Reprise

This position from the last post, with which you are probably now very bored, generated a lot of comment on BgOnline.org.



The story so far. I thought that, although this position is technically to good to double, it was a good practical double. This attracted a lot of criticism, on the grounds that nobody sober would dream of taking this, so you don't ever get a wrong pass. Wrong passes are worth a lot when doubling positions that might or might not be too good.
My reasoning for advocating cashing as a sound practical play was that you get your point for nothing. You can't make errors if you get hard rolls, you can't be jokered and you aren't vulnerable to horrible oversights. This attitude was criticised by several, on the grounds that you can't teach people to play well by teaching them to play badly. I would agree with this actually, if those learning have ambitions to be a world class player. In practical terms though, most players would be very happy, given the limited time that they have to apply to the game, to be a strong intermediate! Think of it as insurance. When you hire a car, you can insure against excess damage claims, typically costing $20 for a $500 excess. As a bet, it's very bad, but for peace of mind it's very good. I like to view giving up some equity to get a solid point as insurance.

Is there anything else to add about this position? One of the players who took some time to look at this in detail was Stick Rice. As he is probably one of the ten best players in the world, you'd better believe that he knows what he is talking about. He showed this to a group of students at intermediate to open level, all of whom wanted to cash. None of them thought that it was too good, which is interesting. He also appended a guide to what he thought we should be thinking about when making the decision to double or play on. I can't improve on it, so here it is.

• Is it too good? (a toughie, I know)
• How too good is it? (the size of the play on)
• Would anyone in his right mind take this cube?
• If things go badly for me is it still likely that my opponent will toss up his hands and pass a cube just because he knew I was playing on the entire time?
• How hard is it to play out for me? For my opponent?

I love to play on in actual play. People generally know you're playing on even if it's a small no play on they get that is what is happening and when things go sour for you they sort of toss their hands up and pass the cube automatically that may very well be a take (or even better yet, a no double) just happy to escape from the game.

The fourth point here is very interesting. Mochy once told me (not that I'm a name-dropper) that it was very unusual for a position to go from too good to double/take in a roll without a massive joker. If of course, the side playing on has only been just too good, then that is much more likely.

I left you with some of the later decisons that you might face after playing on. Here's the first.

6/off is correct. The White blot inboard gives us the licence to take a man off and keep the board.

Here on the other hand, taking two off is a big mistake. The best play is 6/4*/1. Applause if you found that one.

Cube action? We're back in cash or too good territory and this one is double/pass. Both failing to double and taking are big blunders. If you don't double and dance and White rolls 5-1, you can get to this one. Great play by White by the way!

It's still a double because of those four blots and the open 4pt but White's take is now very easy.

Lastly, another cute checker bear-in play.

On auto-pilot we might all play 12/5 or the inferior 8/6, 8/3, but he clear winner is 12/7, 8/6! This gives us the most closing numbers for the 2pt and gives us shots from the bar to put White back on the gammon if she can hit a fly shot. It also gives us awkward 6-6 and 5-5 next, but we mind those much less than usual with White's weak board and blot. Look out for these plays and win admiring looks from the flashy play crowd when you make them. Don't overdo it though. White's board really has to be this bad to make them work.

Thanks to all the GammonLine posters on this, not least because it's just about doubled my average readership! Stick with us guys and until the next time, enjoy the game!

Learning To Love The Cube, part 6

At the end of the last post, we finished with a cube action question and here it is again.



Black on roll, White on the bar and the score is 3-away, 3-away. Cube action?

