the dorbel daily

Monday 26 April 2010

Crawford Rule Change?

Anybody who plays tournament backgammon will have encountered the Crawford Rule. It stipulates that when one player reaches a score one point from victory, the doubling cube may not be used for the next game. If the trailer wins the Crawford game, he can and should double the next game at the first legal opportunity. I have often wondered though, why only one game? If you have reached 10-2 in an 11pt match, but then lose the Crawford game, your opponent will be doubling every game and will effectively be handed four points for nothing! In practice, he doesnt trail 10-3, he trails 10-7 in a match where the cube doesnt count. How can that be fair?
I can see that it is fair that he benefits from winning gammons, that requires skill, but there's no skill to just turning the cube straight away. Changing the rule, so that no doubling was permitted for the rest of the match would be fairer and would incidentally, increase the wins for the more skilful player, a desirable outcome in itself. I have to say that I have yet to meet anybody who agrees with me here!
Why have a Crawford rule at all? Without it, certain cube actions at the end of the match become nonsensical. At the 2-away, 3-away score for example, if the trailer doubles, the leader can take anything at all in a gammon free position! If he passes, he is 50/50 in the match, if he takes and loses he trails 2-away, 1-away, doubles the next game immediately and is still almost 50/50, except for the leader's free drop.

For our newbies it might be good to explain the "Free Drop" and it's close relation, the "Mandatory Take". The Free Drop occurs post Crawford, when the trailer needs an even number of points for victory and doubles. The leader can drop without losing any equity. Having the free drop is worth a little bit, perhaps as much as 1.5% in match equity. When the trailer needs an odd number of points, the leader always has a take, even if he is well behind in the game. This is known as the Mandatory Take. The exception to this comes when the trailer stands to win more gammons than he loses games, but these positions are rare. However a clever trailer may sometimes delay his cube until there is a substantial gammon threat in the hope of getting a wrong pass! You have to be careful though; reaching a position where the leader really should pass would be a disaster!
Another rule change that would slightly reduce the luck factor, would be for players to alternate getting the first roll of the game. Roll dice for it on the first game, then alternate after that.
Any thoughts on these ideas? Any rule changes you would like to see? Use the comment feature and let's get interactive!

Sunday 18 April 2010


A reader asked me if I had a table of doubling and take points for various match scores. I haven't as it happens, but I did try to make one once. The trouble is that it needs to take into account whether the situation is dead cube or live cube or somewhere in between and be different for redoubles and take gammons into account. You end up with something very unwieldy, hard to memorise and hard to use. Old books were full of various tables. It is a good way to fill up pages that you haven't already filled with lots of diagrams! In my experience though, if you want a table telling you something, best to make it yourself. It's more likely to stay in your brain, you are more likely to understand it and you can tailor it to your own needs.
Having said all that, here is a useful table for you that I haven't seen anywhere else.
It is for the particular score 2-away, 1-away post-Crawford. For the trailer, the cube action is easy, turn the cube at the first legal opportunity. There is always a bright lad at the back of the class that points out that actually, there are certain rolls that make it correct for the trailer to play on and try for a gammon. This is probably true and if you are a world class analyst who can spot this opportunity and continue to evaluate it accurately as the game goes on, then go for it. You do gain a tiny bit of equity if you get it right. For the rest of us, just turn it!
For the leader, things aren't quite so simple. If you get the opening roll, then it isn't so bad. With most things you are a favourite in the game, so you can take. The exceptions are 4-1 and 2-1, where you are slightly below or slightly above 50% depending on who you believe. If you have correctly split the back men take or pass makes not much difference either way. When however your opponent has had the opening roll you get to reply before he can double and the question is, can you take or should you pass? You need to be 50% or preferably better to take so do you know all the answers? I bet you don't so here is my version of the truth. Print it out and keep it by you for reference. Refer to it AFTER you have made your decision in a match please, not before. Before is cheating.

The first column is what your opponent rolled, the second is what he played and the then we say what you need to do to get to 50%.
I use the word doublet for 6-6 etc to avoid confusion with the cube action. All plays are numbered from the viewpoint of the player on roll. Where it says "roll any doublet" you do have to make the best play with it as well, but you will usually be better than 50% even if you don't find the best play.

