the dorbel daily

Friday 30 December 2011

A Reader Asks.....

While we wait for the super computer at Dorbel HQ to process the millions of entries received for the Christmas Quiz, here's an interesting query from a reader trying out XG2 for the first time.
"I'm analysing a three point match, it's 1-1 and the analysis says that White should double here, even though she is an underdog in the game. Why is this?"

This is of course our old friend the 2-away, 2-away scoreline, which everybody claims to understand, yet so few below the expert level do. It is, so the experts say, always correct to double at the first opportunity. So, when White started this game with 3-2 and (correctly) played 24/21, 13/11, Black had an optional double, even though he was a very slight underdog. He should do this because he has nothing to lose by doubling. If he refrains from doubling, White will on her turn double anyway and Black will still have a take.
In the position above, XG says that White should double from the bar. This is because even if White dances, Black should double and White should still take! So, White can't lose by doubling, but what can she gain? If she rolls 4-4 and makes the best play, which is bar/17*, 21/17, 13/9 (not an easy play to find!) and Black rolls 6-6, White has actually lost her market and Black should pass!
If you play below expert level (98% of players), then doubling immediately at this score figures to be right for you. Occasionally it will be a minute mistake, of the order of 0.002 points, but not doing it risks making a much bigger mistake later, so turn it at the first legal opportunity. If you are an expert and playing somebody much weaker than yourself, you can get some mileage from delaying it in the hope of an incorrect pass later or occasionally even playing on until the end for an undoubled gammon! Don't try this at home kids! Trust me, at 2-away, 2-away, turn the cube immediately, even if your opponent starts with a 3-1. It's always correct.
Until the next time, enjoy the game!

Saturday 24 December 2011

The Big Christmas Quiz, Part Two

Welcome to Part two of the quiz, five more positions hacked from The Chicago Point of May 1990, with grateful thanks to Bill Davis, who co-authored the the original quiz and kindly gave me permission to reproduce it.

Position Six. Black to play 3-3 from the bar. Money game.

Position Seven. Black to play 5-1. Money Game.

Position 8. Black to play 6-6. Make the play that leaves White the fewest shots.

Position Nine. Money Game, Black to play 1-1.

Position 10. Black to play 5-3, money game.

Answers in the comments section please. Go back to Part One if you haven't already done so. Mr Chow please change your answer for Number Four as I have corrected the score so that White leads, not Black.
There is a small but rare prize for the winner and I will post the answers on or about the 28th of this month.
Enjoy the game and for those who celebrate it in one way or another, Happy Christmas!

Thursday 22 December 2011

The Big Christmas Quiz. Part One.

It's Christmas Quiz Time. Let me say straight away that I didn't compose this quiz. I have lifted it straight out of the May 1990 edition of Chicago Point. It was compiled by Bill Davis and Danny Kleinman and given at the 1990 Midwest Championships, for a $25 entry fee. A stellar list of entrants was topped by Jake Jacobs who scored 6 out of 10, so we may assume that this is a tough quiz! They were restricted to 20 minutes, you can have as long as you like. There will be a prize!

Thank you to Chicago Point , then as now a prime source of backgammon information and it's editor Bill Davis, whose contribution to our wonderful game over all these years is incalculable.

In every position, Black is on roll. You can assume that you are playing an equally strong opponent to yourself. Five positions today, five tomorrow.

Position One. It's a 9 point match and Black holding the cube leads White 6-2. What's the correct cube action for both sides?

Position Two. Money game, Black to play 3-1.

Position Three. It's DMP, how should Black play his 1-1?

Position Four. It's a 7 point match, White leads 5-2 What's the correct cube action for both sides?

Position Five, money game, Black to play 1-1.

An interesting feature of this quiz is that it was composed at a time when bots were in their infancy. The best available was Tom Johnston's Expert Backgammon, a weakling compared to today's heavyweights but a remarkable program for it's time, particularly considering that it was the work of one man. In their answers Bill declared that only positions 6 and 10 were at all debatable, but ExtremeGammon has something to say about that, as we will see. Nevertheless, kudos to both men for an excellent quiz.
Post your answers to these five in the comments section please and I'll put up the next five tomorrow.
Oh yes, what is the prize? The winner will receive a backgammon book! Don't get too excited, it's minute and almost valueless, but it is very old and very cute and will look well on your trophy shelf.
Enjoy the game!

