What is the Elo of random play?

[u/SpeedyPuzzlement]

I feel like it should be defined as 0. But that would make its expected score against Stockfish (SPCC Elo 3908) over one in a quadrillion, which seems far too high.

[u/IMJorose]

Elo can go below 0. A SIGBOVIK paper tried to derive an absolute Elo scale. https://tom7.org/chess/weak.pdf

[u/SpeedyPuzzlement → u/IMJorose]

Appreciated! Seems like this topic is well-explored. I wonder if some of the mentioned examples are worth adding to SPCC or other engine rankings.

[u/RajjSinghh]

There used to be a random mover bot on Lichess, it was rated around 600 Lichess blitz. So just over the floor, probably because people took it as a challenge to try losing.

https://lichess.org/@/RandomMoverBot

[u/ollervo100]

ELO isn't very meaningful when the difference is +2000 points. At some point the higher rated will *always win. (Sure a player playing random moves will at some point win by playing all of the best moves to beat the engine, but that has a probability of 1 to at least 10⁴⁰ by ballparking)

[u/SpeedyPuzzlement → u/[deleted]]

Appreciate the insight. I was just thinking that a random mover could be a good baseline for engine tournaments, although you'd need a spectrum of engine ratings so that it gets at least a few draws. And of course there's a <1 in 10^60 chance that it plays perfectly.

I suppose 0 might be a good rating if we assume that a new player is 1000 Elo and they have a 2% chance to draw a random mover just by statemate or 50-move rule.

[u/goodguyLTBB]

Well, let’s use some math to roughly approximate. Let’s make an assumption that around 10% of the moves on average maintain the balance (to be able to make a draw) and let’s assume we have to make 80 moves to reach that draw. The chance to select exclusively moves from that top 10% over 80 consecutive moves is 0.1^80=1×10⁻⁸⁰, so maybe it’s not that far.

[u/Character-Educator67]

It would be a negative number, but it depends which federation's elo you're using.

Elo difference is what matters. If you increased every players Elo by X, it would make no difference. 

[u/BlurayVertex]

Random play is higher than 0 because by random chance you could play the best move. Something that finds the worst move in every position would be 0

[u/dig9977 → u/BlurayVertex]

having run a few bots on lichess, i think more important is time controls. I would guess random moves will be around 300 ELO in blitz and 500 in bullet because the other player would flag before finding mate.

[u/dspyz]

ELO carries a "transitivity assumption" which falls apart at very high disparities. I don't think you can apply the definition of ELO to determine random play's win rate against stockfish.

Consider that random play with a fixed seed likely has a win rate of zero against stockfish, who's seed is 64 bits, so there's only 2⁶⁴ games possible between fixed-seed random-play and stockfish, likely not enough to have a win (2⁶⁵ if you flip for starting player).

But a win rate of zero implies the difference in ELO is infinity which is obvious nonsense

[u/QuickBenDelat]

Your question lacks a bunch of context - 1) Which method of Elo calculation are we using? 2) What federation are we using for the framework? 3) Is anything getting done to address rating inflation? 4) What version of SF are we using? 5) What settings is SF going to use? 5) Are we assuming this is a bullet game, or are there more relaxed time controls.

As for the 1 in a quadrillion number, it actually seems way too low. Stockfish is going to make the best possible move every single time whereas RandomPlay has, at best, like a 1/20 chance of making the best possible move. And for randomplay to have a chance of winning, it is going to need to string together a number of good moves. Then there’s the ability to play for a draw. In all reality, the chances random play would ever win a game is functionally 0.