Around how many points on the lichess computer analysis means a win for white?

Assuming perfect play from both sides.

See http://chesscomputer.tumblr.com/post/98632536555/using-the-stockfish-position-evaluation-score-to for a detailed answer.

Fascinating! So, 0.99 has 1% of losing for black or draw?

#3 Predicated on and qualified by many assumptions:

* Games are from the chessgames collection (high-rated players of similar strength, classical time control, typically between masters in OTB tournaments)

* The Stockfish used for that test is the same Stockfish used on lichess (the lichess one is newer)

* Asymptotic behavior is asymmetric (that +0.5 is more likely for White to win than -0.5 is for Black to win, even with the "same" position)

then yes, I think so.

I meant: So, 0.99 means white has a chance of 1% of either losing or drawing?
Anyhow, thank you!

No. Any value stockfish gives does not mean a % win/draw/loss. It reflects the position alone. It changes every move. A value of 1 means white is up the equivalent of a pawn. 3 is a Knight and so on.

Generally any value from -.5 to .5 suggests a equal kind of position.

#2 This is a cool graph. I think some more interesting data could be acquired is the data was segmented in different ways, say see the curves for different rating groups, where one would expect the curve to become more shallow as the ratings drop since the lead conversion rate would fall.

Another interesting thing to see would be to segment the data by game phase- how well do players convert an opening, middle game and endgame advantage?

Humans calculate vs Engines analyse:

Humans require inspirational patterns to help calculate which piece will make it there first.

Try this, remove the pawn f7 and see the analyse evaluation. It should show a value of more than one. If it does not, that is because it does not see a depth of 23 moves.

The engine evaluation is mainly affected by two factors:
The depth it can analyse; and
Your positional approach towards the horizon of your plan.

Try different pawn structures (patterns) like the "Stonewall" against an engine or a speed chess player, you might be surprised to see who wins. For the stonewall, it is a king race, so be ready to sacrifice material for a checkmate. The engine evaluation will be in it's favor, until it finally see's your aim.

Toscani, that's highly irrelevant because it is a statistical analysis. Sure you can find exceptions where the engines fail at certain depth but take 750,000 games and you see that the engine evaluation statistically converts to wins.

Point noted: ...

So, how many centipawn points would be required for a sure win by the white engine player? (Using the same engine on both sides).

I believe, the graph should not be generalised, but categorised by classical openings. Generalising the graph with all openings is like our insights that are generalised without sorting or filtering out information. It may give an overall view, but chess statistics require to be specifically filtered to be clear and consise like a yes or no question.

There is lots more in the centipawn numbers, than simply the Alpha-beta pruning of an engine. They need to chunk patterns into the numbers like giving a pawn structure a value.

If you want some sort of rule of thumb to answer the original forum question, then lose two pawns and the balance of winning is obviously pointing towards the other player. Handicap any game by time or material and the balance of power points in another direction.