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!

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!

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!

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!

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!

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!

Lastgamephobia

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!

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!

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!