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

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!

Another Dorbelblunder.

We left Black in this position last week, trailing 0-4 to 7 with the cube on White's side and apparently up the creek without a paddle. What is the correct cube action?
This is a handy reference position, easy to remember as White wins 88% of the games and 8 of those are gammons. At this score Black needs about 10% to take and redouble for the match, because that will be his equity if he passes and trails 7-away, Crawford. We can do lots of calculations to see whether White should redouble, but let me simplify it for you. At this score, it's almost impossible for White to have a correct redouble while there is a chance of a gammon.
Even leaving gammons out entirely, White's doubling window is so small, between 87 and 90% roughly, that her chances of ever being in it are minute. She'll either be not good enough, or she'll have a cash. Doubling now kills White's gammons and puts the match on the line, so playing on until those gammon chances have gone and then cashing is always the plan. In real terms, if White redoubles for the match, she'll be 88%. If she plays on and never redoubles she'll be 87.8%, but clearly she can do a lot better than that by using the cube to cash in all the games where her gammon chances disappear and retaining her 65% match equity in the horror games where she loses.
Player skills come into this. If Black is a world class player playing an intermediate, he should probably pass this, as his theoretical ME of 10% going into the Crawford game will be a lot better than that, because he will outplay White, which he can't really do if he takes this. From this it follows that intermediate White should turn the cube.
However, doubling does have one big plus for White. Humans hate to take and put the match on the line, so if White redoubles here, she will get a lot of wrong passes, from those who underestimate Black's winning chances and from those who know that the take is theoretically correct, but would rather try to win from 7-away, Crawford. In this match White (eberlein a very strong player) doubled and Black (me) feebly passed!
Doh! Tomorrow, if it ever comes, I have some lovely quiz positions for you, all of which were sent to me from Croatia. I forecast that this country has a very bright BG future, with a lot of good players improving fast and the Croatian Backgammon Federation - Hrvatski backgammon-tavla savez, up and running to promote the game there.
Until then, wherever you are, enjoy the game!