Is there any chance that a 1300 rated player can beat a 2700 rated player?

iam abrar ali and how are u

Lets say, for every move to make there are a total of 40 different possible moves. So to pick that one perfect move is a chance that is seen as 1/40. Lets say that the 2700 picks up a random defense (not a string of random moves, mind you, but one of the countless opening available as either black or white, which have so far been tested as 'sound') and this defense lasts a total of 50 moves against the perfect play before the 2700 is checkmated or forced to resign. To keep things simple, lets assume that for each of these 50 moves made, there are always exactly 40 move choices for the random move generator. Now do you know what the chances are of making all 50 perfect moves in the game? The answer is - 1/40*1/40*1/40 ..... 50 times. That is, 1 in 40^50. That is, 1.267x10^80. Which happens to be equal to or greater than the estimated number of atoms in the observable universe. Let's say it takes 1 second for both 2700 and the random generator to make one move (50 seconds for the total game), it would take 2.01x10^74 years for that one perfect game to occur. For reference, the universe is only 13.75x10^9 years old. Of course you could argue that the perfect game could be the very first game, but I think we can see that the chances are very very very slim. So slim, you can practically write it off ever occuring.

Don't forget that chess is basically a draw. If the 2700 plays well, as an 2700 can, he has no reason to lose even against perfect play. There's a relatively wide margin of error in chess, which still leaves you in draw land.

2700s generally know how to stay there when necessary - which is part of their skill set (not obvious or common to someone rated in the 1300's, or even 1800's for that matter), and frequently a strong player can build a safety net to 'minimize damages' when they recognize that they've got themselves in some 'soup' against weaker opposition. 

Perfect play a win does not guarantee. 

By the way, this thread is fairly old, and last time I checked the score was : 2700 - 54, 1300 - 0

I'll keep you updated and we'll have multiplex with the alternate universes in our next broadcast

"Perfect play a win does not guarantee" (solskytz)

That's actually a very good point. Rather than arguing endlessly that epsilon > 0 (I think everybody understands that), I would be interested if our apprentice mathematicians come up with a model to assess drawing chances of a given elo strength against 'near perfect play' (in the computerish sense of the word).

Or to give a practical example : what would be the chance of a strong GM to at least draw a match against a 'near perfect player', if we assume every draw counts as a win for the human ?

Come on guys, give me a mathematical model for this rather than splitting hairs endlessly with your randomly generated 'to be or not to be here till the end of the known universe' monkeys...

If we can solve this, we actually answer another very interesting question.

If a superGM (2800+ rated) has a non zero score against perfect play, we can deduce the ELO rating of a perfect player, therefore the maximum possible rating. I always thought claims that 10000 ratings are possible is nonsense, I actually wonder if it's as high as 4000

I once read some place that perfect play was estimated at 3600. Meaning that a top 2800 should get a draw once in a 50 games, a win once in 100, or any reasonable combination thereof...

You think about someone like Nakamura, Anand, Magnus, the other guys up there on top - maybe also Capablanca, Alekhine, Fischer, Kasparov, Karpov, up there along the best of them... you say - hell, why not?

It is my impression that chess improvement goes like an inverted pyramid - you need to learn very little to get from 500 to 600. More considerable effort and difference in understanding goes on the road from 1200 to 1300. Every 1800 knows that it's hell to get to 1900, and for an 2300 to go up to 2400 - well, it can be the known impossibility of a lifetime (actually this applies for different people in different levels). 

Now, what is perfect play? There can actually be levels within perfect play which won't translate to elo - like, these two 3600's playing hundreds and hundreds of very interesting and highly exciting games, full of multi-layer manouvers, impossible to fully explain to anybody below 3100 or so... of course they draw every time, as they are so perfect (they do manage a 64% score against the less fortunate 3500's, of course), and of course some kibitzer here would call them 'drawnik' (except when playing against 3400 patzers or so) and 'void of fighting spirit' etc., but - 

the amazing thing is that chess is so intricate and with so much of a margin for an error, that it would turn out that 3600 player A always gets 'the better side of a draw' then 3600 player B - he's really more skillful... he's always the one stalemating when a pawn up, or ending up the exchange for a pawn in an impossible-to-win endgame where only he has winning chances, or gets to create that winning endgame up a pawn whereby his opponent will need to sacrifice a piece to get to K+B+wrong bishop pawn against bare K... 

many different possible levels which will not translate into Elo, the Elo system not being sensitive enough to such fine differential of skill between two perfect, incapable-of-losing players. Perfect and 'more perfect' if you want. 

"Or to give a practical example : what would be the chance of a strong GM to at least draw a match against a 'near perfect player', if we assume every draw counts as a win for the human ?"

Thanks for complimenting my train of thought :-) I'll try to answer your question - so of course, 'near perfect' - depends HOW near to perfection :-) Near is subjective, and I had my share of people staring at me in awe, believing I represent personally chess perfection (happened to you too, I'm sure...). "This guy just sees everything!!" Yeah, right... 

But if perfect chess is 3600, then a 3400 is expected to draw the match under the conditions you stipulating (supposed to get 25% against someone 200 points up).

"what would be the chance of a strong GM to at least draw a match against a 'near perfect player', if we assume every draw counts as a win for the human ?"

If we could answer that question, hicetnunc, we would know how to play perfectly.

This is actually a mathematics question, but not for 10th graders...

The statement that it "won't ever happen" will probably not be contradicted; nonetheless, I think it's more accurate to say that it is extremely unlikely to happen, and that it would be foolish to expect it to over the course of your life (in other words, any sort of optimism about this would be unwise).

But if we are talking in practical terms, then of course we can think about questions such as "how valid is my 1300 rating(if you haven't played in a tournament in a while, who knows how much higher it has become)," "is my opponent feeling well today," etc, although this most likely is a very long way from making up for 1400 points, even if it's just on paper.

Chess and probability are joinded at the hip?

What planet (or alternate universe) do you hail from?  Lots of people in this thread are from the "What If" universe, even more from the "So What" universe.

But we need more players from the "WTF" universe, just to balance things out.   

It is impossible- it will NEVER happen.

Coming Soon to a Theater near you.

What the hell, this thing is into 400 posts?  20 pages of peple repeating themselves??

"No, it will never happen"

"lol, maybe"

"there's a chance, but not likely"

"Zero chance, at least practically"

"Infinite universes something something"

The trivial nature of the topic is what makes it so enjoyable.

It's so fun to annoy people in the practical world with infinity arguments . Makes them go crazy.

Anyway, your post is spot on of where the debate has been, and it has basically been a never-ending cycle of those things. Haha, infinite universes...

Ouch hicetnunc! I'm merely doing a masters degree in physics. Would you care to present a solution to your question?

"I once read some place that perfect play was estimated at 3600" (solskytz)

I'd be interested how you would define "perfect play". It certainly can't be "winning by force" because you can't do that in chess, chess is a draw. Would it be "playing any moves which never allow the opponent the opportunity to reach a winning position"? Possibly, but there would be quite a large range of different moves within that definition, and you'd have to find some way of defining non-losing move A as better than non-losing move B.

I remember discussing the same thing in a thread about computer chess and I suggested a computer with "solved" chess would be hit with this problem. At first I thought it could pick the move which gives the opponent the best chance of going wrong, i.e. the highest fraction of the opponent's possible replies are losing moves. But then I realised this isn't much good because it would make the computer swap pieces off aimlessly, because that gives the opponent a wide selection of losing moves (everything but the obvious recapture!). So it wouldn't be too hard to draw with probably.

Just curious how you would define "perfect play" because I've never got my head around it.