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Comment by acadien | Hacker News Reader

Because check mate is a very small subset of possible moves at the end game, I'm guessing the vast majority of games will end(?) with 2 kings moving around randomly for all of time.

This assumes most games will make it past the hump of mid game where its possible the king's motion will be limited and a checkmate can erroneously happen, I suspect this is a rare case as well.

On a side note I wonder what kind of useful information could be mined from a huge set of random-random games. Maybe the relative power of each piece in terms of the number of pieces it captures on average? Also with some heuristic tweeks you could probably start exploring the power of various openings. Of course then its no longer random-random.

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It's not just random vs random. Two extremely weak players will take hours to finish a won game, because the player with the major material advantage does not know how to win!

When teaching kids, it's not uncommon to, after teaching them how to move all the pieces, spend time teaching them how to perform the most basic of mates: KQ vs K, KRR vs K, KR vs K. Only after those three are mastered we have a good opportunity of having beginner games ending in anything other than a stalemate.

This feels almost like a metaphor for teaching young people about anything... step 1:learn to play a game and the rules. Step 2: learn the implied rules for winning, and how to know when you are winning.

That's why game with victory points can be easier to teach.

It's a vague outline for anyone learning anything, really.

I still don't know how to checkmate with two bishops. I mean, I've read how to do it, but if you stuck me in an endgame situation, I'd probably draw. Luckily, I have never actually had an endgame with a king and two bishops versus a king. Same thing with king, knight, and bishop.

I have a humble level and did checkmate both with two bishops and with bishop and knight... yes, I've found both finals. I had learned the mecanics years before, didn't remember exactly how, but it wasn't so difficult to find the path with enough time.

What I don't want to find is queen vs. rook. I played once queen and pawn vs. rook and won, but it was painful. It seems there are some masters that are specialists in drawing in this positions, even if it should always be a win. Computers with end tables have not this problem.

The mate King-Bishop-Night vs. King is a bit elaborate.

From a random position on the keyboard, you typically need around 20-25 moves to achieve it, and there is a rule that draws a game after 50 moves without any pawn moves.

I've seen an International Master offer draw to his opponent in KNB + K game because he didn't remember what the winning method was (I suposo that after 5+ hours playing your eroded mindset also plays a role.

I did remember the general strategy: take the opponent's king to a corner of the same colour as the bishop. There are a couple of moves that must be thought carefully. But the rest comes very naturally, provided you've practiced it a few times.

It's always about creating a "box" where the king cannot get out of, and make the box smaller as you force the king onto the edge or corner, where you can finally get the mate move.

You have to move the king into a corner and block his way out with your king.

Which is also a good recipe for a stalemate.

The principle is the same as king and rook - the two bishops can trap the enemy king just like a rook can, and you can position your king opposite him and then advance one and force him back. You can work that one out reasonably well from first principles.

Bishop and knight is nontrivial to do in the 50 moves you have, but almost never comes up.

More interesting is checkmate with two knights which is only possible if the other king makes a mistake. You cannot force it so if two good players end up in this situation, they mostly agree on a draw.

There's absolutely nothing interesting about a position which is game-theoretically a draw and actually needs a fairly big blunder to be winnable which is why no-one even bothers in practice.

More interesting is that the position is actually winnable if the losing side has an extra piece (a pawn that isn't too advanced up to board).

For those wondering about that: the pawn allows one to move through a position that otherwise would be a stalemate.

The general trick is to block the pawn with one knight, force the king into a corner with king and other knight, and then bring in the second knight for the checkmate so fast that the pawn cannot promote to a queen and then make another move (promotion to a queen is OK if the checkmate immediately follows)

regarding the teaching thing, there's a book that wonderfully describes part of the process behind the "incremental learning", it's not a chess book btw. The book is "The Art of Learning" of Josh Waitzkin.

Really wonderful and insightful book. There's a small part about his vision in how to teach chess and in that part he also shares why he believes it's better to avoid the "learn all the rules than play" but instead to learn the rule incrementally by using actual pieces on the chess table in the most simple situations (2 or 3 pieces max). Then increase the complexity by adding pieces.

Obviously I'm going by memory so I might be a little incorrect into the explanation, but if you love the subject of learning and the subject of chess, the book is worth a look (in fact I'd advise to read the book to almost anyone).

> I'm guessing the vast majority of games will end(?) with 2 kings moving around randomly for all of time.