Tuesday 20 December 2011

Play The Game Not The Player?

One of the difficulties facing every backgammon writer is the necessity to qualify every assertion with phrases like "except when" and "if you are the stronger/weaker player" and "depending on the score". There are many others. In order to make what we write intelligible, we have to omit these and rely on the reader to use his/her commonsense to imagine that these qualifiers are permanently in place. Here are some examples.
Recently I wrote, "The best modern players double like the bots do, aiming to turn the cube at the first moment that it is technically correct." I could, perhaps should, have qualified this with "when they are playing against somebody of their own class". As a reader commented, "Stick doesn't do this. He definitely changes his cube play to adjust to the strength and perceived playing habits of his opponent". Of course he does, but I would expect him when playing another world class player to get that cube across pretty much in line with what the bot suggests is correct. Another reader commented on Stick's criticism of people who "play like donkies" and cash positions that are actually too good. Recently Falafel commented on a cube, "I'm not sure if this is a take, but when in doubt I take". Is this good advice for all of us? The point I am trying to get across is this. Is what the bots do invariably and what the stars do some of the time against some players, good for us to follow? Given our more limited skill set, clearly it isn't. Let's take a look at some actual positions.

Position 1

Black trails 6-away, 2-away. What is the correct cube action? This is a monster pass, nobody takes this, so Black's first consideration must be, "Is it too good?" It's not clear to me that it is. White has a five point board and leads in the race by 15 pips. She might hit a fly shot next turn or improve with 1-1 or 2-2 or if hit, anchor on the 22pt. Over the board I would say to myself, "I think this might be too good, but I'm not absolutely sure, so I'll double." Stick might say, "I think this might be too good, although I'm not absolutely sure, so I'll play on for the gammon this roll".
Who is right? We both are. His judgment of the position will be better than mine, both now and on later rolls when he faces the same question. Furthermore, he is likely to play from here better than me, so approaching or even achieving the theoretical equity of the position. For my part (and probably yours) doubling is a good practical play, putting a point on the scoresheet without having to play at all! The actual equity of this is about 1.05 points for Black if he plays on, so the theoretical cost of cashing now is 1/20th of a point. To me this is a reasonable price to pay to get a point that requires no luck, skill or effort from me before it goes on the scoresheet. Also, as so memorably put by Bill Robertie, occasionally somebody hallucinates and takes, after which your equity goes through the roof. One of these pays for 15 games where you have made a small error and cashed.

What about early and aggressive doubling? Take a look at this.

Position 2

Black is on roll in the first game of a 13pt match. He leads by 4 pips. Is this a double? Black is Falafel, White is Mochy and Black doubles. Black threatens to lose his market with the sequence "make the 3pt, White dance". If this doesn't work, he might be able to keep White primed or just race. In the worst sequences, his bar point anchor will keep him in the game for a while yet. By a tiny margin a double is correct, gaining 0.007 points over waiting! Should we copy Falafel and the bot? Sure, why not? Be aggressive, up the ante now and with any luck you'll grab an early 4 point lead in the match. 20% of the games end with a Black gammon from here. Also, as in the first position, doubling allows your opponent the chance to make a big mistake and pass. Not very likely? I've seen weaker cubes than this passed, though not perhaps by Mochy!

What about "When in doubt, take"?

Position 3

Money game, Black on roll, leading by 37 pips. The cube is pretty clear. What about the take? White has an anchor and a good board, is that enough? I can't say for sure that this is a take and because I usually tend to be too optimistic, I pass this. Falafel on the other hand might well say, "Not sure, so I take". For him, this is a good plan. With his superior checker play he will play close to perfectly from here and get the maximum benefit from cube ownership. Black only has to make one error to make the take correct and in fact the theoretical equity of this position after a take is 1.042. For me and perhaps for you too, a pass costing 1/25th of a point is a good practical option.

Every player can and should consider the practical benefits of adjusting his cube actions to allow for his own and his opponent's strengths. I hope that this article will give you some clues as to what you should be aiming for. Theoretical bot perfection isn't always the best practical option over the board, sometimes yes as in position 2, sometimes no as in positions 1 and 3.
Enjoy this wonderful game!

Monday 19 December 2011

If Early Is Good, How Early Is Early?

