5 - 1 draw contest.

I just noticed that the published Nalimov EGTBs still don't include positions with 5 men v 1 man. These are included in the Lomonosov tables but those don't include 6 men v 1 man.

Presumably they don't bother with the lone king endings because they're mostly won by the other side.

That isn't always true however and in view of the popularity of the ongoing "Illegal positions contest", I thought it might be fun to have a contest for (legal) positions in which a lone king draws against five or more enemy men.

The rules are the same. No priizes or adjudication, no more than one post a week, except you're allowed as many as you like in a day.

FIDE rules prior to 1st. July 2017 are assumed. (The 50 move and repetition rules were dropped after that except in the special provisions for competitions, so many endings that would have been drawn now go on for ever instead.)

I've posted a few examples to start you off. I suggest, in view of the volatility of post numbers that you number posted diagrams consecutively. That might result in duplicates, but it should still be less confusing.

1    White to play and draw.

2    White to play and draw.  (Converse of 1.)

3    White to play and draw.

4    White to play and draw.

5    White to play and draw.

6    White to play and draw.

This might be your last chances to participate in a purely human form of chess before the computers completely take over. Not only are these positions omitted from the EGTBs but if you look at the evaluations of the above draws the computer evaluates only half of them correctly as 0. The others range from -9 to -73.

And a silly one:

 7   White to play and draw.

8                                                   Draw either side to play.

If you look carefully you might notice this one breaks the legality rule, but that, after all, is what rules are for.

(The Engine Analysis gives White a slight edge.)

A justification of the draw follows.

I shall use the term bishop hole to denote a light square not occupied by a bishop and the term home square to denote one of the squares diagonally adjacent to a dark corner square.

Assertion: White cannot force a win from any position that has only the kings, white knights and light squared white bishops if the black king cannot be prevented from occupying a home square with at most one bishop hole on the board.

The given position is one such. (Since all such positions are illegal I should also state that I am not considering positions in which multiple pieces occupy any square or with multiple kings of the same colour or  adjacent kings.)

It is clear that Black cannot win.

Firstly some obvious facts in positions that satisfy the conditions of the assertion..

A single bishop hole cannot be occupied by the black king because he would have to move into check, therefore while there is a single bishop hole the black king must be on a dark square and can be attacked only by a knight in the bishop hole. The bishop hole may move only to a diagonally adjacent square and only if it is unoccupied.

The White king can triangulate only using the bishop hole. If the bishop hole is occupied by a knight it cannot triangulate. Between triangulations of the white king or knight moves, the number of ranks and the numer of files between the kings retain the same parity with the same side to move and have opposite parity with the other side to move.

A knight on a dark square cannot move except to the bishop hole. It neither checks the white king nor blocks its progress.

In the kind of position described in the assertion, irrespective of whether the black king can reach a home square, there are no enforceable mates.

If the black king is away from the edge of the board, since at most one knight can attack the square he's on and this knight attacks only one of the four adjacent dark squares, a checkmate would require the white king to attack the other three adjacent dark squares, which is impossible.

If the king is on a dark corner square, a knight cannot attack both that square and the adjacent home square, so for checkmate the white king must attack the home square. But the black king can move to the corner square only from the home square so the position could not result from any legal sequence of moves. 

A legal sequence of moves could result in checkmates at the edge of the board as below, but these are not enforceable. Checkmate positions in which the kings are in direct opposition can't be reached by a sequence of legal moves so the sequence shown is essentially the only possibility (the white king could start also on b2 and in either case move to c3). Black can bypass the mate as in the variation.

In this and in subsequent diagrams it is assumed that there are zero or more additional invisible white knights on the board arranged at White's convenience (which in this case would mean not on d3 and not on both c1 and c3). If the black king captures invisible knights the capture sign "x" is omitted in the list of moves.  

A       White to play.

It follows that White cannot win unless Black captures a bishop.

Black can capture a bishop only on a8 or h1 with a knight occupying a diagonally adjacent bishop hole (otherwise the black king would be moving into check).

The capture of a bishop can be forced by White from some positions satisfying the conditions of the assertion excepting that Black can force his king to a home square before the capture e.g.

B       White to play.                                                                          

Here it is assumed that some route for the White king to a5, c5 or c7  is not blocked by an invisible knight and there is no invisible knight on c7, otherwise the procedure fails unless some route is blocked only by an invisible knight that attacks b7, in which case that knight could be initially moved to b7 in place of the d6 knight.

The d6 and d8 knights shown could be replaced by any positive number of knights on c5, d6 or d8.

The b6 knight plays no part in forcing the capture; Black is forced to clear the square for the white king and remove the a8 bishop's protection.

 This generic position may be won for White depending on the knight positions.

With Black to play from the same position the procedure fails and the black king can reach a home square or draw by repetition or stalemate.

C       Black to play.

Under construction

To be continued ...

Are you sure it's illegal ? Looks fine to me you just have to queen your 58 pawns

I make it 59 - all the bishops are the same colour.

Edit: As you were; it's 58. As Confucius said, "There are three kinds of mathematician ...".

Edit 2: Not sure it works though. According to FIDE

Art. 3.7.5.1 When a player, having the move, plays a pawn to the rank furthest from its starting position, he must exchange that pawn as part of the same move for a new queen, rook, bishop or knight of the same colour on the intended square of arrival. This is called the square of ‘promotion’.

If a pawn starts off in the opponent's half it cannot reach the farthest rank from it's starting position (which would be the first rank), so it cannot promote and neither can any pawns behind it on the same file without capturing an enemy piece. But you can't have more than 32 pawns starting off in their own half and you wouldn't even be able to promote any of those. Alternatively at least two pawns must have started on the eighth rank and at least one of them should still be there.

But won't the Black king be in check if 58 pawns are present? 

Unless the Black king starts from White's first rank...