+M1 and -M1
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if you in winning position you must be familiar with +M1 (white) and -M1 (black) the M1 will appear if your opponent making a blunder or his winning metre drop to 0% that mean you get +M1/-M1 and if you get M1 or M2 its mean just 1 or 2 more move left to win and if you win you will get M0, M0 its mean you win the game because you found the checkmate move
it'll just show 1-0 or 0-1, not M0
AriaKun123 wrote:
if you in winning position you must be familiar with +M1 (white) and -M1 (black) the M1 will appear if your opponent making a blunder or his winning metre drop to 0% that mean you get +M1/-M1 and if you get M1 or M2 its mean just 1 or 2 more move left to win and if you win you will get M0, M0 its mean you win the game because you found the checkmate move
+M1=whites winning advantage is infinite, and they can checkmate black in one move.
-M1=blacks winning advantage is infinite, and they can checkmate white in one move.
0.0 = drawing position, or the game is over and it's a draw
1-0 = the game is over and white won
0-1 = the game is over and black won
Tipppppppppp wrote:
+M1=whites winning advantage is infinite, and they can checkmate black in one move.
-M1=blacks winning advantage is infinite, and they can checkmate white in one move.
0.0 = drawing position, or the game is over and it's a draw
1-0 = the game is over and white won
0-1 = the game is over and black won
Infinite? You sure about that?
ChessDude009 wrote:
Tipppppppppp wrote:
+M1=whites winning advantage is infinite, and they can checkmate black in one move.
-M1=blacks winning advantage is infinite, and they can checkmate white in one move.
0.0 = drawing position, or the game is over and it's a draw
1-0 = the game is over and white won
0-1 = the game is over and black won
Infinite? You sure about that?
I'd figure about the closest you can get to infinite is a position like White Kh1, Qb8, Rd8 Black Kc1 Qg6. White plays Qb1+ and Black's only legal move is Qxb1#. Up until White's move it may have looked like White's chances were infinite because of the Qb2# option.
Even that is not truly infinite for Black because Black might not see the move and either resign (loss) or flag (loss on Chess.com or draw in FIDE/USCF).
The highest possible chance on anything is 1, the lowest 0 - under the common mathematical interpretation that chance=probability. Alternatively, the scale from 0% to 100% is used.
Though an advantage is quantifiable (the advantage of a rook) a "winning advantage" is merely a logical value. You either have a winning advantage or not. There are no infinities here.
All chances/probabilities between 0 and 1 mean: "I am not sure". Engines of course are not interested in player skills and weaknesses, they only calculate the possible plays and outcomes in a chess position.
When the engine says +Mx that supposedly equates to a winning advantage for white, a winning chance of 1 for white and checkmate after no more than x moves by white. Peculiarly the engine sometimes changes its mind after a while by replacing +Mx with +My. That's OK when x>y which indicates the engine found a faster mate, but it is ridiculous when y>x which I've also seen happen. Which implies the engine lied to us in the first evaluation!
Arisktotle wrote:
... That's OK when x>y which indicates the engine found a faster mate, but it is ridiculous when y>x which I've also seen happen. Which implies the engine lied to us in the first evaluation!
It's not ridiculous. Engines need to prune the tree of variations to achieve high depth. In a mating attack, sometimes the longest defensive line involves the defender playing some spurious interposition (where the interposing piece gets captured right away). These give-away moves are precisely the types of moves aggressively pruned by the engine. (Spite checks, on the other hand, would not be pruned.) Give-away moves are also precisely the types of moves which will delay a forced mate by one more move. Of course in a short mating line, the engine doesn't really need to prune anything. But the programmers ignore that, because winning with mate-in-two gets just as many points as winning with mate-in-one. So +M2 from such an engine means white mates in no more than two moves. There are specialized engines which will accurately solve for mate-in-X. But of course you would first need to know the position is a forced mate, and then switch to the specialized engine. So they are mostly used for verifying composed problems. Just like the practical programmer, the practical player is more interested in "there is a forced mate" than in "there is a mate-in-X". If you really care how long the mate is, use a specialized engine.
You repeat what I wrote: "So +M2 from such an engine means white mates in no more than two moves". What I've also seen happen is the reverse: "M2 changes to M5 after further analysis" and that is ridiculous!
"So +M2 from such an engine means white mates in no more than two moves."
You are correct, that statement by me added no meaning, in fact it muddied the waters. Good job picking out that one poor sentence and ignoring the substance of my post. Strike that sentence out, the rest of what I wrote explains why the change from +Mx to +My, where y>x, is not ridiculous. These are playing engines, not solving engines.