The "correct" answer is that this position is too good to double and White should pass. In round numbers Black wins 84% of these including 24 gammons. Black's equity according to a rollout is 1.121 if he doesn't double on this turn. Nevertheless, doubling here is a good practical play for Black, against any standard of player. Why, you may well ask, is he advocating that we make a cube blunder here?
Cubing now and getting a pass puts a point onto the scoresheet. Without any mental effort and without having to play skilfully, you get your point and it is a real point. The 1.121 points that are your expectation if you play on are theoretical and you have to play perfectly to get them. If you like, you can view that extra 0.121 as a cost that you pay to have your point delivered to your door. Is this price too high? I don't think that it is and here's why.
In order to grasp that extra 0.121 you have to play perfectly from here on, with cube and checkers. Studying this position and playing it a lot, I found that it was very easy to make mistakes that added up to or exceeded that 0.121, even in the first phase where Black is just running his checkers round and White is dancing. When White enters things get harder and if White can enter and hit, it turns into a very tough game indeed. If White's play was equally difficult in each of these phases that wouldn't matter, but it isn't. She can't make a mistake while dancing and if she can enter with a 2, then her play will be pretty easy too. In the "enter and hit" phase things get tougher but I found that it is still Black who is more likely to err, as it will be him who is facing the cube questions. In real life, the actual price is very much lower than the theoretical cost of 0.121 and there is often no cost at all. In a proportion of the games Black will play perfectly of course, usually those where he cashes later, but in some games he will make mistakes that add up to more than 0.121 as well.

Don't believe me? Here's a useful exercise. Set up this position in your bot, use play it from here and analyse each game in turn. If you are any standard below world class, then you will find yourself making errors here.
Some points on how to play this. Freeing those Black checkers in White's home board is top priority, much more important than arranging checkers to close the 2pt. Making the 8pt is nice of course, but if you can't you need to pick it up. When you get into the bearoff, you can play very aggressively because of White's weak board and blot. When she enters it's sometimes double and pass, sometimes you can still play on. it won't surprise you to know that I tend to cash these!
Here's some examples.

Position 1


Position 2


Position 3


Black is on the bar. Cube action?

Position 4


Black is on the bar. Cube action?

Position 5


These are just five of the dozens of tough plays that I found. You can find a lot more yourself if you play this position. All of these can be avoided by just cashing in the first place, saving mental energy, avoiding tough decisions, avoiding the careless mistakes that we all make. Lastly right at the beginning, I said that you should double against anybody, weak or strong. The stronger the player, the better the cash as she will clearly outplay you. Double weak opponents to0. Their play will be simple or forced in a lot of the games anyway, although when it gets tough after a hit they may play badly, but if they are very weak, there has to be a good chance that they will take inj the first place! An 11% chance of a bad take makes the original position a correct double.

In the play-off semi for Fibsleague 55, BushSucks edged out stukatz in a tough and exciting match, so the final will be, ahem, BushSucks v. dorbel. I'll let you know when that is scheduled.

Until the next time, enjoy the game!

Learning To Love The Cube part 5

So, with all this talk of aggressive doubling, I expect that you want to see some examples. They aren't hard to come by. Almost every match has a crop of them. Clearly the most potent are those that have a large gammon component, gammons for you when successful and lots of wrong passes when Gammon Fear strikes at the heart of your opponent.

Game One, 0-0 to 7, Black on roll and White on the bar.


Forty pips up and with White on the bar, it's pretty clear that Black has a double, but can White take? Well, she is anchored, she doesn't have any more blots hanging about and there are plenty of Black rolls that don't cover both blots. 6-6 and 6-5 don't cover either! Even when Black can cover both, White is still a favourite to enter and often has some indirects to spice it up a bit. Cubeless, Black is going to win 66% from here with 27 gammons, but White's cube ownership is enough to give her a comfortable take. A pass is a blunder, but White passed.
A hidden plus point for Black when he gets a pass here is that it's a big tell for future games. Information about how White handles dangerous cubes is very valuable indeed. So, in game Two, now leading 1-0, I reached this next position and turned the cube.



You can see straight away that Black is nothing like so strong here. He only leads by 11 pips, 142-153, White isn't on the bar and Black's hitting fives are duped. White also has the stronger board, but that is cancelled out by havingtwo checkers out of play, so the positional variants won't be so easy to play for her. However, I doubled and White took. The double is an error costing about 0.057 technically speaking, but 11% wrong passes is enough to make it correct. Does White pass this that often? Probably not, but anyway, I've doubled her into a game where I win 65% of the time with 22% gammons, so not so bad! A long game saw me get hit and closed out after bearing off 8 checkers and eventually we got down to this next position, where White finally gets a chance to use a 4 cube.