6-5..24/13. Roll any doublet.
6-4..24/14. Roll any doublet or hit on the 11pt.
6-4..24/18, 13/9. Roll any doublet, hit on the 16pt or make the 7pt.
6-3..24/18, 13/10. Roll any doublet, hit on the 15pt or make the 7pt.
6-3..24/15. Roll any doublet or hit on the 10pt.
6-2..24/18, 13/11. Roll any doublet, hit on the 14pt or make the 7pt.
6-1..13/7, 8/7. Roll 4-4, 3-3, 2-2 or 1-1.
5-4..24/20, 13/8. Roll any doublet, or make the 5pt.
5-3..8/3, 6/3. Roll any doublet (except 5-5) or make the 5pt.
5-2..13/8, 13/11. Roll any doublet, hit on the 14pt, make one of the 7, 5 or 4pts.
5-2..24/22, 13/8. Roll any doublet, make one of the 5, 4 or 3pts.
5-1..24/23, 13/8. Roll any doublet or 6-5, make one of the 7, 5, 4 or 2pts.
4-3..24/20, 24/21. Roll any doublet (except 5-5), make the 5pt or 4pt.
4-3..24/20, 13/10. Roll any doublet, hit on the 15pt or make the 5pt.
4-3..24/21, 13/9. Roll any doublet, hit on the 16pt, make the 5pt or 4pt.
4-3..13/9, 13/10. Roll any doublet (ex 5-5), hit in the outfield or make the 5pt.
4-2..8/4, 6/4. Roll any doublet (except 5-5)
4-1..24/20, 24/23. Roll any doublet (ex 5-5) or make the 5pt.
4-1..24/23, 13/9. Roll any doublet, hit on the 16pt, make the 5pt or the 2pt.
4-1..13/9, 6/5. Roll any doublet (ex 5-5) or hit a blot.
3-2..24/21, 13/11. Roll any doublet, hit on the 14pt, make the 5pt or 4pt.
3-2..13/10, 13/11. Roll any doublet (ex 5-5), hit in the outfield, make the 5 or 4pt.
3-1..8/5, 6/5. Roll 6-6, 3-3, 2-2, 1-1.
2-1..24/23, 13/11. Roll any doublet, hit on the 14pt, make the 5 or 4pt.
2-1..13/11, 6/5. Roll any doublet (ex 5-5) or hit a blot.
There you have it. Will it be any use? Practise with it. Set the board up, make an opening play and then roll the response. Note what you played, then do nine more before checking your answers. Nine out of ten is a pass mark!
Let me know how you get on.

Some interesting points. You will notice the weakness of 5-5 as a response in many cases, even though it is 20 pips. Note too that at dmp, splitting on the opening roll is preferable to slotting. Note the 24/20, 24/21 play for an opening 4-3. This is still a well-kept secret best play for this roll at this score, as is 24/20, 24/21 for 4-1. As well as being technically best, people who haven't met these before don't always know how to respond.
Some of the weakest reponses that still indicate a correct take are marginal and some of those just below the line are very close. let me know if you can see any that I have wrongly included or omitted. Thanks for reading and as it used to say in the Beano, more fun next week!

Tuesday 13 April 2010

Backgammon, Luck or Skill?

A perennial discussion among players is the old, "How much of BG is luck and how much skill?" You'll get as many different answers as there are players in my experience, but clearly the game is a mix of the two. Even the best player can't win every match, even the worst can't fail to win some. The longer the match, the greater the winning chances of the better player, because over time the luck is more likely to even out. In shorter matches though it is rare to see even luck or anything close to it.
Can we define luck? The bots assess the luck factor when they present the statistics for a match and they do it like this. Before every roll of the dice they make an estimate of the equity of the position and then look at all the 36 possible rolls and estimate what the equity will be after each of those rolls if the roller makes the best play with them. At the end of the match, the bot sums the equity gains or losses for each side and divides them by the number of rolls and that's your luck factor.
However, this can't be a complete picture of what is happening, because occasionally you can have the best of the luck and play the best and still lose! Can we say why this is?
Every match is made up of a number of games of course; a five point match for example may be decided in a single game or very rarely take 9 games. Sometimes a match can be won by the less lucky player, but if you begin to look at the statistics for individual games you will see that they are almost invariably won by the side with the greatest luck. In 1% of the games at best is the luck so nearly even that the better player can overcome "bad" luck and win the game. So where is the better player's edge? It's pretty clear that it lies in his cube handling. When he gets the bad luck, he keeps the cube as low as possible, when he gets the good luck it's as high as possible. Heresy I know, but all that skill handling the checkers matters less than we like to think. The real trick is to use the cube well.

