## Wednesday, October 31, 2007

### Counting as narrative

When there is a sequence of trades and there is no queen involved that is standing in front her rooks or her bishop, then there is no need for going through the actual sequence. You can predict the outcome by just counting the values of the pieces according to the following method.

The usual way of counting, i.e. comparing only the #attackers with the #defenders is insufficient since it doesn't take the value of the pieces into account. That gives wrong answers when one side has two rooks while the other has one or none.

The maximum gain you can get is determined by the value of the victim. You can get never more since the defender simply stops trading.

There are 2 situations.

The value of the victim exceeds the value of the first attacker.
In that case you always win wood.

The value of the victim exceeds NOT the value of the first attacker.
In that case it depends on the values and # of attackers and defenders if you will get the value of the victim or not.

The method:
• Take as many attackers as there are defenders. Take the sum total of the value of the attackers (A).
• Take as many defenders as there are attackers. Include the victim. Take the sum total of the value of the defenders (B).
• If B exceeds A, you will gain wood, otherwise you will lose wood or stay equal.

At first sight there is no reason to presume that this method is limited to a trade sequence that takes place on one single square. I'm going to check if it works on multiple squares too. Besides that I'm going to look especially after the role of threats.

1. And what about tempo, Tempo? I remember that one important point in your original position has been a knight check zwischenzug, and I think such tempo moves change quite a lot in your counting formula. Often it is a rescue issue, saving one of the attackers from being re-taken, but in may also be additional material gain in a second scene of action.

2. Christian,
this first step is to eliminate the necessity to imagine a whole sequence of simple trades before the minds eye. To me this is already a quantumleap forward.

Of course there can be a whole bunch of tactics that interact with a sequence of simple trades. I can't guarantee that my counting method can be extended to cover all this. If so, the method will probably not be simple anymore.

Second step what I intend to investigate is if my counting method is applicable when the trades take place at multiple squares.

The third step is to investigate if it is possible to unite this simple counting method with the law of conservation of threats. If that is possible, it is my take that that comes close to what you are asking for. I can say nothing beforehand if this is possible. If so, it would eliminate an enormous amount of calculation.

The least thing will be that I enter a more complex position with a less taxed short term memory.

Thanks

Getting to 2000:
www.gettingto2000.blogspot.com

4. 2000,

5. A good start at a solution to the beancountin

It seems to leave out that either side can stop trading at any time, so you need a kind of running count such that if at any time the sum is negative, the sequence of exchanges is bad. You can't just look at what happens if everything is traded.

Indeed, this is a kind of generalization of your first special case. Just as if you should make the trade if your initial attacker is worth more than the target, so you should not make the trade if after you capture, he captures, and you capture, he will be up material. He can then just refuse the capture.

So, let sum(AxD)(i) be the sum of material the attacker has gained after i captures. Let sum(DxA)(j) be the sum of defensive material gained after j counter-captures. If there exists an i such that sum(AxD)(i+1)<sum(DxA)(i), then the sequence shouldn't be initiated.

This is nice, as you need no special case, and it can be used for both sides, and it is easy to implement in a computer, and is easy to think about.

It assumes no in-between moves, all captures on one square, but that happens fairly frequently so isn't a bad assumption for lots of practical cases.

6. First sentence of previous post should say "A good start at a solution to the beancounting problem." I think I cut it off.

My coach was always on my case about beancounting.

7. The problem with my method is that you can't just count everything to decide. You have to calculate the running count to make sure he can't just stop in the middle. So while this makes things more complicated, it also will avoid errors such as your B takes his P, his P takes your B, your B takes his P, and he just doesn't recapture and is up, even though you have two minor pieces more attacking and he has major pieces defending.

I think this was implicit in your previous post, but it should be explicit.

8. Blue,
I finetuned my rules such that it automatically reckons with stopping to capture halfway. That is the reason why you can never gain more wood than the value of the victim, for instance. The outcome of the method is binair: should I start to capture yes or no? You don't know beforehand what you are going to gain exactly due to stopping halfway. But I wanted to keep the formula simple.

Have you found a situation where the decision to start the capture is wrong?

9. There is more implicit in the formula. It doesn't have a correct solution if the victim is a pawn and the defender is a pawn. Because I think that you already know what you are doing when capturing such pawn.

But then again, it is supposed to be practical correct, not scientificly.

10. Ultimately this is all very simple. Count the material and see if you come out ahead in the exchanges. That's why they call these counting problems! You have to count twice: number of attackers and defenders (the first rule taught to beginners), and then total material gained (the second, and more helpful rule, taught to beginners, as in Wolff's book and Heisman's articles).

All methods will involve beancounting. The more they save you from visualizing every possible exchange, the better!

11. I think my formulation is more practical, as aside from the assumptions there aren't any exceptions to remember.

12. Which gives us unsight in the character of a grandmaster. He just assumes that such counting formula is correct without an itching need to check it out first. I never dared to assume it was so simple so I always checked it by visualizing the moves.

And so I have to suspect that the grandmaster will have a lot other empyrical rules too what prevents him from calculating the obvious. Obvious with hindsight that is.

I, always worried about correctness, has to muddle 5 days through the mist before it starts to dawn. Maybe I should make empyricism my inner god in stead of logic. DK would love that.

13. I think you might be right that yours is more practical in one sense: start with that. If it works, then you still have to check to make sure there aren't in-between moves, refusal to capture (stopping the sequence short), etc.. It's like forming an intitial hypothesis and then looking for data that will refute it. I think in practice that may be easier than looking 'forward' at each possible step first.

OTOH, if the original big picture view doesn't work (e.g., he has more defenders than you), it would be a mistake to stop looking. Perhaps you can start, but not finish, the sequence of exchanges. I don't see any way around the cumulative sum approach (cumsum for short).

My coach just saw the results of counting problems without actually doing the bean counting. I am better at it, compared to a beginner, and need to explicitly count less now. It is only when my pattern recognition is broken that this comes into play, as you pointed out before. But he "solved" hard counting problems immediately, saw them as quickly as if I had moved my Queen to an illegal square or moved my King into check, just an instantaneous gut reaction, Oh that's bad, you've got to count your beans!

Partly because of that rapid unconscious ability many GMs would probably make horrible coaches as they don't realize just how hard these things are sometimes for patzers.

14. If we're gonna just be pragmatic, then Heisman is probably sufficient.

15. This is making a lot more sense now that you've put it into words. I looked at your examples from yesterday, and looking at the diagrams it was easy to acertain whether the attacker was gaining wood or not.

However when I looked at the formulas you came up with, I found myself having to scroll back up and see what each part represented. I'm not sure if in the heat of the battle I can work my way through the process using the formulas. Math has never been my forte despite the fact that I'm a chess player. (In college I was the only member of the chess club that was not majoring in either math or computer science.)

16. is that you in the photo? honestly, seriously. i ALWAYS wondered what you look like.

17. Polly,
that's the problems with a blog. It reflects your thoughts while not quite crystalized. That makes it look more complicated and highbrowed than it actually is. On the other hand, that's the charm of it.

18. So did this fellow throw the dog?
Or is he simply upset that he found him jumping on his bed?

19. Tak,
the title of the photo was "dog toss"