Well, I still have issues with that. All analysis is about probabilities of final scores but "mate" is not a probabilistic animal and it has no margins. To present it in such a way you'd need an extra dimension describing "confidence". E.g. "+M5 99.7" could mean a 99.7% chance it's mate in no more than 5 moves. As long as you can't guarantee "+M5 100" the evaluation presentation "M5" is misleading. IMO!
mathematically, the winning advantage at the end of the game is either 0.0 or the amount of points worth material a king is. A king is worth infinite, and getting checkmated is the same as blundering a king because if you get checkmated, the king has no spaces to move to so it doesn't matter what move is made and it will get captured after the game ends. Blundering a king is the same as losing infinite points of material, and obviously that would make the position a specific color having an infinite advantage. Basically, 1-0 means an infinite advantage for white, ad 0-1 means an infinite advantage for black. M1 or M2 would be less than infinite because of the fact that there is still more to do.
Equivalent advantages to number of moves for mate:
0.0 = draw
Anything below a 1.5 is a forced draw.
1.5 = checkmate in 70 moves
2.0 to 5.0 is checkmate in 60 moves
5.0-10.0= checkmate in 50 moves
10.0-20.0= checkmate in 45 moves
20.0-30.0=checkmate in 40 moves
30.0-40.0=checkmate in 30 moves
40.0-50.0=checkmate in 25 moves
50.0-60.0=checkmate in 20 moves
60.0-80.0 =checkmate in 14-20 moves
80-100 =checkmate in 13 moves
100-120 = checkmate in 12 moves
120-150 = checkmate in 11 moves
150 = checkmate in 10 moves
200=checkmate in 9
300=checkmate in 8
500=checkmate in 7
1000=checkmate in 6
10,000=checkmate in 5
100,000=checkmate in 4
1,000,000=checkmate in 3
1,000,000,000=checkmate in 2
1,000,000,000,000=checkmate in 1
infinity=1-0 or 0-1
(I believe that there was a random update to the engine or something, so Im updating it)
ok
As for the "value" of Mate-in-X, one approach I have seen is to store the evaluation in a signed 16-bit integer, and rely on "normal" evaluations not exceeding the total non-king point count on the board, with 8 pawns promoted to queens that's 103 :
- 32767 White has mated black
- 32766 White mates in 1
- 32765 White mates in 2
- 32767-X White mates in X
- "normal" evaluations in the range +103 .. -103
- -32767+X Black mates in X
- -32765 Black mates in 2
- -32766 Black mates in 1
- -32767 Black has mated white
Is a win really infinity? What if after the game, the person who won is disqualified due to something or other?
Tipppppppppp escreveu:
mathematically, the winning advantage at the end of the game is either 0.0 or the amount of points worth material a king is. A king is worth infinite, and getting checkmated is the same as blundering a king because if you get checkmated, the king has no spaces to move to so it doesn't matter what move is made and it will get captured after the game ends. Blundering a king is the same as losing infinite points of material, and obviously that would make the position a specific color having an infinite advantage. Basically, 1-0 means an infinite advantage for white, ad 0-1 means an infinite advantage for black. M1 or M2 would be less than infinite because of the fact that there is still more to do.
Equivalent advantages to number of moves for mate:
0.0 = draw
Anything below a 1.5 is a forced draw.
It depends on how easy it is to make blunders which is why it is not always 0.0.
1.5 = checkmate in 100 moves
If there are more than 100 moves to checkmate, stockfish doesn't see it and will say 0.0.
2.0 to 5.0 is checkmate in 90 moves
5.0-10.0= checkmate in 85 moves
10.0-20.0= checkmate in 75 moves
20.0-30.0=checkmate in 60 moves
30.0-40.0=checkmate in 50 moves
40.0-50.0=checkmate in 35 moves
50.0-60.0=checkmate in 25 moves
60.0-80.0=checkmate in 15 moves
80.0-100=checkmate in 10 moves
200=checkmate in 9
300=checkmate in 8
500=checkmate in 7
1000=checkmate in 6
10,000=checkmate in 5
100,000=checkmate in 4
1,000,000=checkmate in 3
1,000,000,000=checkmate in 2
1,000,000,000,000=checkmate in 1
infinity=1-0 or 0-1
Sir, could you PLEASE present that mathmatical prove? That kind of information would be much apreciated for me!
alanegewarth wrote:
Sir, could you PLEASE present that mathmatical prove? That kind of information would be much apreciated for me!
Everything that the guy wrote is complete nonsense with no connection to reality.
Tipppppppppp wrote:
M1 or M2 would be less than infinite because of the fact that there is still more to do.
M1 or M2 means mate is forced, so if the game is evaluated in terms of king capture, you can force the capture of the enemy king. If the value of the king is infinite, which I think is a reasonable approach, M1 or M2 still has an infinite evaluation, since you can force the game to go to the same value as 1-0.
Infinite is easy to say, not so easy to represent in a finite number of bits. And since engines as of today still rely on some underlying hardware, neither the king nor mate-in-x can be expressed as infinite.