So, what do we mean by using the cube well? Good cube action, whether doubling or refraining from doubling, passing or taking has one central characteristic. It increases our equity in the position. What is equity? It's just what the position is worth to you on average. In a position that you win 60% of the time, then your average gain if you play the position 100 times will be 20 points, 60 wins minus 40 losses. Your equity is 0.2 points per game.
It might appear that if you are the favourite, then doubling will exactly double your equity, but in practice that is rarely so, because owning the cube has value for your opponent, a lot of value if the game has a long way to go, much less if the game is near the end. Sometimes of course, if it is the last roll for example, it may have none at all and then your equity will indeed double with the cube turn.

Expert players can and do put a price on a position, estimating often with great accuracy their winning chances and using the cube accordingly. They rarely miss an opportunity to double correctly and they almost never make very bad takes. For those of us who lack the skills to assess positions in this way, there exists a golden rule that infallibly leads to good cube action in positions where we are considering a cube turn. It is called Woolsey's rule and it goes like this. "When considering a double, look at the position from your opponent's point of view. If you are in his shoes, are you certain that this is a take? If you are not certain, turn the cube."
Wow, can it really be that simple? Yes it can and using it can only improve your win ratio. You may of course be assessing the position incorrectly and making a mistake, but you have to back your judgment at some point. Not only that, doubling has several things going for it, particularly if you are a weak player. It gives your opponent the chance to make an error and pass. He can't make this error if you don't double. Also, it shortens the match, definitely in the favour of the weak player.

The reverse of this rule doesn't hold. Sometimes the take is absolutely clear and it is still correct to double. Sometimes the pass is absolutely clear, but it is correct to refrain from doubling and play on for a gammon. The decision whether to cash or try for the gammon is often a very tough one, but if you are uncertain, turn the cube anyway. Even if playing for the gammon was the correct decision, getting a pass puts a concrete point on the scoresheet, whereas the more-than-a-point that you get on average by playing for the gammon is theoretical and may well need a lot of skill along the way. Another upside to cubing in these positions is that sometimes they take and then your equity goes through the roof!
So, if you play at any level below advanced, it is highly likely that bolder doubling will get you more wins. Does this mean bolder taking too? I don't think that it does. You must take of course if you think that on average you will lose less than a point after taking, but if you are not sure, give it up and go on to the next game. A small theoretical loss is usually a price worth paying to keep your losses down, particularly in games where a substantial part of your equity relies on you making a recube at the correct point. If you are going to risk more points, it makes sense to take the risk in games that you are winning.

The phenomenon of shorter matches favouring the weaker player accounts for a well known strategy to boost your rating on, the First Internet Backgammon Server, a popular free play site. There are always a number of bots available to play and of course they play at a very high level. If your rating is normally below 1700 as most are, then playing these bots in 25 point matches can seriously boost your rating, provided you adopt the strategy of doubling immediately, taking any recube and redoubling at the first opportunity until the cube reaches 32. Your chances of winning the match are probably about 5% if you play normally, but have to be much greater if you can reduce the match to a single game! Once you get to a rating of about 1770, the law of diminishing returns catches up with you and you won't increase much further. This process will get you a satisfyingly high rating, but of course you will gain fewer points when you win against humans and of course drop more points when you lose, so it is ultimately self defeating. Moreover it will seriously damage your skill level, as you can't learn to play well while playing badly!

A very useful tactic when trailing in shorter matches is to use Uncle Jake's Law. This is essentially, "Develop some sort of gammon threat and ship it in"! As above, can it really be that simple? Yep, don't worry about how many gammons you may win or indeed lose, if you are a solid favourite and there are more gammons around than there was at the start, just turn the cube. Here's a good example from a recent five point final in a Bagolympic tournament.

