The disadvantage of the other two pairs of minors is that they cannot mutually defend. This configuration makes it impossible for a queen to capture either.
Three bishops of the same colour draws against a queen. Two don't despite mutally protecting!
I believe it took computers to prove a Queen beats two bishops.
And that it could be done under 50 moves.
Yes, two knights can save your king. They are a strong unit when mutually protecting. But your king needs to be in the right place.
Generally it helps for the knights to be away from the edges (worse still the corner), but sometimes the K+Q can have a mate if the defending king is in the wrong place (even near the knights).
Yes, this is a tablebase draw:
Actually, it is often a draw! Just been trying some positions.
There's usually exceptions with most basic endgames.
But two bishops against Queen - while 'basic' looking ... it seems that it will never come up even once in all the lifetime games of most players.
An endgame that can apparently be won in some positions is when you have a rook protected by a pawn with its King right there ...
versus a King and Queen.
How does the other King ever cross the rank controlled by the rook?
I believe many players would just agree to a draw there.
(the win - if I remember correctly - depends on if there's enough ranks behind the pawn for the Queen to get behind and check the defending King from the rear)
it's funny how INSTANTLY productive the conversation got once tygxc left.
it's funny how INSTANTLY productive the conversation got once tygxc left.
Definite change.
But its very noticeable how tygxc suddenly took an 'extended vacation' after two years of 'on duty' and 'mission'.
tygxc hasn't logged on to chess.com for ten days.
if he hasnt logged on at all that probably means he's just on vacay, so unfortunately we can probably expect to see more of tygxc's delusion in the future.
if he hasnt logged on at all that probably means he's just on vacay, so unfortunately we can probably expect to see more of tygxc's delusion in the future.
Hi MEGA ! Always good to see your posts.
I think its 70-30 tygxc will be back.
As to reason or cause he's offline for 10 days - may never be known.
Considering the amount of time and attention he's put in here - and how 'front and center' he's been ... not likely he's not retired.
As to 'solving chess' the opening poster had his own take on what that is but was gone from the website two days after starting this forum.
'Solving chess'.
The possibilities are probably limitless as to what that could mean to different people.
I was watching a movie yesterday where chess figured heavily in the movie.
Maybe the first such movie with leading actors in it.
In a way it was about 'solving'.
Jason Statham and Ray Liotta (Goodfellas) both very famous although Ray died young.
Chess had more than a 'cameo' role in this movie.
s
...
Perhaps it makes more sense to observe that we have tablebases that give strong solutions of a lot of small variants of chess with up to 7 pieces, for basic rules and (if I am not mistaken) chess with an n-move rule. ...
so long as by "n-move" you mean "50-move".
This is a tricky point. Just how much can we deduce from the information here, say, if you reach this position with an n-move draw rule with m plys already used up, for different n and m?
I can see that if analysis of any later positions includes a 50 move rule, that would limit the scope. But a single number can tell us "what m-move rules would this position be won with?" (the value is a monotone increasing function of n if the position is won with n=infinity, and a monotone decreasing function of n if it is lost with n=infinity).
Read Guy Haworth's proposals for DTR (distance to the rule) tablebases.
The more general question is "if there are m plys left and there is an n move rule, is there a win?". The value is monotone in both m and n in the way described for just n above. Describing the range of possibilities would need a modest sized set of numbers for each position rather than one or two. They could be generated very efficiently by retrograde analysis.
Unless I am missing something, this is a level of functionality beyond Syzygy.
Given that you said, "we have tablebases ..." exactly why I said, "so long as by "n-move" you mean "50-move"'.
Its been coming up more than once -
that if a King is facing two knights but that King has a pawn on board - that instead of drawing - that King is lost because he has that pawn.
Causes me to think:
That must mean that the two knights and King can force the target King to the edge of the board. And then 'Lock' that King.
Otherwise - no way to win.
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Does it have to be a corner or just the edge will do?
Yes, two knights can save your king. They are a strong unit when mutually protecting. But your king needs to be in the right place.
Generally it helps for the knights to be away from the edges (worse still the corner), but sometimes the K+Q can have a mate if the defending king is in the wrong place (even near the knights).
Two knights can theoretically save your king in about one third of positions under basic rules, so long as both knights are not at the edge of the board, and about 27% of positions otherwise.
In practice they can save your king almost all the time because people can't work out how to mate with the queen (making basic rules or competition rules irrelevant).
The average mate depth under basic rules is < 16 but apparently too much for most humans. SF can manage over 45, but max. is 72 under basic rules (probably higher under competition rules).
According to world champion Fine circa 1950 they can generally save the king, but using @tygxc logic.
Under competition rules they can save your king from almost 100% of positions.
Yes, two knights can save your king. They are a strong unit when mutually protecting. But your king needs to be in the right place.
Generally it helps for the knights to be away from the edges (worse still the corner), but sometimes the K+Q can have a mate if the defending king is in the wrong place (even near the knights).
Two knights can theoretically save your king in about one third of positions under basic rules, so long as both knights are not at the edge of the board, and about 27% of positions otherwise.
According to world champion Fine circa 1950 they can generally save the king but using @tygxc logic.
Under competition rules they can save your king from almost 100% of positions.
The two knights would have to be close together though - and their King with them too.
Else the Queen will romp and a knight will soon fall.
Or - the King and Queen just go ahead and mate directly.
In King and Queen versus King mating nets - can the side with the Queen always make every move a check?
No. Because the attacking King has to move to get mate.
Which means that knights on the board 'get to do something'.
Its been coming up more than once -
that if a King is facing two knights but that King has a pawn on board - that instead of drawing - that King is lost because he has that pawn.
...
Actually, if the side with the two knights converts into the ending the chances of winning are theoretically about the same for either side (because the King has that pawn), but it's close to 80% drawn whoever converts under competition rules or 70% under basic rules.
Its been coming up more than once -
that if a King is facing two knights but that King has a pawn on board - that instead of drawing - that King is lost because he has that pawn.
...
Actually, if the side with the two knights converts into the ending the chances of winning are theoretically about the same for either side (because he has that pawn), but it's close to 80% drawn whoever converts under competition rules or 70% under basic rules.
That's not what I've been seeing.
Yes I'll google it but I'm getting the impression that there are 'claims' that the presence of its pawn dooms that side.
Inferring that its King can be driven to the edge of the board.
Doesn't look exactly 'effortless' with two knights.
But they can create a 'wall' three squares wide and then the King could 'plug one end' but that could get comical if the pawn is then 'on the move'.
Apparently there's a Troitsky line - which refers to a 'line' on the board rather than a sequence of movies.
Described here: https://en.wikipedia.org/wiki/Two_knights_endgamewith the two knights versus a pawn about a fifth of the way down the page.
The disadvantage of the other two pairs of minors is that they cannot mutually defend. This configuration makes it impossible for a queen to capture either.
Three bishops of the same colour draws against a queen. Two don't despite mutally protecting!