No need to prove anything, since it's rightly a draw according to the rules.
I hate the threefold repetition rule
No need to prove anything, since it's rightly a draw according to the rules.
How is it a draw under the rules?

Change the rule to allow 1000 full moves or 2000 ply to account for the 8 piece endgames that can take over 500 moves to win!
Change the rule to allow 1000 full moves or 2000 ply to account for the 8 piece endgames that can take over 500 moves to win!
The 7 piece endgames can already take over 500 moves to win. The question of what you would need to allow in the n move rules is separate and not available from the current tablebases.
Why would limit it to 8 men anyway? the positions with 32 men are likely to need much higher values.
@jetoba:
The other massive blank in the FIDE rules of the past years is related to the automated 75-move and 5R draws as well. MARattigan described it and I support him with some context. In the past a position couldn't be declared "dead" on the basis of a nearby 50-move line because claiming a draw on the 50-move line is optional and therefore not predictable. However, now the 75-move and 5R rules produce mandatory draws and a position could be considered dead at the very moment it is no longer possible to reach a checkmate before a mandatory draw takes effect. Doesn't look that interesting except, of course, in the case of flagging. Black's flag falls and he commonly loses by the available checkmate potential. But now it's gone because the 75-move line is too close. Can't get mated before it. Does he get a draw? The fundamental question is whether or not FIDE intended to incorporate the states of 75-move and repetition counters to be included in the dead position evaluation. Personally I don't know the answer but I do know the laws say nothing about it. It's time that somebody looks at it!
Who came up with 75? Why not just make it an even 100 full moves?
It was thought to be sufficient in all cases (which weren't at that time computer generated).
The 75 move rule in the current FIDE laws first appeared in 2017 at which time it was well known to be insufficient for all cases.

Change the rule to allow 1000 full moves or 2000 ply to account for the 8 piece endgames that can take over 500 moves to win!
The 7 piece endgames can already take over 500 moves to win. The question of what you would need to allow in the n move rules is separate and not available from the current tablebases.
Why would limit it to 8 men anyway? the positions with 32 men are likely to need much higher values.
I hope ten piece tablebases are eventually developed.
So how can that occur with a ply count of 142 since the last capture or pawn move? It obviously can't so it isn't relevant.
It already happened that professional players passed even the 75-move marker and played on. About a year ago someone reproduced a number of those games on chess.com. And obviously there are many more who called it a day before they were at 75. Some are programmed to achieve, they might check out any time they like but they will never leave ...
@jetoba:
The other massive blank in the FIDE rules of the past years is related to the automated 75-move and 5R draws as well. MARattigan described it and I support him with some context. In the past a position couldn't be declared "dead" on the basis of a nearby 50-move line because claiming a draw on the 50-move line is optional and therefore not predictable. However, now the 75-move and 5R rules produce mandatory draws and a position could be considered dead at the very moment it is no longer possible to reach a checkmate before a mandatory draw takes effect. Doesn't look that interesting except, of course, in the case of flagging. Black's flag falls and he commonly loses by the available checkmate potential. But now it's gone because the 75-move line is too close. Can't get mated before it. Does he get a draw? The fundamental question is whether or not FIDE intended to incorporate the states of 75-move and repetition counters to be included in the dead position evaluation. Personally I don't know the answer but I do know the laws say nothing about it. It's time that somebody looks at it!
Now you are looking at a difference between FIDE and USCF rules. The rest of this paragraph is an irrelevant and essentially specious argument but under USCF rules the 142-ply position above has four moves left before the 75-move rule. White can win with 1 Kf2 Kh1 (illegal but not called) 2 Bg2+ Kh2 3 Bf4# (checkmate with the checkmating move being a legal move ends the game).
Now we move on to a real answer. Under both USCF and FIDE the game is not automatically drawn until the full 75-move rule has actually kicked in. Until then a player may flag or resign. The dead position rule does not mention the 75-move rule and only says that checkmate must be reachable via legal moves. So using the 75-move rule is overreaching when trying to declare a dead position in advance of actually reaching 75.
... The fundamental question is whether or not FIDE intended to incorporate the states of 75-move and repetition counters to be included in the dead position evaluation. Personally I don't know the answer but I do know the laws say nothing about it. It's time that somebody looks at it!
Whether or not that was their intention, they did.
I don't believe the laws say nothing about it. They say the rules are included.
I would guess that they hadn't noticed the problems it would cause for arbiters.
It's not just a matter of counting shortest helpmates (bad enough). The arbiter has to decide if all the positions reached on his boards are dead under either rule or a combination of the two.
Example, here are the last few moves of an hypothetical legal game showing the latest position.
Is that position dead?
Yes. By a combination of the 75 move and quintuple repetition rules.
It looks like the one in #345, but all you can say about the question I asked there is, "insufficient information".
(Who'd be an arbiter.)
... The fundamental question is whether or not FIDE intended to incorporate the states of 75-move and repetition counters to be included in the dead position evaluation. Personally I don't know the answer but I do know the laws say nothing about it. It's time that somebody looks at it!
Whether or not that was their intention, they did.
I don't believe the laws say nothing about it. They say the rules are included.