Hah, that's what I got on my second run: http://i.imgur.com/joLf3BX.png

The game stopped right there, though.

Edit: Hah! Again! http://i.imgur.com/2ItU89S.png

This is a drawn game according to the rules of chess, since checkmate is impossible.

Other draw conditions include:

* Stalemate (=The side to move has no legal moves)

* 50 moves in a row without any permanent changes happening ("permanent changes" means a pawn moving or a piece being captured)

* Exactly the same game state occurs for the third time ("game state" is whose turn it is + status of castling ability + status of en passant possiblity + which pieces are where)

* Agreed draw

Fun fact: In normal time controls (not blitz) at competitive levels, chess games virtually never end in one of the termination conditions. I don't have statistics on hand but I would expect resignations and agreed draws account for 98%+ of grandmaster-level games.

As I understand it, the threefold repetition rule does not mandate a draw, it just allows either player to claim a draw upon occurrence.

I believe 50 moves rules is the same. But in that case, one player is more interested in the draw than the other. In the case of repetition, both players are avoiding a move that gives the other the advantage. It's not so much a mandatory or not question, but if one of them is more willing to try a different move than to draw.

That's right, see article 5.2.d under the FIDE Laws of Chess:

http://www.fide.com/component/handbook/?id=171&view=article

Yes, its because no other piece can take a king but a king can take all other pieces. The case for taking a king is actually quite rare!

I saw one game quickly become a lone white king against six black pieces. The king eventually captured three of them, and then the game gave up after some number of fruitless moves.

Even with that advantage, black couldn't randomly stumble across checkmate.

Are you sure you didn't end with a stalemate?

That's what I got and I think once you get to the end, a stalemate with an imbalance of pieces on one side may be the most likely.

I only watched one game, but it seems that:

1) Yes, most games will end in stalemate. 2) Most wins would occur when one side has enough passed paws such that they chance upon promoting to a few queens.

3) The random-promotion significantly lowers the chances for checkmate. Promotion to a queen is so common that many players who play online chess set paws to automatically promote to queens, so they don't waste the 2 or so seconds it takes to click the "Queen" button.

There are only a few circumstances where you would not promote to queen.

The first is if promoting to queen would cause stalemate. In that case, you would probably promote to bishop instead, because rook would cause the same problem as queen, and knight is harder to force mate with. In the rare case where a bishop would cause stalemate, you promote to rook instead.

The second is if promoting to knight would force checkmate faster or more surely than queen, which is so rare you practically need to play with the intent of making it happen.

Either one is trivial to determine in a chess-playing program.

Check 1: would a knight promotion cause immediate checkmate? If yes, then promote to knight.

Check 2: would a queen promotion cause immediate stalemate? If no, then promote to queen.

Check 3: would a rook promotion cause immediate stalemate? If no, then promote to rook.

Check 4: would a bishop promotion cause immediate stalemate? If no, then promote to bishop.

Check 5: would a knight promotion cause immediate stalemate? If no, then promote to knight.

Otherwise, promote to queen and take the stalemate.

Or you could simply make queen promotion the automatic default unless you advanced the pawn using a context menu to promote to a different piece.

This comment is as far from true as the decision is far from trivial. That is to say, very far.

By far the second most common piece to promote to is a knight, simply because a knight moves in a way a queen cannot. In my 10 years of playing chess, I have probably seen about 5-10 tournament games where promoting to a knight is the correct choice.

Here is a FEN of an example where the only saving move for Black is to play 1...e1=N+: "8/8/8/8/8/3K4/R3p3/3k4 b - - 0 1"

You are right in that the only reason to ever promote to a bishop or rook is to avoid stalemate, yet there is only one practical example of such, here: "8/2P5/8/8/3r4/8/2K5/k7 w - - 0 1".

White must promote to a rook, since if they promote to a queen Black will play 1...Rc4+, forcing 2...Qxc4, which is stalemate. I cannot even find a practical example of when promoting to a bishop would the best choice.

if anyone doesn't capture anything or move a pawn in 50 moves its an draw (better train on that bishop & knight endgame :)... if anyone claims it, so uh, not sure how that counts :) However if an checkmate is impossible with the remaining pieces it's automatic

edit: missing pawn from sentence

> if anyone doesn't capture or move anything in 50 moves its an draw

You didn't quite state that right--every move something moves, so it is not possible to go 50 moves without moving anything. :-)

The rule is 50 moves without a pawn moving or anything being captured.

