even tough when looked at closely. This one is. It is of course the next play in the game, but now things have changed radically. One feature of the last position was that White would only be forced to leave a shot with some sixes, but now all the fives (except 5-5) leave a shot too, so plays like 9/3, 5/1 or the panel's choice of 9/3, 6/2 are less palatable. You have to volunteer a shot with 9/5, 9/3.
When White hits and you dance, you are of course sad, but you aren't dead yet and besides, that sequence only occurs 12/36 x 16/36 or about 14%. The rest of the time you are very glad indeed to have the 5pt. 86 glads and 14 sads is a good ratio. 0/3 for the panel.

Position 3


Different match, this position is double match point, that is, any position where the cube is dead and if either side wins the game, they win the match.
In Position One, we saw that aggressive slotting worked well when the opponent was still unlikely to leave a shot immediately and in position two, we saw that 5pt ownership was essential. Both of those guidelines work well here too. I'm not sure what the best play is, but it's one of these. 6/5, 4/2 or 4/1 or 3/1, 2/1! Whichever of these you choose, you can see that either the 5 or 6pts is slotted, essential for Black if there is going to be hitting. The Panel scored 2/3 here.

Position 4


I love this one. All the panel voted to keep the shots down with 14/8, 14/10, but it's right to play 13/3! Why volunteer 4 extra shots? To generate a double hit after 6/5, 6/3, 6/2 and 6/1. It's just about worth it.

Position 5


Not too hard. Black trails 3-away, 2-away, although that is not very important. It's all about volatility with 15 numbers to make the 2pt on White's head and another 17 to hit loose. I doubled this and rolled 6-3 after White correctly took.
Here's a handy tip to quickly calculate the number of rolls that make the 2pt. It's the square of the direct hitters, minus any non working doubles. Here that's 4 squared = 16, minus 5-5 which doesn't work. Saves a lot of work. All our intrepid panel doubled this and only one wasn't sure of the clear take. Thanks to them for their efforts, thanks to you for reading. Until the next time, enjoy the game!

The Sharp End

These are some problems I encountered recently, all coming at the sharp end of the game where there is still a lot of contact and truck loads of equity are at stake on every roll. The first two are from a match I played. Black is on roll, trailing 6-7 to 9. What's your play?

Position One


The second best play is a double blunder, so be careful.

Position Two


And this is the next roll, another opportunity to make a double blunder. What's your play?

The very next day I had a match to analyse for a student and these two positions reminded me of the two we have just seen.

Position 3


It's double match point, so what is Black's play. You can't make a big mistake here, but it's good to get it right and know what you are trying to do, because it's dmp and the wrong play can cost you two wins in a hundred.

Position 4


Same game, next turn. Again, you can't make a big mistake but it is dmp, so even a small mistake can lose you one game in a hundred. What and why please.

Lastly, the bastard child of Positions 1 and 2. I got down to this, trailing 3-away, 2-away. Black on roll. Is it a cube? If it is, is it a take?

Position 5


Fun for all the family! If you get all these right, my hat is off to you. If you know why you are doing it, then you are either Stick Rice or God, certainly a better man than me in either case!

Until we come back to these, enjoy the game!

Answers

These are the answers to the last post, so please go back to "Keeping An Eye On The Masters" if you haven't seen it already.



Black to play 6-1. Mochy played bar/24, 13/7 to keep his anchor, leave fewer shots and bid for a prime of his own.
The cost of this is of course that being hit costs 18 pips and allows White to leave his anchor with a tempo, but by a small margin it is the best play. Bar/18 is a small error.



Should White double this? By a hairsbreadth, this is not quite a double technically, but as a double would in theory cost you 11 thousandths of a point (after a 1296 game rollout), it is in my view worth a punt! It's pretty volatile. If White is a much weaker player than Mochy (as 99.99% of players are) then I think that she should double this and hope to get lucky. Here, White is Paul Weaver, a world class player in his own right, so he reasons that handing a very takeable cube to a man who is arguably the best player in the world is not a good plan!



Now White is on roll. The correct cube action for Black is not hard to find. It's an enormous pass. Is White too good to double? By a small margin he is and doubling is an error costing 0.054 of a point. However, a double is, in my view, a good practical play. Although White has an equity of 1.054 points if he plays on, that is theoretical and he will have to play well to get it. When he doubles he puts a solid point onto the scoresheet without even having to roll, much less play. To me, 1/20th of a point is a reasonable price to pay for that.
All of these positions are from Game One of a 13 pointer between Mochizuki Masayuki and Paul Weaver and this match will soon be available as an annotated file.

