Chess will never be solved, here's why

@8376

"none are true" ++ To the ignorant detractors.

++ To anyone who has difficulty believing six impossible things before breakfast.

I'm good with Tromp's study and his 10^44.6 number.  I am not good with any of Tygxc's numbers.

I have some quibbles with the number (it depends on what you mean by "position"), but it's adequate for discussing solutions to basic rules chess (suitably amended to be soluble). But

1. It's not 10^44.

2. It's not adequate for discussing solutions to competition rules chess  (suitably amended to be soluble).

Below are two partial games

The final positions (shown) in both games are mate in 16 for White in both basic rules chess (suitably amended to be soluble) and competition rules chess (suitably amended to be soluble).

In basic rules chess (suitably amended to be soluble) any solution of the final position in the first game is a solution of the final position in the second game and vice versa.

In competition rules chess (suitably amended to be soluble) any solution of the final position in the first game must begin with 35. Ra1 and any solution of the final position in the second game must begin with 35. Rb2, so the positions have no solution in common.

The FENs for the two positions are identical.

Tromp therefore counts the two positions as one. 

He also counts any positions with the same diagram and side to move but ply counts  in the range 69-150 as the same as the two shown, because he ignores the ply count, though all those are drawn.

The top Nalimov move shown by Wilhelm and the top move shown on the Syzygy site is Ka2 for both positions, which draws immediately by triple repetition in either. (Another reason why @tygxc's point 3 is wrong.)

It would be possible in principle to produce a tablebase that took into account the kind of difference I've just exhibited, but a tablebase for just KR v K may be beyond our current resources. (It might be possible to solve it as a mathematical puzzle using one's biological computer - I'll need to think about it some more).

An interesting problem you might like to try, is to produce the lowest upper bound you can find for the number of competition rules chess (suitably amended to be soluble) positions in KRvK, where positions are regarded as the same when the same set of legal continuations is possible for each. I asked @tygxc earlier, but, natuarally, he didn't even get as far as "++". He just repeats, "there are 10^17 relevant positions pretty Polly pretty Polly pretty Polly ...".

Still waiting for you to demonstrate what you know to be true against SF, @Optimissed.

It is worth elaborating on my earlier point that for practical purposes, basic chess analysis (with just an n-move drawing rule, no repetition rule, say) suffices in many cases.

For example, when an engine uses a basic chess tablebase for competitive chess with a repetition rule, there is no problem. The reason is that the sorts of problems that could occur would already have been avoided given access to the tablebase.

Say a tablebase position is reached and you fear that it won't work because a previous double repetition of a position in the fastest mate line. If this position had been previously reached, a faster mate would have been chosen, with no repetition occurring.

Likewise every strategy that has a vulnerability to repetitions from a winning position can be easily replaced by a more efficient strategy that avoids pointless repetitions when it is winning.

The special cases I referred to in the second sentence include positions that do not repeat a prior basic rules position as defined by Tromp, nor include prior repetitions on the same basis. Those obviously include ply count 0 positions which, for given material, are always the first positions reached in a full game so the Syzygy tablebases are sufficient for the purpose of game play, Fully agreed.

Also any solution that provides a winning strategy that includes repetitions can be reduced to a strategy that doesn't (though not necessarily easily enough to still qualify under my "timely" constraint). 

But you appear to be talking about a solution that has already been arrived at.

If you plan to produce a 32 man tablebase then you can refer only to basic rules positions and still arrive at a weak solution of the initial (ply count 0) position. No argument there.

On the other hand, if you plan to produce a solution along the lines described for checkers using SF, it will happily repeat positions whether it thinks it's winning or losing which in any case correlates only loosely with whether it is actually winning or losing. Neither, in general, do seven maids with seven mops know any better than SF until the fat lady sings.

What would be your algorithm for avoiding positions that repeat prior basic rules positions for that approach? Would it work without modifying SF?

The solution of checkers amounts to two drawing strategies, each with help from a tablebase (and some handy symmetry-based simplifications).

Being able to repeat positions suffices to draw, so the opponent of each strategy needs to avoid this. This allows truncation of all lines that repeat positions in the analysis that generates two drawing strategies (which is mostly about dealing with the large number of opponent options, first by trying the highest evaluation move, then if that fails the next highest, and so on).
At least that's how it seems to me.

When the objective is to find a winning strategy, any repetition can be viewed the same as a loss: these need to be entirely avoided (to have an efficient winning strategy, with no unnecessary waste of time).

It's worth clarifying one of those concepts - when seeking a winning strategy, you may as well strengthen the objective and seek an efficient winning strategy (one that never repeats a basic chess position against any opposition). It seems impossible for this to not be more economical in computing time. In fact if your strategy provides a single move for each basic chess position, this has to be so (as then a repetition can always be turned into and n-fold repetition and a draw by the opponent).

And another. When seeking a drawing strategy, you can effectively view a single repetition as a draw. The opponent needs to be able to avoid these (by finding an efficient win) to refute your strategy.

And, put like that, it is clear the two are closely related.

Why don't you submit this to Tromp?  There's a bounty of up to $256.  I'll only take a 20% commission ...

Of course, I know that there will continue to be some incremental improvements and the number should drop further.  Before Tromp the best number was 10^46.7.  Do I think such improvements will ever take the number under 10^40?  No.  I have seen discounted studies (prior to Tromp's work) that claimed 10^43.  

Until then, I will stick with 10^44 as the number of unique positions to traverse, knowing there might be somewhat less, but no more.  

Lul

That was an informal statement of a mathematical proposition for a class of games similar to chess in many ways (which can be axiomatised) that I am confident is true, and was understood by others here.

By contrast, a narcissist who does not understand reacts like you did.

Let me show you a rough proof of the proposition:

Suppose you have a winning strategy which sometimes repeats a position when used. One of the moves the strategy plays in this position - call it M - must not permit the opponent to force a repetition of the position when the strategy is executed, because if all of them permitted this, the opponent can draw. Simplify the strategy by always playing M in the position. This gives a simplified strategy that has one fewer positions that ever gets repeated.

Induction proves the result □

Your reaction was pathological. The specific pathology is some type of narcissism.

Another 100's Post I made.

That is like 4th or 5th Time, doing this.

optimissed im not sure that you realize what tygxc means when he claims that chess is ultra weakly solved.

"  Steinitz, Lasker, Capablanca, Fischer, Kasparov, Kramnik, Carlsen, Nakamura said that and millions of human and engine games prove it" 

btw none of them ever said that.

and "millions" of games means nothing in terms of mathematical proof.

I am not at all sure @tygxc does either.

lol

optimissed the reason why i asked about ur understanding of the ultra weak solution is that you agreed with tygxc's false claim that chess has been ultra-weakly solved.

I don't even know what this thread has degenerated into but I guess I could pitch my two cents.

The question whether chess can (theoretically) be solved (=outcome is clear from any position) can be easily answered. There is a finite amount of positions. I hope nobody's arguing that. On top of that if you accept that there is a finite amount of moves from any position until an outcome is reached, which is true with n-fold repetion and n-moves rule, one could theoretically check each position one by one, playing all possible ways the position can develop.
This would solve chess.

Now, realisticaly, that's obviously not possible. Not even with supercomputers.

yes.  this thread is basically one guy claiming that it could be solved in 5 years and the rest of us telling him how hes wrong.