# Can black convert a +5.6 game into a draw (assuming both players play optimally)?

This shows a +5.6 winning for white at depth 33 (Stockfish 13+). White does have a bit of material advantage (knight) and black has more pawn islands. Can black convert this into a draw (assuming both players play optimally) or will this necessarily lead to white winning the game?

``````[Title "Game: White to play"]
[FEN "8/2p3pk/2p4p/p2r4/4p1P1/1Pr5/P1PRK1N1/7R w - - 0 1"]
``````
• No, the eval shows the score with perfect play, so the position after 7 moves would be greatly in white's favor. Jun 8, 2021 at 5:49
• @MikeJones Right, that's essentially why I asked if with perfect play, black will necessarily lose or be able to draw the game? Jun 8, 2021 at 6:01
• An interesting question. Espacially it would be to nice to know where the threshold is for a forced lost game. I did not find something on this on the internet. I think in your example it is relatively clear that it is a forced loss for white because white is a knight up, blacks pawn structure is horrible and black can as far as I can see it not take advantage of his passed pawn. Jun 8, 2021 at 8:31
• I don't think this question deserves the downvotes; I think it is quite interesting and cogently asked. Jun 8, 2021 at 18:51
• I suggest the following conversion factors. My current ELO is ~2100, but I'm still a 2300 in an endgame. Thus: +6, I win against a computer, +4, I win against a grandmaster, +2, I win against myself. :-) After Ne3, everything is under control, too many pawns are left on the queenside, I win against a computer even if blitzing. Fits. Jun 9, 2021 at 12:41

When a chess engine shows an evaluation of a position, there are typically 3 possible values, all of which are based on the engine's attempt to simulate perfect play for both sides:

(1) If the engine sees a forced checkmate [meaning, when one side plays perfectly, no matter what the other side does, the winning side can checkmate], it will indicate how many moves are needed to complete this. Something like "#3" to indicate checkmate in 3 moves has been calculated. I would expect in all modern engines that this number is 'perfect' - ie: I would tend to assume that if the engine has actually calculated mate like this, then it is not 'missing' any possible tactics or moves that the losing side could do to ultimately prevent checkmate.

(2) If the engine detects a checkmate or strong advantage on one side, but also finds a forced-stalemate that the 'losing' side could activate, then it will typically indicate as '+0' or similar, basically saying "there is a draw here, available to the person who should want to use it".

(3) If the engine cannot explicitly find mate, it will attempt to assign a numerical value to the position, where a '+1' assigns a slight advantage to white [about as much as a human would evaluate a 1 pawn advantage], or where '-5' assigns a large advantage to black [about as much as a human would evaluate a 1 rook advantage, although you should be aware that far more goes into these numbers than just 'counting pieces', the analogy is given as a frame of reference, only].

Note that this value provided is only as good as the engine that gives it; an engine that only looks 2 moves ahead might miss that there is a 3-move tactic that loses a queen. More likely, the engine may miss broad-stroke concepts that limit or enhance one side of the board. Notoriously, the most common 'missed elements' that a chess engine has difficulty evaluating is typically where there is something like a 'fortress'; that is, a position where a human might quickly see that no progress is possible due to a locked-in pawn chain [or similar concept].

Generally speaking, modern engines are quite good at evaluating positions, and may also be more conservative when projecting high-value numbers. So for a modern engine, I would expect that any '+5' evaluation is quite likely to be a confident number. Now remember - If the engine could calculate enough moves to find mate, it would tell you - so it doesn't yet know how mate would come, just that there is an incredible strength to one side.

Of course there are cases where +5.6 additional 'material' wouldn't lead to mate; for example, you can't checkmate a king with only 2 knights on the board, so even if someone were "2 knights up", that would still end in a draw. Depending on what other material is on the board at the endgame, 1 extra pawn might be able to promote and win, whereas 2 minor pieces have no effect.

So let's try to figure out "how likely" it is that a +5.6 position leads to mate. Going back to a simplistic assumption that a +5 evaluation means more or less "a rook up", let's consider whether you could win a game if you were a rook down, with no immediately compensating tactics or position. We can consider this by looking at the idea of giving 'piece odds' as a handicap method when players of different strengths play. Based on this answer, it looks like a difference of a knight would be about the same as a 700 ELO rating difference. What is the required Elo to beat a Grandmaster with queen odds?

