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

• 10 hours ago · Quote · #3341
Elubas wrote:

"So, yeah, no reason to believe this is accurate I think."

How is it really any different from how we calculate the odds of a 100 point difference?

It's reasonable to say it's not accurate to 10 decimal places. For example we would need rating adjustments to occur in the billionths of a unit instead of 10s of units.

The number for 100 Elo difference is:
35.99350001%
Or we say the lower rated player will score about 36 points every 100 games.

And for 2900 difference (which my comment was in reference to) is:
0.00000562%
This is saying the lower rated player will score about 56 points every billion games.

Elubas wrote:

I would just say, there is no reason to think we know how to change the math as we please.

I didn't make any suggestions to change the math

• 10 hours ago · Quote · #3342

So following this logic of probabilities, a player rated 1 will have a chanch. Ever so slight of winning a game vs a 3000 because the ELO rating system mathematically predicts it. I'm out a here, too pig headed and illogical. Never heard or seen a bigger piece of baloney in my life. Been fun!

• 10 hours ago · Quote · #3343

I mean... it's either use the elo prediction or just make up whatever number you want. Are you really so proud of doing the latter?

• 9 hours ago · Quote · #3344
Elubas wrote:

It's either use the elo prediction or just make up whatever number you want.

Not at all. All formulas have their implied limitations. In any real world problem you have to interpret the solution, examine how you got it, etc.

Lets take a more tangible example. Lets say we fill a bathtub using a bucket. Each bucket of water can hold 2 gallons easily without it spilling over the edge. We carefully fill each bucket to the 2 gallon mark, and in the end we've used 25 buckets to fill the tub.

Now, we also have with us a number of other containers. Can we reliably guess how many times we would need to use the measuring cup to empty the tub? Sure.

Can we reliably say how many times we would have to use the ounce-sized container to empty the tub? Well, within reason. We might expect to be off a few here or there.

How about teaspoons? How about something 1000x smaller than a teaspoon? A million times smaller?

The fact is that even though we were careful to fill each bucket to the 2 gallon mark, it will will not be accurate to such a small amount. Residual water in the bucket after each dump, for example, would change the answer considerably. We would also have to adjust for things like evaporation so we would need to know the exact temperature loss of the water, of the room, the humidity, etc.

So back to chess ratings. If the chances are 1 in a million to win the game, as measured by a bucket (the Elo formula), then we already know there will be problems. Not only was the bucket itself not accurate to that degree (lets link this to rating adjustments) there will be other factors like contempt that may cause the higher rated player to error (lets link this to evaporation).

Can we expect it to be accurate for a 100 point difference? Yes. For a 10,000 point difference? No.

• 9 hours ago · Quote · #3345
mdinnerspace wrote:

So following this logic of probabilities, a player rated 1 will have a chanch. Ever so slight of winning a game vs a 3000 because the ELO rating system mathematically predicts it.

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.

• 8 hours ago · Quote · #3346
[COMMENT DELETED]
• 8 hours ago · Quote · #3347

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.

• 8 hours ago · Quote · #3348

"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.

• 8 hours ago · Quote · #3349

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.

• 8 hours ago · Quote · #3350
Elubas wrote:

"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.

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.

• 8 hours ago · Quote · #3351

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.

• 8 hours ago · Quote · #3352
Elubas wrote:

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.

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.

• 8 hours ago · Quote · #3353

"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.

• 8 hours ago · Quote · #3354
Elubas wrote:

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.

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 ;)

• 7 hours ago · Quote · #3355

You guys/gals are reading in to it too much

• 7 hours ago · Quote · #3356
Jion_Wansu wrote:

You guys/gals are reading in to it too much

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

• 103 minutes ago · Quote · #3357

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.

• 99 minutes ago · Quote · #3358

maybe he can in online but not OTB! THE 1300 will we too excited and will either lose on time or blunder the game.