In my next post, which will be later today if the Good Lord's willing and the creek's don't rise, I have four ultra tough checker plays for you, all from the sharp end of the game when there are huge amounts of equity riding on every roll. You'll love 'em so stay tuned.
Until then, enjoy the game!

Keeping An Eye On The Masters

On GridGammon I've had the pleasure of watching two superbly played matches between Mochy from Japan and Paul Weaver of the US. I am annotating these and hopefully they will be available in a couple of weeks for students. To whet your appetite here are some cute positions from Match One, Game One.

Position One


Mochy (Black) to play 6-1 from the bar. What should he play?

He played bar/24, 13/7, leaving Paul Weaver White on roll in position 2 below.

Position 2


Should White double?

In the match, he elected to roll and rolled 3-3, correctly playing 24/18*(2). Mochy entered with 4-1 played bar/24, 6/2, probably right, leaving White on roll again in position 3 below.

Position 3


Should White double and if he does, should Black take?

Find out tomorrow! Comments welcome as always. Until then, enjoy the game.

Starting Out

It's important to get each game going with a good play. All the old text books had advice on what the best plays were and the arrival on the scene of Jellyfish, Snowie and Gnu meant that keen students could check the accuracy of ideas on the opening plays by playing the starting position over and over again until there was an answer that lay within the program's margin of error. The latest bot, Extreme Gammon 2, is by common consent the most powerful yet and it incorporates a "book" of opening plays and some replies that is the closest yet to being definitive. For your convenience I reproduce a table below of the plays that XG will make on the opening, all of which have been exhaustively tested by a high level rollout.
There are four columns, the first is the correct play for money and for all practical purposes you can assume that this is also the best "normal" play for early in a match, when scores are level or very close. The second column is the best opening at Double Match Point and you can also use this column for Post-Crawford 2-away and 2-away, 2-away games, where the game is very likely to be cubeless and gammon free. The third column is Gammon Save, to be used in the Crawford game when it is important to avoid a gammon, i.e. Crawford, 2-away, 4-away etc.
You can usually use this column when leading towards the end of a long match and in any short match too. The last column is GammonGo, to be used in the Crawford game when it is important to win a gammon, e.g. 2-away, Crawford, 4-away, Crawford etc. You can usually also use this column when trailing towards the end of a long match or in a short one.
You can of course print this page off and use it to cheat, but I hope that you won't do that. Keep it by you and check after you have made your play. That way you will soon learn it.

Opening	$	Dmp	GS	GG
65	24/13	24/13	24/13	24/13
64	24/18, 13/9	24/14	24/14	8/2, 6/2
63	24/18, 13/10	24/18, 13/10	24/18, 13/10	24/18, 13/10
62	24/18, 13/11	24/18, 13/11	24/18, 13/11	13/5
61	13/7, 8/7	13/7, 8/7	13/7, 8/7	13/7, 8/7
54	24/20, 13/8	24/20, 13/8	24/20, 13/8	13/8, 13/9
53	8/3, 6/3	8/3, 6/3	8/3, 6/3	8/3, 6/3
52	24/22, 13/8	24/22, 13/8	24/22, 13/8	13/8, 13/11
51	24/23, 13/8	24/23, 13/8	24/23, 13/8	13/8, 6/5
43	13/10, 13/9	24/21, 13/9	24/21, 13/9	13/10, 13/9
42	8/4, 6/4	8/4, 6/4	8/4, 6/4	8/4, 6/4
41	24/23, 13/9	13/9, 6/5	24/23, 13/9	13/9, 6/5
32	24/21, 13/11	24/21, 13/11	24/21, 13/11	13/10, 13/11
31	8/5, 6/5	8/5, 6/5	8/5, 6/5	8/5, 6/5
21	13/11, 6/5	13/11, 6/5	13/11, 6/5	13/11, 6/5

Some of these plays have very close alternates and for one of them, 64, don't use the money column in match play. At the start of a 3pt match, play 24/14, while for 5pts or more, play 8/2, 6/2. These are not big differences, a few thousandths of a point, but I mention this before somebody else does!

Tip of the Week. The simplest way to improve is to allow yourself a little more thinking time on tough plays. The simplest way to achieve this when faced with a roll where the play is not immediately obvious, is to let go of the mouse while you think! Try it.