So if you consider that a 700 ELO rating differential implies that the weaker player has something like a 1% chance to win (per here: https://www.318chess.com/elo.html), if you are a rook's-worth of material worse than your opponent, what is your chance of winning? In this estimation - less than 1%. I offer this merely as a thought-experiment, to again provide a frame of reference for how good a "+5.6" evaluated position would actually be.

In conclusion, the engine hasn't 100% confirmed that mate exists, but the odds of escaping mate as the losing side are vanishingly small. The odds of stalemate are perhaps stronger, but that's hard to say. If the computer detected the chance of stalemate it would indicate it as such per 2) above, so this would have to be a stalemate that only becomes visible after many further moves of perfect play, beyond the engine's line of site.

• "700 ELO rating being something like `7 standard deviations greater chance of winning' would mean probably something like 1/10,000 chance of winning." - That's way off (and that's not what the standard deviation is.) You'd need about a 1600 point difference for a supposed 1/10000 chance (although the theoretical odds are known to be not so accurate at that much of a ratings difference.) 700 points would be more like 1/57 if my math is correct.
– D M
Jun 8, 2021 at 20:01
• @DM Thanks, I have edited to fix this misunderstanding. Jun 8, 2021 at 20:07
• The engines are notoriously poor at seeing conclusions from end games. You can be up a lot of material and still be able to set up a fortress. This particular example could end up as a knight and pawn endgame, something the engine would score highly but is drawn. Jun 9, 2021 at 12:18
• An important further point is that the probability of a turnaround is actually much smaller still than your estimate, because giving material odds from the starting position (1) is known to cost more elo as you rise in elo, and we are talking about perfect play here, and (2) because Stockfish evaluates us as a Rook up in an early endgame not opening. That's a much more decisive position to be in. Jun 9, 2021 at 18:50
• "for example, you can't checkmate a king with only 2 knights on the board, so even if someone were "2 knights up", that would still end in a draw." Although 2N vs 1P can have forced checkmates, due to the ability to use the opponent's pawn to lose a tempo. So if you find yourself in 2N+P vs P, you may have a forced mate even though you're only two knights up, as long as you don't capture your opponent's pawn. Jun 9, 2021 at 20:50

White is a piece up and has a completely winning position. Black could try to create some counterplay profitting from the fact that White's pieces are a bit uncoordinated right now.

But realistically, any decently skilled player should be able to convert this position into a win for White.

Finally, note that there's no threshold for which positions can be won or drawn (otherwise the engine would just output "White wins", "Black wins" or "draw"). There are some won positions that will be evaluated as +0.5, and some drawn ones that the engine will think they're +1.

• Good answer, though after Ne3, White's pieces don't look all that uncoordinated. I don't see much possibility for any counterplay. Jun 8, 2021 at 22:37
• @JohnColeman you're absolutely right. For some reason I thought it was Black to move! Jun 8, 2021 at 22:49

It's hard to prove with 100% certainty, but White will very likely win with optimal play. An advantage over +5 is way too much. There are some theoretically drawn endgames where Stockfish claims one side has a very large advantage, but this position isn't one of them. There are too many pieces and pawns still on the board, and they are able to move around quite a bit. The game isn't constrained enough to fall in the category of a theoretically drawn endgame that Stockfish cannot assess properly. And even if the game was more simplified, a +5 evaluation should still be assumed as completely winning unless you have strong reasons to think otherwise.

Generally, once you reach an evaluation of roughly +1.5, that's when there are good chances of the game being won with optimal play.

• +1 for Stockfish to show +5.6 and fail to convert, the best bet is there's either 1) a fortress or 2) OCBs. This position is neither. Jun 9, 2021 at 0:27
• @Allure Yep, basically any position where SF doesn't learn anything extra from searching deeper, and has to rely only on the quality its evaluation function. Although with the new neural net in SF 13, the situation seems to be improving even in these types of endgames. E.g., compare the SF 13 and SF 11 evaluations of 8/8/5k2/3B1PbP/6P1/5K2/8/8 w - - 0 1. Jun 13, 2021 at 11:54

If black has perfect play and white doesn't, black can draw or even win. But if white has perfect play, chanses are low a draw will occur and white will probably win.

Conclusion, probably no draw and white will probably win

• It says both players play optimally Jun 8, 2021 at 12:06
• Chanses are high white can make a win out if that position Jun 8, 2021 at 12:38