This is exactly what I have been talking about when I say that a lot of equity for the taker lies in her ability to use a 4 cube correctly. This one isn't hard to work out. White wins 1/6th of the games straight away with a doublet and when she only rolls a singleton Black has 19/36 misses. 1/6 + 5/6 x 19/36 equals 131/216 or a shade over 60%. Tragically White failed to cube, a 0.194 blunder. This pays for my initial cube error three times over!

I'll leave you with this nice position to think about. Black is on roll, White is on the bar and it's 0-0 to 3. What's the correct cube action for both sides?



Let me have your thoughts please and we'll come back to this in the next post.

There's a good match on Fibs tonight (Monday) at 1900 UTC, stukatz (USA) plays BushSucks (Germany) in an 11 pointer, the semi-finals of Fibsleague 55 play-off. These are both experts so it should be a good battle. Whisper only please watchers.

A reminder that entries close for Escoffery's Fibs Spring Open on March 25th, so don't delay, get an entry in today.
http://www.escoffery.com/spring.html for all the rules, contact address etc.
Until we meet again, enjoy the game!

Learning To Love The Cube, part 4

In the last three posts, I've been making the point that very early doubling, particularly in positions where there is a strong gammon threat, is a tactic likely to lead to more wins for all of us. It's the way that the bots play and it's the way that the best humans play too. Even when the cube is too early to be technically correct, it can still reap benefits in two ways. It can generate a wrong pass, not common but it does happen and it also means that you can't then miss a string of correct doubles and wind up cashing when you are too good, a very common occurrence. A student makes the point that when this happens the bot doing the analysis assigns an equity loss to each of these events and adds them together. "This can't be right" he says. I put this point to the leading technical expert Rick Janowski and I quote his reply word for word, as I can't better it.

RJ: Your student has a point. XG adds all the errors together which over-emphasises the scale of the error.Taken to its extreme a run of several very similar cube errors could result in a total equity error much greater than the overall value of a game, which cannot be right. Nevertheless, missed cubes can still result in substantial cumulative overall equity loss, whereas early doubles do not carry the same ongoing risk.

In the comments, Robert Fontaine takes me up on a side issue, where I said that an ace point anchor on its own is always a pass. "Is this true?" he asks. Like almost any statement in bg, I could hedge this one round with lots of ifs and buts, but it's mostly true once the attacker has escaped to the midpoint. Here's a case in point, from the very next game after RF wrote his comment funnily enough.



Black is on roll in the first game of a three point match, at which score this is a huge pass. It's still a pass for money too. White just doesn't win enough games. A very important factor to consider in any position where hitting a shot is vital is, "Is my home board ready to contain a hit checker?" Here it isn't and White must give it up.
When you put this position and others like it through the bot that you use for analysis, you will find that not doubling in this position is only a very small mistake in terms of equity loss. This is because you can almost always cash next turn anyway and will rarely become too good to double. However failing to recognise that this is a cube is a big conceptual mistake! People commonly play on here thinking, "I'll just wait and see if this gets more gammonish, as he's certain to pass if I double now and I'll only get one point". True, but (a) he may get a joker sequence after which you won't even have a cube and (b) if you double now, you may get a wrong take anyway and (c) you don't want to have to keep making "Should I double?" judgments for the next 15 or 20 rolls. It's something of a truism that people playing on for an undoubled gammon against an ace point anchor are either making a mistake or have already made one! In certain positions though and at certain scores, this does become a more attractive option.



I'm playing Black here, leading 1-0 to 5. White, a decent checker player but notoriously timid cube handler, has missed five opportunities to double me in or out in a prime/prime battle, after which I rolled 6-6 to end up here. With White having three men on her anchor, this is too good to double even though there are a few joker sequences that can lose for Black. The tragic sub-plot is that I accidently clicked on double and White gratefully passed!

