Can 1 elo program beat 1000000000 elo program?

[Turk]

İ asked this question to you before:


İf A can beating B in sometimes...

İf B can beating C sometimes.

"A" must can beating "C" sometimes?İs it true according to you?

İf you are saying "yes",look at this.

1 elo program can beating 2 elo program sometimes.

2 can beating 3......

1 can beating 3 sometimes?

And

1 can beating 10000000000000(forever zero) sometimes?

Best regards and peace.

[Dr.Wael Deeb]

İ asked this question to you before:


İf A can beating B in sometimes...

İf B can beating C sometimes.

"A" must can beating "C" sometimes?İs it true according to you?

İf you are saying "yes",look at this.

1 elo program can beating 2 elo program sometimes.

2 can beating 3......

1 can beating 3 sometimes?

And

1 can beating 10000000000000(forever zero) sometimes?

Best regards and peace.

[Dann Corbit]

İ asked this question to you before:


İf A can beating B in sometimes...

İf B can beating C sometimes.

"A" must can beating "C" sometimes?İs it true according to you?

İf you are saying "yes",look at this.

1 elo program can beating 2 elo program sometimes.

2 can beating 3......

1 can beating 3 sometimes?

And

1 can beating 10000000000000(forever zero) sometimes?

Best regards and peace.

Using USCF calculation -->
Elo difference:
9999999999999
Win expectency for a difference of 9999999999999 points is 0

The actual value might be slightly larger than zero, but it is small enough that it could not be represented with floating point double. (IOW the expectency is smaller than 1e-308).

I think it is safe to say that we expect the opponent to lose every game (even a draw after quadrillions of games would be very surprising).

[Ovyron]

There's a point in elo in where theoretically one chess entity will be able to not lose a game against a weaker entity and differences in elo against stronger entities can only be measured by how many games can be won against weaker entities that can still lose.

Such non losing entity would resemble 32men tablebases playing, and should never play a move that changes the outcome of the game for the worse. Once the opponent makes a mistake, this entity would beat them 100% of the time. The problem is that this entity may look so deep into the game as to refute all its own moves and not be able to differentiate between moves like 1.f3 and 1.e4, so it could be very trivial to draw against this engine, and it could get a lower rating than an engine that can still lose games, but wins a lot more of them.

The ELO formula isn't ready for cases like this in where engine A beats engine B clearly, but both engines seem of about the same strength against C (when C is the non losing entity.)

The elo of C was calculated at Rybka's Forum to top in the 3800 ELO range, but maybe that needs a recalculation because many were surprised with the huge jump in strength of Rybka 3 yet it's clear that Rybka 3 is very far away from the theoretical non losing entity.

Getting much higher rating than that is extremely hard, assuming a chess entity that still loses games and has a rating of 4000, you'd need:

An engine that beats the 4000 elo rated engine almost 100% of the time to achieve 4400 rating (or close.)

An engine that beats the 4400 elo rated engine almost 100% of the time to achieve 4800 rating (or close.)

etc.

So you see, that getting to 1000000000 rating seems pretty much impossible (specially if the 3800 non losing entity can exist and you can't beat it more than 50% of the time.)

[irvstein1]

in human chess a 2200 rated player might be a bad match up for a certain 2500 player yet a 1900 rated player might be able to beat the 2200 rated player because the openings they play and the style . but i think when the ratings approach 600 diff i dont think it matters anymore . the 600 higher rated player is going to win unless he just simply blunders .

[Ovyron]

the 600 higher rated player is going to win unless he just simply blunders .

The point is finding what is the chance of that player blundering. At these very low ratings the chance is very high. I once beat an opponent 800 rating points stronger than me as he overlooked a mate in one.

But when the ratings get to a certain point, chance of blundering approach 0, and these ratings are several orders of magnitude less than 1000000000.

[swami]

Duh...?

[Ovyron]

Duh...?

I think the question was interesting, for a 1000000000 elo program that loses now and then, how much games would you need to play for the 1 elo program to win? and if the 1 elo program never wins, what is the elo difference needed for one program to be 100% certain of never losing a game against another?

[Zach Wegner]

It is an interesting question, but one which is unfortunately impossible to answer. The problem is that the Elo formula doesn't distinguish between wins and draws. So if a player gets 1% of the points, it can because he won 1% of the time, drew 2%, or anywhere in between.

So perhaps the answer is "yes, it's possible", but I'm pretty sure you can't prove that based on the Elo theory (H.G. and others are free to correct me!).

[Dann Corbit]

It is an interesting question, but one which is unfortunately impossible to answer. The problem is that the Elo formula doesn't distinguish between wins and draws. So if a player gets 1% of the points, it can because he won 1% of the time, drew 2%, or anywhere in between.

So perhaps the answer is "yes, it's possible", but I'm pretty sure you can't prove that based on the Elo theory (H.G. and others are free to correct me!).

This is a very interesting point. In fact, from an Elo estimate, unless an Elo score is greater than yours I do not know if we can prove that the opponent will ever win.

E.g. give some pool with Engine one, Engine two, Engine three, ... etc., :
1. Engine one has Elo 2499
2. Engine two has Elo 2499
Can we prove that in a one trillion game match that Engine one will sometimes win verses Engine two?
Certainly 500 billion draws would give the expected outcome also.
{And, of course, both engines might repeat the same move sequence if there is no randomization and so all draws might be a very realistic outcome -- we may even see 500 billion identical games}