Also, it can be a draw, but it does not have to be. When the last 50 moves have been without a pawn move or a capture, the player on the move can claim a draw if he wishes, but does not have to do so.

Recently, FIDE added a 75 move rule. It is similar to the 50 move rule, except that it is a draw even if both players wish to continue the game. (They also did a similar thing with the 3-fold repetition rule, which like the 50 move rule is only a draw if a player claims it. There is now a 5-fold repetition rule that draws even if neither player wants to claim a draw).

Also, the reason it is 50 moves <em>without a pawn move or capture</em> is because both pawn moves and captures are irreversible.

In fact, the only irreversible move that doesn't reset the 50 move rule is castling (or losing the right to castle), as having the ability to castle technically changes the position.

I just got a checkmate first go, rather quickly actually.

> what kind of useful information could be mined from a huge set of random-random games

Whether there is a real advantage to start with white instead of black ?

Does it matter if there is an advantage to playing white vs black if both players are playing completely randomly? It should only really matter if there is an advantage when both players are playing optimally.

One of the biggest innovations in computer Go has been the idea that you can evaluate a position in "monte carlo" fashion, by just playing a few random games from that position and seeing who wins. I don't know whether the same idea extends to Chess.

Monte carlo chooses some possible moves at random, then evaluates which is most successful and has a bias towards the more successful ones.

This has the randomness but without any bias or evaluation of effectiveness.

But really, Monte Carlo in Go can basically be thought of as a lazy, intelligent brute-forcing method.

if completely random, you may prove that there is an empirical advantage to starting the game without taking in account the level of any player, because two players playing randomly should be equivalent. I'm not entirely sure, though.

This is technically correct, but does not result in a very useful information, as P(A|B) can be a very different beast than P(A).

Imagine a really simple game where there are only 2 moves: saying 1 and saying 0. The player who first says 1 wins. So of course the player who has the first turn will in practice always win, but when both players move randomly it's 50/50.

Not true. Assuming both players move completely random (both choose either 1 or 0 with 50% probability each) and independently (past actions don't influence the current event) player 1 has a 2:1 advantage, i.e. he will win with probability 2/3. This is because player 1 can win after an even number of rounds (including 0) with 50% probability. So his total chance of winning is 1/2 * (1 + 1/4 + 1/16 + 1/64 + ...) = 1/2 * 4/3 = 2/3.

Yes you're right. Quite the embarrassing mistake I made there.

The program stops when nobody has enough pieces to force a checkmate. In three tries, I've seen that twice, and one rook/pawn checkmate. It's a nice Javascript demo.

If it's impossible to checkmate then it's a stalemate. So if one side has one king and the other side one king (or even one king and a pawn, bishop, knight or rook) then it's a stalemate and the game ends.

edit: forgot you can checkmate with just a king and a queen

Pawn wouldn't be stalemate because it can be promoted to a queen.

I think it's also possible to checkmate with a rook + king (if you corner the king and have your king cover the escape route from check).

Yup, you're right! The algorithm works like this: (each "move" is an implicit "continue" in the pseudocode)

    while no checkmate:
        If your rook is about to be taken, move it to the other end of the current rank.
        If the enemy king is on rank n and your rook is anywhere but rank n-1, move your rook to rank n-1 (unless it can then be taken, in which case move it to the end of its current rank.)
        If your king is anywhere but rank n-2, move towards there.
        If your kings are on the same file, advance the rook to rank n (unless it can be taken...)
        If |file of your king - file of opponents king| is odd, make a wasted move with the rook (keeping it on the same rank).
        If you've gotten this far, move your king towards the opponent's king (staying on the same rank n-2).

Rook + king is a simple checkmate (http://www.chesscorner.com/tutorial/basic/r_k_mate/r_k_mate....)

You can easily checkmate with a king and a rook, it just has to be along an edge of the board.

In rare circumstances you can checkmate with a king and a single bishop: http://www.chess.com/forum/view/more-puzzles/mate-with-one-b...

Any piece (well, except the king) can checkmate with cooperation from the opponent's pieces. The standard sets (queen, rook, two bishops, bishop and knight) are those with which you can force a checkmate against an opponent who just has a king.

Stalemate is a very specific term that means that the side to move has no legal moves. If checkmate is impossible this is generally called a "draw by insufficient material".

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