Red is on roll and trails 0-2 to 5. Is this a double? Technically no, he has a tiny lead (5 pips), but his back checkers have yet to get under way and his major asset, the four prime, is devoid of builders as he still has an awkward stack on the midpoint. The take is trivially easy. Snowie thinks that he will win about 59% here including 20 gammons. However, 20 is more than the 13 that he started with, so by Uncle Jake's Law a double reckons to be a good practical play, even though technically it is a small error. Why is this? Bots asess positions assuming that both sides will play as near to perfectly as possible from here, including using the cube if opportunity presents itself. Here though, White's play reckons to be very difficult, as she will constantly have to balance trying to win the game and trying to avoid being gammoned. Red's play reckons to be fairly easy, splitting his back checkers soon, bringing down builders from that fat midpoint and attacking White's blots with abandon. He can do this because of course his gammons are very valuable, getting him straight to the Crawford game whereas White's gammons are much less useful to her, because she will waste one of the four that she might win overshooting the target. The cube is not very useful to White either, as she will find it quite difficult to double Red into this correctly. Her doubling window, the area of opportunity between the first point at which she can redouble correctly and the point at which Red should pass is very small, between 76% and 84% at this score.
In the match things went Red's way with a spectacular backgammon! Boldness be my friend is the key. Backgammon isn't a game for the fainthearted, it's a game of aggression and the more aggressive player is the more successfull player. Let this be you!

Woolsey is Kit Woolsey, great teacher and brilliant player, particularly strong with the cube. His writings, webpage and matches are a rich mine of valuable information and you should take every chance to study these, particularly on the occasions when he plays a match on FIBS.
Uncle Jake is Jake Jacobs, theorist, writer and much travelled player. One of the most amusing men in the game, his easy going manner masks his very real skills. Very technically minded students may like to study "Can A Fish Taste Twice As Good?", his work with the late Walter Trice on adapting play to adjust for skill differential.

Friday 9 April 2010

Race Cubes Are Not Always Easy.

This week I got knocked out of the Fibs Spring Open in the second round. Nothing new there of course, but the disappointment of losing was very much less than the crushing knowledge that I had played with all the tactical acumen of a fencepost. I got two race cubes wrong at the sharp end of the match and here they are for your edification. The first comes when I lead 6-5 to 9 and White doubles in the position below. What would you have done?

White leads in the race 72-83, 11 pips. In an pure race (one where both sides have equal distribution) then that is about 2 pips shy of a take. I mentally adjusted a couple of pips to allow for the fact that White already has two men on the ace point and decided to ignore his gap on the 5pt on the grounds that it would probably fill as White bore in. Marginal take I thought, so allowing for this being skill free and me leading and me thinking that I play better than my opponent (usually!), I passed. To my horror, snowie (and gnu) tell me that this is only a marginal double at best for White and my take is very easy! Let's dissect it a bit further to see why.
The first things to note come in the distribution. Not only does White have two men on the ace point, but three on the deuce as well and I should be allowing for the extra man there as well. The gap on the 5pt may fill, but not necessarily and if White has to play checkers to the 6pt it may be long lasting, with every 5 adding more checkers to the ace point. On my side, the gap on the 3pt will fill nicely from the fat 6pt and the gap on the ace point hardly matters at all. All this makes for a fairly easy take for money, but the big surprise comes when we look at the match equities for a four point match and see that I can take very late at this score! I'm sure I've known this in the past, but just let it slip out of laziness. Here's how it looks.
Leading 3-away, 4-away I can pass and retain a ME of 50%. If I take and win I go to Crawford, 4-away or 82%. Take and lose has me trailing 3-away, 2-away or 40%. Thus the take risks 10% to gain 32% and my cubeless take point is 10/42 or 23.8%. Clearly I can do even better than that if I use the cube correctly at some later stage, so I should be snapping this one up. A sad pass.
Lesson to be learned? Review late match take and pass points! I should have all these comitted to memory. Don't make snap race judgments about positions with unusual distribution.

Later I led 7-6 but White, having got the message that I was wary of race cubes doubled in this position.

White leads 67-72, only 5 pips, surely this must be a take? As before, if I pass the match is tied so 50% ME for a pass. Take and win gets me to 100%, take and lose sets me back to Crawford, 2-away or 31%. Risk is 19%, gain is 50%, so I need 19/69 to take or 27.5% cubeless! I don't have that here, White is already about 74% cubeless to win this one and I should pass. In case that seems a lot, note that I will probably waste a lot of pips bearing in, with sixes and fives going deep into the board and I have an extra crossover. Taking is an error costing about 0.09.

You can bet that I am going to be taking more time over this type of position in the future. I may still lose of course, but at least I can have the satisfaction of knowing that I played it right!

Wednesday 7 April 2010

When should I think about doubling?