Finally, if our attitude towards doubling should be bold and aggressive, pushing the boundaries of what is technically correct, how should we view our take/pass decisions? Falafel, perhaps the best player in the world, says, "If in doubt, I take". This works well for him, because his superb checker play and the possibility of his usually inferior opponent making errors, means that he can approach or equal and sometimes even exceed the theoretical equity of the position. Should we imitate this? I'm not sure that we should. In all positions other than simple races and holding games we will struggle to approach the theoretical equity and may also fail to use the recube efficiently if things go our way. Having always been in the "inclined to take" camp, I am now trying to pass the close ones, even if this means giving up some equity here and there. This is because I now use XG and its collected stats show me that I lose more from wrong takes than I do from wrong passes, particularly of course, the ones that have a lot of gammons attached. Look at it like this. We can be inclined to be bold when we double, because these decisions occur in games where we are winning. Take/pass decisions occur in games where we are losing and we only get one chance to get it right. The hardest of these are unquestionably blitz positions and I will trawl up a selection of them for you to look at in the next post.

Until then, as ever, enjoy the game!

Learning To Love The Cube. part 3

A Reader writes, "It's all very well saying that you think that we should double as soon as we think that it might be a double, but what should our winning chances be to make it right? When should we first think about doubling?"
This is a very good question. Let's take the second part first. When should we first think about doubling? I would say, whenever something good happens. You hit and they dance, you roll a great number to make a vital point, you escape, you roll a useful double. All of these represent a big leap forward. If one of these things happens, it's a great indicator that the cube is hot. If you are a beginner, just using this as your wake up call will work well, but the real trick is to get your double in before the good roll! If you can anticipate the likelihood of a big swing next turn, then you'll be doubling like a pro.
Now the first part, what winning chances do we need? Usually of course, you need to at least be the favourite, but there is no set threshold where it becomes right to cube. Your chances might as little as 53% and it be clearly right to redouble, or as much as 70% and still not have a initial cube. The key factor usually is the volatility. If it's a race or you are bearing in against a holding game, then things aren't usually very volatile and you don't need to make the take too easy. A correct cube will probably be in excess of 70% wins. If on the other hand it's a blitz or a position where the next roll will decide things one way or the other, then something much less can be enough, particularly if there are some gammons about.
So, what sort of thing are we looking for in order to anticipate our good roll and get the cube in before the party starts? Look at this position.

Position One


Black is on roll and leads 1-0 to 5. This isn't an immediately obvious cube, but it's actually quite strong. What are we looking for? Black leads in the race 140-158, more than two average rolls. He's made his 5pt, while White has no points yet and Black has also escaped a checker. White too has one loose checker and her back men haven't moved yet. Black is already very strong, winning about 68% if the game is played to the end, with around 17% gammons, but crucially this is actually quite volatile. Black has a range of threats. He can hit the blot or make the bar or another inboard point, or escape to the midpoint. When he can't do any of these things, he can just make a safe quiet play. After that it will be White's roll and on her turn, she has almost no threats and some difficult rolls of her own with those awkward stacks. This recipe, a variety of threats and no really bad rolls, is always the basis of a cube.
In the match, Black didn't double and ran out with a 5-4, then White rolled 5-2 and made her 4pt.

Position Two.


Nothing much has happened but Black has lost his market and this is now a clear double and pass. The race has got shorter, Black has increased his lead and White now has to try and win with an ace point holding game. In real terms, Black's wins have jumped to 73%, but his gammons have dropped to about 11%, although I wouldn't attempt to calculate that over the board. I just know that an ace point game and nothing else is a pass!
If boldness is our guide when doubling, should we be bold takers too? We'll look at that tomorrow.

A new site to me is WarpGammon but it comes well recommended. They have regular tournaments, mostly free entry, but there is one that costs $11 to enter which should be fun.
You can play your matches on various servers, including SafeHarbourGames , a nice friendly site where I have played once or twice. Venture out!

Fibsleagammon season 55 has now finished. Provisonal result. From Master A perennial rivals dorbel and BushSucks will cross swords with stukatz and Mason_Verger from Master B in the playoffs.
These should be terrific matches with a high standard of play, so I'll try to tell you when they are scheduled.
Until tomorrow, enjoy the game!