Gallon Jug describes players on Play65, presumably in money games, doubling as soon as the game starts and appearing to do very well by doing so. What is actually happening here? We can start by looking back at a favourite hustler's proposition from the old days when they were lucky enough to hook a fish. "I tell you what", he would say, "I'll let you have 1-1 as the opening roll every game. However, we have to start with me owning the cube on 2." On roll in this position, the hustler is only around 42% to win the game, but he is hoping that his better play and most importantly his cube ownership will pull him up to being a small favourite. Cube ownership is so valuable for two reasons. Firstly if things go the way of the fish, the hustler will stay in the game until the end. Fish has to get to 100% to claim the points. Hustler however, only has to get to around 75% to turn an optimal cube to 4. He has only to climb from 42% to 75%, whereas Fish has to climb from 58% to 100%, a longer ladder. Secondly, the greater part of the Fish's wins will come at the two level, but a lot of the Hustler's wins will be at the 4 level.
What about Play65? Well if players at all levels below world class are reluctant doublers, which I believe to be true, they are even more reluctant redoublers, so cube ownership for them is less valuable than it is for the Hustler in our example above. Moreover, Play65 is a money site and they make their money by taking 10% of every settled game. The player who wins pays this. Thus if at the end of a game at a dollar a point, you win $2 you collect $1-80. This has a very considerable effect on your take point. Normally as you know you need 25% cubeless to have a marginal take, but on a site with a 10% rake, you need 26.32%. It gets worse too. GJ doesn't say so, but the site allows you to cap the amount that you can lose in any one game. If it is capped at twice the stake, then they will double at any advantage at all. Why not if cube ownership is valueless? If on the other hand you don't follow this policy and wait for a more normal doubling point, you lose equity on each turn. If the game is capped at 4 times the stake, the player owning the cube at 2 should redouble immediately they become the favourite, particularly as it is easier than usual to lose your market anyway. If they do this and you don't, they gain.
Of course if they see that you are as aware of these wrinkles as them and can also play the checkers fairly well, they quickly move on to look for other fish. The key skill in any money game is to select your opponent carefully.
Can you make money on a site with a rake as high as 10%? Yes, if you are prepared to be completely ruthless, can play very well and concentrate very hard for hours at a stretch. Ideally you cheat as well by using a computer. Wouldn't the site monitor the games and close the account of anybody doing this? No, why would they? They don't want to ban a player who plays for long periods every day, because they get their money whoever wins the game. Occasionally a cheat will be outed by the other players, but not by the site itself.
Enjoy the game and by all means play for money, but at a 10% rake, I can't advise it to anybody.
Until tomorrow, have fun!

Friday 16 December 2011

Lastgamephobia II: The Sequel

Those of you who read the comments will have seen Timothy Chow's comment on the last post. I reproduce it here for those who didn't. Thanks Timothy, but I fundamentally disagree with you. Here's why.

"There is one reason you may not want to double at 4a2a as aggressively as the bot says you should. A lot of positions that the bot drops at this score will be easy money takes and therefore will be taken by many players. If your opponent is likely to take next turn even though it is technically a drop, then you can't actually lose your market."

This is worth looking at more closely. The examples that I gave are not early doubles in the sense that they are technically wrong, they are correct doubles and to wait a turn loses equity. If we wait until there has been a market losing sequence and yet our opponent incorrectly takes, we don't gain anything. It's the same game with the cube in the same place as it would have been when we doubled correctly earlier. In order to reach that point we have to make one or more cube errors and then rely on our opponent to make a mistake in order to avoid losing equity by losing our market!
Lastgamephobia afflicts both doublers and takers. If you open with a 3-1 and the opponent rolls a lemon, 6-3 say, then believe me you can and do get wrong passes by correctly doubling immediately. At this score, lastgamephobia sufferers also get sudden attacks of gammonphobia. You can't gain by missing a correct double at this score, only lose.

Traditional cube play technique was to try and double as close to the point where a take becomes a pass as possible. There are several drawbacks to this.
First, it requires very precise judgment to identify when you have reached this point and balance it against market losers. Doubling at the first correct point is a lot easier to spot, because you only need to be in the ballpark.
Second, you almost always have to miss several correct doubles to get to that point. Doubling early means that you might make a mistake when you double, but it will be the only one that you make in that game.
Thirdly, if you double at what was traditionally considered the optimum point, i.e. at the place where you gain a theoretical point by getting a take or an actual point when the opponent passes, it isn't then possible for the opponent to make a mistake! She loses a point either way. Doubling early allows her to make a big mistake by wrongly passing.