"When should I think about doubling?"
This question first came up for me in a seminar I gave before a BIBA tournament in the 1990s. The obvious anwer is "Before every roll of the dice", but that isn't very helpful and I was stumped for a moment. Mark Adkins provided the answer for me and it was, "Whenever something good happens!" Sometimes we can slowly improve in small steps until we are just good enough to turn the cube, but very much more often we arrive there in a sudden big jump because something good has happened. We hit a shot and the opponent dances, we fill in the prime or we roll a big doublet and when that happens, we need to raise a mental flag which says, "Something good! Cube?". Here's a good example of what I mean.

This is the first game of a five point match and Red has a 3-3 to play. He is already close to a double before the roll and if this comes as a surprise to you, consider these factors. He has a small lead 142 to 147, he has made two key points, the golden 20pt and his own 4pt, while White has done nothing except move a checker all the way from her 24pt to her 4pt. A double is a little premature but not actually far wrong. Now Red rolls 3-3 and fairly obviously fills the 5pt and the 3pt. White rolls 4-3 and plays 8-4, 6-3. She might also have played 13/6 and the more adventurous 13/10, 8/4 is also good (note the duplication of fives to hit), but for Red the "Something good has happened" flag needs to go up. He rolled a big number that filled two key points and White rolled a smaller number that only made one point. Note also that the idea of "a good roll" is deceptive; we need to think of sequences because your opponent always gets a turn after your good number that may modify it or of course nullify it completely. Then we have the position below with Red on roll again.

Now Red is much stronger, the best four point board, the best anchor and a ten pip lead and I am sure if Red had mentally flagged "Something Good" after his 3-3, then he would have been alert and turned the cube here, but sadly he didn't. He has already lost his market and this is quite a big pass.
For those of who for whom Market Loss is a new concept it is any sequence of rolls that mean that your opponent no longer has a take if doubled. Red has gone from not quite good enough to double to having a clear cash. Does this mean that he should play on for a gammon? Not in this case; just turning the cube and taking the point is good enough.
Now these positions are fairly straightforward presented on the page as problems and I expect that you didn't have much trouble with them, but over the board they took a decent player by surprise and he got it wrong. Because he rolled almost instantly, we can assume that it was lack of alertness that caught him out, so don't let this happen to you! When something good happens, raise that flag and think "Cube?"

It's A Lifetime Session

Backgammon, a lifetime session! Once you've learned how to play, learning how to play better has to be the object. This brings two benefits. The first is that you will win more often, always more fun. The second is less obvious, which is that the game will be more enjoyable.
No matter how much you learn, this is not a game that can ever be mastered. Even if you become a world class predator, with the top tournaments and high stake chouettes your natural home, there will still be positions, games, whole matches that will be a puzzle to you.
Let me tell you a story. Before backgammon, my passion was tenpin bowling and very early on I went on an instructor's course. This was great fun and I got a big kick from teaching people the basics. When I got the chance to go on an advanced instructor's course I jumped at it. This was to be hosted by Frank Klaus, the legendary American coach. Well there we all were, assembled and ready and he swept into the room, looking more like the traditional image of a drill sergeant than was possible, iron grey hair with a military cut, shoes shining, trouser crease like a knife edge, starched bowling shirt, the works. His preamble went like this.
"Good Morning. My name is Frank Klaus. I have been bowling for 32 years, my lifetime average in sanctioned play is 205, my season's high average is 223, this ring contains the diamonds taken from rings awarded to me for sanctioned perfect games and there are 13 of them, I have won this tournament and that tournament ( I forget!) and I am a member of the ABC Hall of Fame etc, etc" Well, just at the moment we were all thinking, "What is all this?" he broke off and said, "But let me tell you this. Even after all this, I am still learning and I learn something new about this game every time I walk into a bowling alley. let this be you too."
This is of course a good life attitude and it is just perfect for backgammon. Every game, something new. Sometimes that something is something old that has been forgotten or worse, half-remembered, but the games where the play takes a simple path, easily followed, are as rare as hen's teeth.

This blog is going to be devoted to learning. I'm no Frank Klaus, but I have sometimes lifted the winner's trophy in a tournament, I've given a few seminars and I've written a lot of articles. I'll be posting here several times a week and bringing you positions that have puzzled and interested and often defeated me in the matches that I play. If they interest you and inspire in you the same love and respect that I have for this game and its players, then it will all be worthwhile. Welcome to Dorbel's Daily!