Learning To Love The Cube Part 2

More Fibsleague news. In Master A dorbel and BushSucks will be going into the playoffs, where they will be joined from Master B by stukatz who produced a late burst to finish 9-4. The second place there will go down to tie points between the players who finished on 8 wins and as it stands Mason_Verger leads that pack. The Gold, Silver and Bronze divisions have thrown up some rising stars who will be looking to do some damage when promoted. _loak from France has compiled an 8-2 record in Gold A and MISS_IRAN has topped that with 9-2 in Silver A. pilogen (Italy) has had an outstanding season in Silver C with an 8-3 record and it's great to see that perennial Fibs favourite MacMom topping the Bronze division on 8-3, just ahead of fellow American twist on the same score. Last but not least, the Sesame division has seen lots of action with players from 9 different countries, including Ukraine and Hungary and all these players will of course be in Bronze next season. Mention must be made here of Alexander from the UK, currently on 7-0!

I'd like to expand a bit more on what I said about doubling in the last post, in the light of several very interesting comments. I think, in fact I am sure, that players below expert level are too cautious with their doubles. I don't think that this is because they under-estimate their winning chances, because they don't really think of positions in that way. Part of it is just pessimism. "What if she turns this one round, I'll be losing two points instead of one". Weaker players don't win as often, so they do tend to have a pessimistic outlook!
Here's a position that illustrates this, from a match with a student.



White is on roll and on the bar, and it's 0-0 to 5. Cube action?
This is in fact not a commonplace position and if you said, "I have thought about this and I don't think that it is a cube", that's fair enough. It's a huge blunder not to cube and we all make huge blunders from time to time, but what the student said to me was, "All I could think was, 'What if I dance?'" All he could see was the dark side, the 16 rolls where White danced and not the 20 rolls where White entered. This pessimism stopped him from even considering a cube.
In practice, if White does dance, Black is probably a very small favourite, certainly not good enough to recube, whereas he will be a huge underdog if hit and struggling even if White just enters. Very volatile positions like this are often cubes. I like to ask myself, "If I roll my worst, can he redouble?" If, as here, the answer is no, then that is a very strong pointer towards doubling. Still struggling to see this as a cube? Set up the board and play it 50 times with the cube in the middle and 50 times with Black owning the cube. You can actually do this simultaneously using 2 cubes. You'll learn something about the position, which is nice, but much more importantly, it will do wonders for your attitude in the future.
There is too a natural human tendency to want the match to last as long as possible. I don't know what the reason for this is, but it is very common. I saw this position passed recently.



It's 2-2 to 5 and Black redoubled to 4. White passed. It's pretty easy to work this one out, White wins the match every time Black throws a one, so White will win 30.5% of the time from here. If she passes, White will have to win the next two games, so her match winning chances are 25%. Passing hands over 5.5% of the match equity. How bad a mistake is that? It is the equivalent of resigning the first game of a nine point match before you roll the first die!
I asked White why she passed. She said, "I didn't want to put it all on the dice." This remark is actually fair enough if she considered herself to be much the stronger player of the two, but no she didnt think that, she would just rather play than end the match right here.
How much stronger do you need to be to consider passing this? If you think that you can win a cubeless game against this Black player 55% of the time, that's probably good enough to make this a marginal take/pass.
What if it is Black who is the 55% better player? This is by the way a very big skill advantage. Should Black even be doubling? No, if he is that much of a favourite, redoubling here is a big mistake.
We've digressed a bit here, because whenever I discuss cube actions you should always assume that the players are equal, but for the player trying hard to be more aggressive, if you are distinctly the weaker player, positions like these where the dice decide should be meat and drink to you. In these positions, both players are momentarily equal and you should be delighted to see the cube rising.
One more interesting sideline on the subject of escalating the cube and of course shortening matches. At one time the GBots on Fibs used to play 25 point matches. The reason that they don't do that any more is that some players worked out that their chances of winning a 25 pointer against a GBot were better, considerably better, if they could finish the match in one or two games than if they battled it out playing properly. The tactic was to cube immediately, take any recube and immediately recube to the next level, ideally getting the cube to 32. Against a bot, this is a brilliant and entirely legitimate tactic, increasing your wins in a 25 pointer from about 5% to about 18%! This doesn't work against a strong human, because he won't treat you as an equal, but the bot does and this flaw is what you are exploiting.

We've by no means covered all that there is to say on this subject of becoming a more aggressive cuber, so I'll go on with it again tomorrow. Until then, as ever, enjoy the game!

