More Midgame Cubes and Recubes

For the player trailing in a short match, his cube strategy can be summed up in the immortal words of Uncle Jake (Jacobs), "Develop an enhanced gammon threat and ship it in". Not very difficult, certainly a lot easier than entering the murky world of gammon prices and match equities at this stage. It is an infallible guide, in which the worst that you can do is give the cube away a bit early. It is worth expanding slightly on what constitutes an "enhanced gammon threat" though. At the start of any game you have about a 13% chance of a gammon if the game is played to the end, so around 20% gammons can be considered "enhanced". However, we can face some difficult decisions, notably when we have thrown a joker and suddenly jumped from not good enough into the "Am I too good?" area.

Position One


Black trails 0-1 to 5 and has just thrown 6-6 to hit three checkers and make his 2pt. White has fanned. Too good to double? Over the board I felt that this was much too good, after all, isn't it a bit wimpy to cash when your opponent has three men on the roof? A rollout suggests though that Black has the same equity whether he doubles or not, 1.00pt. Note that as advertised here ad nauseam, the cash is a real point, the play-on is theoretical and you have to play to get it. This is actually a reference position, although probably too rare to be of much use.
I rolled and covered the 4pt and White entered a man.

Position Two


This is now clearly too good. Black has improved his board and White's entering checker isn't enough to balance that. Everybody plays on, nobody takes, but note that Black's equity after rolling is still only about 1.1ppg. What happened next?

Postion Three


Black hit loose and White entered with a hit to leave this position. In the previous two positions it's been in my mind that even if White enters with a hit, I'll still be able to double from the bar and here it is, Black cubes. This is a big pass. Positions where you have a four point board and a man on the bar and another blot to shoot at are almost always passes. Here White still has two on the bar! Nevertheless, it's bonanza time for Black and White took, a double blunder and Black's equity jumps to around 1.2ppg.
The game took some wild turns from here as White entered everything with a 3-3, followed swiftly by a 4-4 to build a board and here is White on roll considering a recube. Remember she leads 1-0 to 5.

Position Four


Recubes are very tricky indeed for the leader. If she doubles and gets a take, she'll be redoubled for the match with gammons not counting, so the great majority of White players holding the cube at this score are reluctant to turn it, yet another reason to give it to them in the first place!
Black can take with better than 25% winning chances as his equity at needs 5, needs 2 is 25.64%.
Here, he is just a little short of that, but White wins around 37% gammons from here, so by a small margin it is technically correct for her to play on. Her match equity is about 75.5% if she doesn't double and the same if she doubles and gets a take. If Black passes that drops to 74.64%.
Phew! Is there any way to sort all that out over the board? Not for me there isn't. I would play on here thinking myself too good and you can arrive at this correct decison just by fudging it if you say "No idea what's right so I'll take a roll!" However, once again, turning the cube is a good practical move. You score two points if you get a cash for which you pay a small premium and when Black makes a small error, your ME reverts to what it would be if you hadn't doubled!
Whatever you ultimately decide, you must get into the habit of allocating a lot of time to positions like the above. Run through a mental list of rolls, decide how you play them, put them into groups. In this position, I don't ultimately think that it is going to help you decide what you should be doing, because the differences between right and wrong are so small and the complexities are so large, but there will be positions where the process of "reading the numbers" makes your cube action very clear. If you haven't practised it a lot, with positions like this you aren't going to be able to do it in a match.
In live play you have to do this in your head and you are supposed to do this online as well, although I suspect that pencil and paper is sometimes called into play. This is actually cheating, but it isn't cheating to practise like that. Practise playing this one too, it's very instructive!
I'll bring you a bit more from this game in the next post.

BushSucks won the Fibsleague season 55 play-off for a record equalling fifth title, defeating your correspondent in a 2 hour battle over 13 points, so back to the drawing board for me. Until the next time, enjoy the game!

Blundalonga dorbel, part 26 of a never-ending series.

One of the beauties of this game is the bewildering variety of different scenarios that you have to master. There isn't just technique, there are techniques in endless permutations, some you may only see once a year, some once a week, some daily. There is no doubt that working on daily situations will pay the biggest dividends, but now and again it's nice to look at something a bit different. Here's a series of doubling decisions from a recent match.



White is on roll, it's 0-0 to 5 and Black is on the bar. Cube action?
It's my guess that you will take longer over this here than you would in a match. Perhaps it should be the other way round! Anyway, White has semi-escaped and leads by 31 pips (105-136) and Black is on the bar against a four point board. White doubled, correctly and passed the headache to Black. I can tell you what went through Black's head, because it's me. I thought, "I've seen this before and it might be a close take, but I'm really not sure, so based on the fact that I've taken a lot of passes lately, I'll give this one a miss".
Tragically this cost me about 0.3 of a point, a triple blunder! Here's a list of the mistakes I made.
I didn't take long enough to think about it.
My decision was influenced by recent events, rather than viewed in isolation.
I didn't consider carefully every checker on the board.
This last was the worst. Here's what should have steered me towards a take.
White has seven checkers out of play, so from here she can only use eight checkers. All my checkers are in play.
White hasn't completed her escape. Move those two checkers on the 16pt to the 13pt and this is a very powerful double, worth 0.903ppg after double and take, compared to about 0.685 in the position above. This true even though it leaves White with a stack on the midpoint and a single blot in the outfield, a famously weak formation. This position is much more like what I thought I remembered.
White also has to cross an untenanted outfield, again a big positional defect. Move a checker from the 13pt to the 8pt in the above position and White's equity jumps to around 0.987 after D/T, making this a very valuable reference position, so here it is.



Now White has a landing point, no immediate blot and an extra checker for attacking. This is as near to a marginal take/pass as you can get, so worth remembering. Any improvement for White, it's a pass, any improvement for Black, it's a take. We haven't really said anything about Black's checkers, but that powerful four prime is very important. It would be even better if it wasn't "front-loaded", with the spares balanced on the inner edge, so any improvement there would help Black for example.
As I say, well worth remembering, even though you won't see one close to this very often, but there is a whole family of other positions where Black is on the bar and White has a four point board with a big hole in it. Doubling these generates a lot of wrong passes and if you would have passed position one, perhaps remembering this one will give you more confidence in the future.
We'll look at some more from this match tomorrow.

On Saturday 24th at 0900UTC, I am playing BushSucks in the final of Fibsleague season 55. It will be a 13pointer and I hope well worth watching. Whisper command only for watchers please.

Also this weekend, on the 25th, David Escoffery will make the draw for the Fibs Spring Open. There's already about 100 players in, generating a $5,000 prize pool, so why not give it a go? Rules on http://www.escoffery.com/spring.html , get your entry in quick. You can pay after the draw, but paying with entry is worthwhile as only paid entries can receive a first round bye.
Hope to see you there, until then, enjoy the game!

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!