One of the fastest and most interesting ways to improve is to study the matches of the best players, particularly when annotated to explain why a play is good (or bad). I have two annotated matches for sale, featuring Mochizuki Masayuki, the 2010 World Champion. They are annotated by me with the approval of and some comments by Mochy. Each is $10 and comes as an XG or Gnu file, with commentary based on XG analysis. For those who prefer to read the plays and use a real board, it also comes as a word document with many colour diagrams for $15 and this includes the XG file.
Mochy v. Falafel, 13pts
Mochy v. Carlo Melzi, 13 pts.
Orders and PayPal to me please at dorbel(at)gmail(dot)com.

Tomorrow a look at some aggressive cube actions when trailing. Until then, enjoy the game!

Back With A Blunder

Quite a gap since my last post, as my ancient computer took a week off and went on holiday. It's back now, looking relaxed and tanned, but on its return I took the opportunity to give my own game a much needed overhaul. Like the great majority of players, I miss a lot of doubling opportunities. I would go as far as to say that it is the worst single mistake that humans make. I have been concentrating on getting that cube over earlier, even if it means sometimes doubling too early. Better that than missing a double.

So here are a few interesting positions from a recent match against a world class opponent.
White is leading 2-0 to 5 here and I am on roll. This looks like a good number, what would you do with it?



The first thing to note here is that this a correct double (and take) before I rolled the 6-1!
So what did you want to do with it? I went for 8/2*/1, a blunder. 18/17*, 11/5 is better but best of all is 18/17*/11.
Is this obvious? Now I know the right answer I understand what's going on! Two points; firstly 18/17* costs White 17 pips, compared to 2 after 8/2*/1, secondly leaving the blot on the ace point is actually safer than covering it. Count those shots. Even without these two obvious signposts to the correct way forward, a comparison of the two sides shows quite clearly that Black has a strong positional advantage. He has the deadly 6-5-4pts block and he still has the midpoint and all his checkers are in play. White has the less than deadly 3-2-1pts block which equates to 7 checkers out of play and her midpoint is long gone. What all this means in practice is that Black needs to be playing strategically, rather than going for the tactical option of making the 1pt. (In backgammon, tactical means hitting).

Later on in the same game, after some fairly lively exchanges, we got down to this next position, with me on roll and the cube of course still in the middle. Cube action?



The point I need to make here, is that if I had doubled the first position, I wouldn't have a cube decision to make now, even if, as I thought at the time, it was too early! Doubling means that you can only make one doubling error in the game. Leaving the cube in the middle means that you can make a mistake later and sometimes a whole string of them.
Pretty clearly if Black doubles here he will cash. Nobody takes this. A very useful rule is that if you are in the air against a four point board and your opponent is shooting at a second blot, give it up. It's almost always a pass and usually a correct double. Here though Black has a chance to pick up two blots and that's enough to push this position into the "too good to double" bracket.
I'm sorry to say that I cashed this, a blunder, but note that it is a blunder I couldn't have made if I had correctly doubled position 1. This is the hidden benefit to early cubing. It keeps doubling errors down to a maximum of one per game.

In the next game, with White leading 2-1 to 5, she came on roll in this position and made an excellent double.



If you can't see this as a double, particularly when leading, it is the two Black checkers out of play on the ace that are my weakness. You really do need 15 checkers to play with, as White has. It's a fairly comfortable take though, as White's gammons only win three points and the cube is very useful for Black, as if it is turned to 4, he can use all the points. However the key feature is this. A lot of Black's equity lies in his cube ownership and if he isn't going to make good use of it, he should probably pass.

At this score (White 3-away, Black 4-away) White can pass a 4 cube and still retain 40% of the Match Equity at 3-away, 2-away. It follows that Black should be pretty aggressive with the recube and his doubling window actually opens at around 30%! White failed to jump my prime and bust her own with a 5-5, so we came down to this.



It's not often that you get the chance to recube with two men still on the roof, but I reasoned, "I have to throw two sixes and so does she, but I get first go". I recubed. It's a small error. I can lose my market here by throwing a 6 when she doesn't, but it's just as likely that I don't and she does or that we both do, in which case I will be very sad. Better to wait one turn even though I am in the window. Then if neither of us rolls a 6, she has to play and burn one or both of those useful outfield checkers. Then I'll have a correct cube and of course she should take. Note this feature where Black keeps his prime when he dances, but White has to keep playing and busts her board when she can't roll a six.

I learned a lot from looking closely at these decisions and I hope that you did too. With any luck, I'll have something else for you tomorrow, so until, enjoy the game!