Learning To Love The Cube

There are several ways to approach improving one’s checker play but for me, the most important feature is your attitude to the cube. How do you view it? I want to divide this into Doubling and Taking, because the two skills are actually quite different. I see doubling as being much more important. This is because we typically face many more doubling decisions than taking decisions, as obviously we only consider a take when we get cubed, but have to consider doubling several times in every game.

World Class players, without exception, are eager to turn the cube at the first reasonable opportunity. They actively look for chances to double very early, as early as the bots and much earlier than players below expert level. There attitude is, “I think that this might be a cube, it’s certainly very close, so even if it is a small mistake, I’ll turn it now.”

If you are not actively looking for these opportunities as soon as you think that you have an advantage in the game, you are certain to miss them. Bear in mind that they adopt this policy even when they are playing another player of their own standard, so they have worked out that this attitude is technically correct. For the rest of us playing opponents that are anything but World Class, it is even more likely to be the right policy. Why? Look at it like this.

Doubling on the first roll that you think that you may have a double has some hidden benefits. The first is that it allows your opponent the chance to make a mistake. Choosing not to double does not do this. “But”, I hear you say, “If I double very early then there is no chance that she will make a mistake and wrongly pass”. There is less chance certainly, but there will be some wrong passes and when they do come along, they will be huge blunders. One blunder that gives away 0.3 or 0.4 of a point (and these do happen) will pay for a lot of slightly early cubes. There is more. Once you have cubed, you can’t then make subsequent cube errors in that game, unless of course you get recubed later. There is more too. Part of the equity of the player taking the cube resides in her ability to use it efficiently later, but only very, very strong players do this. If your opponent isn’t an expert, the chances are that she will miss her chance to redouble you in later and/or cash when she is too good to double. By giving her the cube it’s true that you give her some theoretical equity, but that will only help her if she uses it well and the chances are that she won’t. By cubing early then, you not only kill your own chances to make a later cube error, but you open up the possibility that she will do so!

“If I wait until I am stronger, then there is much more chance that she will make a bad pass”. This is absolutely true, but there are two things to consider here. The first is that you risk losing your market. The second is that the possible mistake that she can make is much smaller. If for example you wait until your equity is say 0.95 of a point after a double and take, then it is true that her take/pass decision will be very difficult, but if she makes the wrong decision, it only costs her 0.05 of a point.

The second kind of doubling decision is, “Am I too good to double?” This is one of the nicest decisions that we face of course, difficult to get right but always meaning that we are in a very strong position. I have a very simple rule for this. I only play on for a gammon if I am 100% certain that I am too good and if I do, I make sure that I keep reviewing that decision on every roll. How does this work in practice? It means that I make some small errors when I am technically too good (i.e. worth more than a point a game on this roll). However there are two compensating factors that more than make up for these errors. The first is the possibility of wrong takes, which are always huge blunders. Not very likely? Show me the player who has never taken a cube that was actually too good. I have and Iam quite sure that I will do again. They come up a lot and it only takes one of these every now and then to pay for a lot of small errors when they correctly pass.

The second is that when they correctly pass, it puts a concrete point on to the scoresheet. It isn’t theoretical equity, it’s a real point and I don’t have to play to get it!

So, we need an aggressive attitude that actively wants to double and we need a way of approaching each roll that gives us the time to consider a cube. Now of course we get to the difficult part, which is trying to figure out our winning chances so that we can see if we should be doubling. I’ll digress for a moment though, to say that experts never think to themselves, “What if he takes and turns it round and I lose?” They only think, “Is it a double?” However, looking at the position from our opponent’s point of view can paradoxically lead us to the correct cube action. This is the legendary Woolsey Rule. Invented by the great theoretician and player Kit, it simply states, “Are you 100% sure that this is a take?” If not, it must be a double.” Even easier, you can simplify it further to the dorbel rule. “If I was him, would I want to be doubled here?” No? Ship it in!

Food for thought? I hope so. Let me know what you think of this and please, ask questions.

Tomorrow we'll look at taking and passing and actually look at some real positions.

Until then, enjoy the game and get that cube moving!