The bots, who play better than humans 24/7, double early. The very best players and there are a few who consider a PR in excess of 2 to be playing badly, double like the bots do. We have nothing to lose and everything to gain by trying to emulate them. In the process, we will certainly make matches shorter, but dont be afraid of that. It's a game of aggression. Make aggressive doubles and reap the rewards.
Enjoy the game!


The player reaching 4-away, 2-away in a match can use the cube with a great deal of freedom, as the cube turn kills the cube and the opponent's gammons and activates his own gammons as match winners. This statement is so obvious to strong players that you often see them doubling on their second roll of the game.

Here's a typical position with Black trailing 4-away, 2-away and on roll. He leads by a pip, has already made a point and White has three blots, a recipe for a strong cube at this score but most intermediates and many advanced players will leave the cube in the middle here. The intermediates as a group are reluctant doublers at the best of times and they routinely miss doubling opportunities. The advanced players know intellectually that they ought to be doubling but they fall victim to a crippling malady which I call Lastgamephobia. They don't want to put the match on the line, even though they know that they should.
If you too don't like to double this position and many like it, think of it as a money game, where your opponent is not allowed to recube and she is not allowed to win a gammon but she can lose one! Why wait? How can you gain? By cashing a point and going to 3-away, 2-away?
Black often gets these chances on his second turn and White usually has a take, although yesterday I saw the sequence Black 3-1, White 6-3 doubled and passed by somebody I would call a strong player.

Lastgamephobia strikes in many ways. On the same day I saw this redouble passed in the first game of a three point match.

Actually Black, perhaps also suffering from the dread disease, had already missed two cast iron opportunities to turn the cube to 4 and put the match on the line, but when he turned it here, White passed. She elected to play at Crawford needs 3, with a Match Equity of 25% rather than take her 30% chance of winning the match from here.
Can you justify White's decision if she is the stronger player? Yes, if White thinks that she is good enough to win 56% (or better) of one point matches against a player of Black's strength, then she might be right to pass. This is though very hard to estimate. Ratings vary so widely that they are not much help as a guide and there is also the fact that if you poll players after matches, 70% of them think that they were the stronger player!
The same principle applies all through our matches. Double early, double often. Better to make one small mistake with a cube that is a bit frisky than make a string of mistakes failing to double your opponent in and then cashing when you are too good, a sequence that you can see day in, day out anywhere the game is played. Be bold and above all, don't be afraid to make this game the last one if it is right to do so. I know two players on Fibs of roughly equal strength with the checkers; in tournaments and fibsleague I play both of them fairly regularly. One is a dashing cube handler, who turns the cube with boldness and isn't afraid to redouble aggressively too. The other is reluctant to double until he is very close to or actually past the point where it is a pass and never, ever recubes unless it is a pass. One beats me often, the other almost never does so. Guess which is which?
Enjoy the game!

Wednesday 14 December 2011

More On "A Reader Asks..."

Timothy Chow has helpfully pointed out that Neil Kazaross recently updated his famous "Neil's Numbers" chart and for that you need to go to this.
That was a very exciting moment for me. I just worked out how to make a hyper-link!
Will I be learning the new values? I might, but the benefit of from doing so is very small, as the real problem in most cases is putting a sufficiently accurate figure on the position in the first place! The best method for getting to grips with the one above is to learn how to operate Walter Trice's Effective Pip Count. I could write it all out for you but best if you just go here.
The EPC won't entirely answer the position above for you, because it doesn't allow for White dancing and it doesn't include her chances of hitting a shot later. However, what it does do is to provide you with a method for comparing a home board with a home board and a straggler, when the actual pipcount is more or less meaningless. It's the AK-47 of the bg world. You won't often need it, but when you do, nothing else is half as comforting!
The promised 4-away, 2-away positions are in the pipeline and I may even write them later today, but for now, cooking lunch for mrs dorbel is more important.
However, I will take this opportunity to remind you of the annotated matches that I have for sale. The first is;
Mochizuki Masayuki v. Matvey Natanzon, a 13pt IIBGF Match.
Every important move analysed and commented on by me, with the approval of and some comments from both players. These are arguably the two best players inthe world right now.
The second is ;
Mochizuki Masayuki v. Carlo Melzi, a 13pt IIBGF Match.
Annotated as above.
Please order from dorbel(at)gmail(dot)com, $10 for either match. The file is ideal for Extremegammon, but please say if you use Gnu or Snowie and I will send you a suitable file.

