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

Well, no. The Elo formula is a specific tool. It's not designed to answer whether there is a chance or not. It's also not designed to reliably predict chances so small.

GIGO (garbage in, garbage out). We can plug in the values for an Elo of 1 vs an Elo of 5000 and it will give a number. But that number wont necessarily mean anything.

I don't think the analogy really holds though because ratings are all kind of interconnected. A player 200 points stronger than another player will have all the benefits of the 100 point rating difference, plus more, because he's required to defeat the skill of the guy 100 points stronger before he can increase his rating. And then a player 300 points stronger will have to do the same thing, but more. The relatability never really changes because the same thing is happening every time.

I mean, we can take half of something as many times as we want... the concept of half doesn't lose relevance even if we did it 5000 times. One half of 1/4 is 1/8 and one half of 1/89012 is 1/178024... it doesn't matter how far you go down because the logic is always the same.

There could be something special going on with the ratings, but it's really up to someone to specify exactly what that is and how it would work... otherwise I would say whatever number they come up with has much less of a basis than that of the elo system.

Like I said I don't deny that there are psychological factors for example, that may affect things a lot. But I would consider it an incredible claim to think that such intangibles would make you go from predicting 1 in 3000 to 1 in a million... that's unbelievably drastic and would be very hard to justify. And besides, we already kind of have some grasp of the psychology of large rating differences -- even a 500 point difference may have essentially the same kind of effect.

"According to the formula, player B will need ~181,000,000 less games to score a point because he is rated 0.01 higher than player A."

He will? In any case that's not automatically a bad sign. Maybe both players need 5000000000000ish games to win, in which case 181,000,000 would be a small fraction.

You before said something like, at some point the heuristics for the much stronger player will win out 100% of the time in certain situations. I don't deny that that's possible, I just don't see why that's plausible. I don't see why I should assume that without any real reason to. For one thing there is the fact that anyone can just malfunction at any moment... I don't think there is some true "anti-mate in 1" mechanism that literally works 100% of the time. It seems more likely that there will always be some non-zero chance of the lower rated player winning in any situation barring ones where there is not enough material to mate, etc.

Yes, that is the right number.

I deleted the comment because I wanted to change it to what I thought would be a more striking example. E.g. when a player rated 0.0000000001 higher only need 100 more games or something. But it got a little ridiculous so I stopped.

Yes, it is only a small fraction. The total for each player was about 3.14 trillion.

In reply to your comment above that. Yes, the concept of a half of a half of a... etc is definitely there. It's just a concept though. In practical problems you need the right tools. A measuring cup can divide in two. But implicitly it is not a useful tool when dividing droplets.

But the ratings basically all are abstract math, like the halves. There is no physical act that needs to be taken place when measuring. In your example the problem wasn't with the logic, it was that physically you couldn't always represent that logic as well as you needed to.

Chances are talking in general and use approximations. 

What I was saying back there was that it's conceivable (through some super advanced technology) that every game that two individual players can generate could be constructed. In such a case, an anti-mate in 1 would only need to work for each time the 1300 would threaten mate in 1. This may only be 1000 unique positions.

I suppose this gets into free will though.

"In such a case, an anti-mate in 1 would only need to work for each time the 1300 would threaten mate in 1. This may only be 1000 unique positions."

Well, I guess that would be a bit more plausible at least, haha. Thanks for clearing that up. Still... I don't know though lol.

Exactly. So you have to look at what the formula does, and what assumptions it makes, to decide how accurate it is.

I'm not a mathematician of any kind, so I can't do that. But I promise there is some range.

Alprad Elo was just a person. His formula is just a tool. It's not a fundamental rule of the universe that on average a 1300 player will score 3599 points every 10,000 games he plays vs a 1400 player as is "expected" by the formula (actual numbers BTW ;)

You guys/gals are reading in to it too much

Yeah, but some personalities like thought experiments and have fun asking questions.

011.. The math is all fine and good. Does not change the fact it is being used as a proof it is possible for a 100 to win vs a 3000. The accuracy could be way off, but it still predicts it to be so. The real world says otherwise. The chanchs are 0. No matter the math. Someone wants to believe anything is possible, this assumption 1stly gets made, then mathematical equations are applied in an attempt to verify a philosophical belief. Sorry, but reality doesn't work that way.

Don't all you jump on my case about "no such thing as 0 chanch". I've read all the arguements. Well, basically it's the same one. The math of statistics says otherwise. I do not believe the two co-exist in this instance. I look at it as a difference of philosophy, not a difference of science

A better example or thought experiment is the monkey and typewriter producing Shakespeare. Enough monkeys and enough typwriters over enough time and it is possible for the monkey to produce a novel. Some believe this to be true. I believe the typwriters get broken the 1st day, everyday and will till the end of time. Giving a 0 chanch.

"The real world says otherwise. The chanchs are 0. No matter the math."

You can't know that if you're actually taking all the rational steps toward knowledge. You have a number of possibilities that are not contradicted with our information. You decide to contradict (one of) them. That's arbitrary. No one is saying you can't weigh different options, see which ones are more plausible, but rationally speaking you can't just take away possibilities just because you want to or you don't personally care about them.

Would the 1300 player be playing other games with other people as well as with the 2700?

If we're taking all rational steps towards knowledge I think we have to ensure that the lower rated player's rating is at least somewhat believable (by having them play rated games with other people besides the 2700), just in case they score a nigh miraculous win! 

Just like lottery, if enough games are played, someone will play the best moves just by chance, that's how he is going to beat the 2700. Just like if you type every letter possible letter combinations, you will eventually type every great books ever written, might take god knows how many years though.

But he or she might hit 1400 before winning... and then the scenario is no longer 1300 beats 2700! 

I can rationally eliminate the possibility that a monkey will ever type Shakespeare. It is my choice to do so. It is called logical thinking. I do not except the romantic notion that anything is possible, mathematics says it is so. Like I've said it is a difference in how you perceive reality. Using mathematical theorems to support the silly notion, anything is possible, is simply faulty reasoning imo.

Mdinnerspace, effectively you're arguing that 10^-100 is so small that it might as well be zero, therefore 10^-100 = 0, which is just wrong. It's probably true that it's so small that it might as well be zero, but that doesn't make it equal to zero. I think we agree that the probability of a 1300 beating a 2700 is so small that it's safe to say it will never happen. That doesn't prove that there isn't a theoretical possibility.

If the 1300 used an engine, it is possible. If the 1300 is Donald Trump who will bribe his opponent, it is possible.