5

Following on from this question, it was suggested in answer and a discussion in the comments that an evaluation of a board of +1.5 is 'decisive' in the sense of allowing an estimation of which side would win with reasonable certainty.

However, this was debated as to whether it would hold at a professional or amateur level as a rule of thumb. Thus, my question:

What evaluation at the amateur and professional level is sufficient to make a reasonable determination of the outcome of the game, barring highly anomalous moves by either party?

  • The problem is that for humans there is a difference between very complex, difficult positions, and very easy positions where not much is going on. In the first type amateurs can botch +10 easily, in the second +2 is usually enough even for amateurs. Computers don't care about that sort of thing. – RemcoGerlich Apr 7 '17 at 21:43
2

You need to realise that any number given as answer (including the 1.5) is just a rough estimate which depends on many factors. Professional players were mentioned because their play will be close to that of computers so that blunders/mistakes do not affect the statement. An evaluation around 1-1.5 in the midgame often means that the player can make use of his advantage further improving the evaluation. On the other hand in an endgame with few pieces on the board a similar evaluation can be a lot more drawish because there are few options to improve.

And there are many other reasons why you can't really give absolute numbers.

If you want to discuss the situation for amateur players it gets really vague as you need to make assumptions about the blunder rate. Perhaps the following is useful....

When analyzing a game in lichess, the engine knows three levels of error: blunder, mistake, inaccuracy corresponding to a change in evaluation of 3, 1, 0.5 respectively. So for instance if you start from an advantage of 5, you can make a blunder and still have a won position.

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2

Also there are times when the numerical edge doesn't mean much, or the computer can't see far enough ahead to realize it's a draw. Endgames can be particularly thorny. An extreme example is above. My chess engine (Fritz 11) gives +4.8 for White, but it's drawn. Black shuffles the rook between a2 and a1 and leaves the king at h7. A computer might see this given infinite time, but if we are looking for a relatively quick evaluation, it will misfire.

[fen "R7/P6k/8/8/8/8/6KP/r7 w - - 0 1"]

Another classic example is opposite colored bishops. Fritz 11 gives me +2.0 for White after 5+ minutes in one of the linked games ("Illustration of a drawing concept"), but Black's fortress means Black can either force e6 or exchange a bishop for two pawns.

How do you draw in an opposite color bishops endgame with two pawns down?

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2

In the great book "How to win better positions", it was calculated that an advantage of about +1.50 is enough to win, provided both sides play PERFECTLY. If the evaluation is less than +1.50, it should be a draw if, once again, both sides play perfectly.

That being said, no one plays perfectly (not professionals, or beginners). However, it is safe to assume that professionals are much closer to this "perfect" level of play. So we only need to increase the +1.50 by a small amount. +1.80 to +2.00 should be enough to more or less guarantee a win for one of the sides in a match between two professionals.

However, there are other variables to take into account. If the position is simple and one side is up 2 clear pawns (giving a +2.00 advantage), then there is a +99% chance the professional will win. Conversly, if the position is very complex and one side is up 2 points just by the engine evaluation, then the outcome is not at all certain. The engine may evaluate a complex position to be +2.00, but for humans in a practical game it could seem equal to them.

For amateurs, we need to increase the margin far greater, since they are far from the margin of "perfect play". To guarantee a win for an amateur, one would probably need to provide at least a +3.00 advantage, due to the possibility of blunders and mistakes. Even at this level of an advantage though, it is not certain that an amateur will not make some game losing blunder.

For beginners, there is likely no advantage you can give that will ensure a win. Beginners make game losing blunders very frequently, which makes an engine evaluation more or less moot. There is no evaluation that would guarantee a win for beginners, due to the unpredictability of their skill.

To summarize, for top level professionals about a +2.00 advantage is needed to secure the win. For amateurs, you'd probably need at least a +3.00 advantage. For beginners, there is no number. For engines that play "perfectly", at least a +1.50 advantage is needed. However, it is important to keep in mind that it depends on the type of position too. Simple positions provide more certainty that the better side will win. Complex positions make the result far more uncertain.

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