Work in progress, Mochy v. Paul Weaver. A 13pt IIBGF match.

Until the next time, enjoy the game!

Monday 12 December 2011

A Reader Asks........

"Why shouldn't I redouble this position?" writes A Nonnymouse of South Africa. "I'm a huge favourite in the position and I lead 8/2 to 11, so White can't win the match after a redouble, yet Gnu marks my redouble as an error."

The first thing to say about this is that Gnu 2-ply is not very good at assessing this type of position. It does mark this as a substantial error, but the rollout marks this is being a very marginal double/no double, with Black winning the match about 93.25% whether he doubles or not. As White might pass, I suppose that doubling figures to be correct, because a pass will take Black to Crawford - needs 9 where his equity will be about 94.5% according to the MET that I use. If Black is the weaker player he should definitely cube, as the position is entirely skill free.
Extreme Gammon agrees with these figures.
So, don't ever take a bot evaluation as gospel. Always check it if you are interested in the position.

Nr Nonnymouse got it right. This is just about a redouble and a correct take, but I would imagine that many players would be very reluctant to turn the cube here and risk an 8 point loss when they can only win 3. Black is actually a 90% favourite to win here, so how would one arrive at the correct decision over the board? We do a risk/gain analysis.
Note that for this, I round all percentages down to the nearest whole number to make the arithmetic easier and I assume when I say "Black no double" that he never doubles. In practice he will do a bit better than this figure if he redoubles correctly later. Of course White always redoubles to 8 immediately.

If Black doesn't redouble and wins, he gets to Crawford - needs 9, ME= 94%
If Black redoubles and wins, he wins the match, ME = 100%
We can see that Black stands to gain 6% by doubling.
If Black doesn't redouble and loses, he gets to needs 3 - needs 7, ME = 76%
If Black redoubles and loses, he gets to needs 3 - Crawford, ME = 25%
We can see that Black risks losing 51% by doubling.

So, Risk/ Risk + Gain = 51/51 + 6 = 51/57 or 89.5%.
Balck needs to be a 90% favourite to redouble and that is almost what he has.

Can you do this in your head over the board? Very strong players can. It depends on being able to put a very exact figure on Black's game wiining chances, which in itself is very hard and then being able to remember your Match Equity Table.
Memorising Match Equity Tables is very hard for anybody. Kit Woolsey says that he can't even remember his own, although I am sure that he knows all the figures for shorter matches. For this reason, most players rely on an approximation and the most popular is Neil's Numbers.

It looks like this.
The leader's percent probability of winning the match is 50, plus the number of points by which he leads multiplied by Neil's number. Look at the top line to see how many points the trailer needs and the appropriate Neil's Number is underneath it. Some of the numbers don't have a whole number, so you have to fill that in for yourself. As originally designed, the user was intended to extrapolate, so for example the number for trailer needs 7 would be 6.5.

This handy gadget was designed by Neil Kazaross about 20 years ago ans is startlingly accurate even when compared to today's computer generated tables. However, don't use it when the leader only needs one or two points to win as it breaks down there, but these lines are quite easy to learn anyway.

One can of course use pencil and paper when playing online which helps and also have a printout of a match equity table to hand. Don't do this when playing a human. It isn't fair and it is cheating and you will feel very sneaky after doing it. However, if you do use a pencil and paper for your calculation when playing a bot, you will be learning how to do it until the day when you can do it mentally. The small fraction of a rating point that you might gain by this doesn't matter much, if at all!

Tomorrow, I want to look at some 4-away, 2-away positions. Until then, enjoy the game!

Wednesday 30 November 2011

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!

Monday 28 November 2011

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!


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!

Friday 25 November 2011

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.

Tuesday 22 November 2011

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.












24/18, 13/9



8/2, 6/2


24/18, 13/10

24/18, 13/10

24/18, 13/10

24/18, 13/10


24/18, 13/11

24/18, 13/11

24/18, 13/11



13/7, 8/7

13/7, 8/7

13/7, 8/7

13/7, 8/7


24/20, 13/8

24/20, 13/8

24/20, 13/8

13/8, 13/9


8/3, 6/3

8/3, 6/3

8/3, 6/3

8/3, 6/3


24/22, 13/8

24/22, 13/8

24/22, 13/8

13/8, 13/11


24/23, 13/8

24/23, 13/8

24/23, 13/8

13/8, 6/5


13/10, 13/9

24/21, 13/9

24/21, 13/9

13/10, 13/9


8/4, 6/4

8/4, 6/4

8/4, 6/4

8/4, 6/4


24/23, 13/9

13/9, 6/5

24/23, 13/9

13/9, 6/5


24/21, 13/11

24/21, 13/11

24/21, 13/11

13/10, 13/11


8/5, 6/5

8/5, 6/5

8/5, 6/5

8/5, 6/5


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!

Thursday 10 November 2011

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!

Wednesday 26 October 2011

Three On The Ace

The least useful place to have a spare is on your anchor and as the 24pt is the weakest anchor, it follows that having three checkers on it is very bad. It's practically an invitation to the cube, so should Black, who is on the bar double this? If Black doubles, should White take? It's the first game of a five point match and Black did double this and White (dorbel) passed. Give it some thought and then read on.

If you thought that Black is actually too good to double then I would say that that is a reasonable view, given that White already has three back and three more blots are waiting to be hoovered up. OTB I thought that might just be the case and so passed very quickly. To my surprise, this is a correct take. What is happening here? To find that out, you have to revert to the only technique that we had before bots, the hand rollout. In the old days, this involved hours, sometimes days, of playing the position over and over again, ideally with a friend, often alone! There were some techniques for reducing the dice variation, notably changing the opening roll each time, but the number of games that you could complete and the inevitable playing errors made the results of little value in determining the most likely outcome. However, it did give you some practice and a little confidence when you met something like it in the future. We can still do this now, but using the "Play from here" feature on the bot. It will set the pieces up, play one side and tell you afterwards how you played too, allowing you to improve your play in the position as you go on. You can swap sides.
I did this with this position and discovered several things. The first is that because of his awkward position, Black's play is far from straightforward, so in order to achieve anything close to the bot cubeful equity of around 0.9 he will have to play brilliantly. The second is that the position White fears, where she finds herself in an ace point game with several checkers behind a prime just doesn't happen! When she isn't hit, her blots become slots and builders. When she has one or two checkers sent back, she still has lots of play because Black only has a two point board and can't develop it quickly because of his awkward position. All this is not to say that Black is not hot in this game, he will win about 62% from here including 33 gammons, but White does have a take and must seize the chance to play a long difficult game owning the cube. This is particularly true at this score, where the recube can come earlier than usual.

As so often happens, I quickly saw something very like it again.

Also in the first game of a five pointer, but as you can see with several features that improve Black's game. He isn't on the bar and White is, one of his back men has escaped and his forward checkers, although still stacked, are a bit better placed for an attack. I would have passed this, correctly, but Black decided to play on for the gammon. It's quite a reasonable view to take, as he can usually cash later if he wants to, but double/pass is correct. I always repeat a little mantra here, culled from early reading. I think it's Robertie. "The side playing on for an undoubled gammon against an ace point game is either making a mistake or has already made one". This is a very valuable piece of information, although there are scores where playing on is clearly correct, usually when an undoubled gammon wins the game for you.
At the risk of repeating myself to my regular readers (Sid and Doris Bonkers of Neasden), my philosophy is to only play on for the gammon when I am certain that it is correct. When it's a close decision but playing on is correct, this sometimes costs me a small piece of theoretical equity, but it does put a real point onto the scoresheet without having to play to get it. Also, the icing on the cake, sometimes they take!

So, the next time you see a position and you ask yourself, "What is going on here?", play it. You'll learn a lot more from it than you will reading books, or indeed this column.
Until the next time, enjoy the game!

Mochizuki Masayuki v. Matvey Natanzon, a 13pt IIBGF Match.
Mochizuki Masayuki v. Carlo Melzi, a 13pt IIBGF Match.
The XG files for these matches, annotated by me and approved by Mochy are now available, $10 each. Gnu and Snowie users can have a Gnu file with the commentary on a separate word doc. Both matches show brilliant play at the highest level and are very instructive for students at all levels.
PayPal please and enquiries to dorbel(at)gmail(dot)com.