I would guess that they hadn't noticed the problems it would cause for arbiters.
It's not just a matter of counting shortest helpmates (bad enough). The arbiter has to decide if all the positions reached on his boards are dead under either rule or a combination of the two.
Example, here are the last few moves of an hypothetical legal game showing the latest position.
Is that position dead?
Yes. By a combination of the 75 move and quintuple repetition rules.
It looks like the one in #345, but all you can say about the question I asked there is, "insufficient information".
(Who'd be an arbiter.)
The dead position rule does not include the 5-fold or 75-move rules, and should not include them. It merely looks at whether or not a checkmate is possible by any sequence of legal moves and in the cited position a checkmate is possible. The opponent can resign. The opponent can flag. The opponent can be mated after 90 moves and the (earlier provided) link to the FIDE commission members discussing that case says that if the arbiter learns of that almost immediately then the result should be changed to a draw, but if the arbiter learns of it a few days later then the result remains decisive.
Now we move on to a real answer. Under both USCF and FIDE the game is not automatically drawn until the full 75-move rule has actually kicked in. Until then a player may flag or resign. The dead position rule does not mention the 75-move rule and only says that checkmate must be reachable via legal moves. So using the 75-move rule is overreaching when trying to declare a dead position in advance of actually reaching 75.
Actually I wasn't looking at USCF or FIDE but I trusted MARattigan had set up a good example since there are many good examples to illustrate the point! But I think you did get the essence of the matter. I feel for your argument as I also feel for the opposite argument. The core issue is what counts as a "legal move". If a game was just terminated by a mandatory 75-move draw, can you still play a legal move? By stating that the 75-move rule only kicks in when it happens in the actual game you effectively undermine the concept of the dead position rule which is to grant a draw when it is impossible to be checkmated by simulating game continuations with the game rules in force at that point.
Interestingly, MARattigan claims that the rules clearly imply that all rules would function in evaluating dead positions as they would in a real game.
I have a middle position in this discussion in that I believe FIDE never even thought of this situation. Probably 50% of the rule clarifiers will say it's obviously a draw when the 75M/5R situation kicks in by preventing checkmate and the other 50% will say the opposite. When I read the text of your link I noticed a strong inclination to honor wisdom and reason and not so much the formal text in places where the rules only murmur or are ambiguous. Here is one!
A safe prediction: this will cause trouble as did the other issues around the 75M/5R rule as your linked discussion has shown!
I disagree.
The game should be played according to the published laws, not the arbiter's handbook or the intentions of the authors of the laws.
The dead position rule in the published laws is
5.2.2 The game is drawn when a position has arisen in which neither player can checkmate the opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’. This immediately ends the game, provided that the move producing the position was in accordance with Article 3 and Articles 4.2 – 4.7.
In the position I posted in #361 it's clear neither player can checkmate the opponent’s king with any series of legal moves under Competition Rules, Black because it's difficult when you have only a king, White because no sequence of legal moves can produce checkmate before the game terminates under either the 75 move rule or the quintuple repetition rule.
It is possible that that was not FIDE's intention (and clearly not yours) but it is the law.
I disagree.
No, you don't. I have not taken a position. I merely elaborated on your position and Jetoba's which is opposite. You claim the rules are not blank on it and so does jetoba. Which leaves the middle position to me
Wasn't talking to you - you posted in between @jetoba's post and my response.
Sorry!
@jetoba:
The other massive blank in the FIDE rules of the past years is related to the automated 75-move and 5R draws as well. MARattigan described it and I support him with some context. In the past a position couldn't be declared "dead" on the basis of a nearby 50-move line because claiming a draw on the 50-move line is optional and therefore not predictable. However, now the 75-move and 5R rules produce mandatory draws and a position could be considered dead at the very moment it is no longer possible to reach a checkmate before a mandatory draw takes effect. Doesn't look that interesting except, of course, in the case of flagging. Black's flag falls and he commonly loses by the available checkmate potential. But now it's gone because the 75-move line is too close. Can't get mated before it. Does he get a draw? The fundamental question is whether or not FIDE intended to incorporate the states of 75-move and repetition counters to be included in the dead position evaluation. Personally I don't know the answer but I do know the laws say nothing about it. It's time that somebody looks at it!
Now you are looking at a difference between FIDE and USCF rules. The rest of this paragraph is an irrelevant and essentially specious argument but under USCF rules the 142-ply position above has four moves left before the 75-move rule. White can win with 1 Kf2 Kh1 (illegal but not called) 2 Bg2+ Kh2 3 Bf4# (checkmate with the checkmating move being a legal move ends the game).
Your game ends with 1...Kh1 at which point it's no longer a chess game.
Better, under basic rules, is 1.Bb5+ Kf7 2.Kf2 Kg6 3.Kg3 Kh5 4.Be8#
That is a sequence of legal moves terminating in checkmate. Nevertheless, under competition rules White can't checkmate with that sequence (or any sequence) from the position in #345 because the game will necessarily terminate before checkmate occurs.
The requirement in 5.2.2 is not that no sequence of legal moves exists that terminates in checkmate, but that neither player can checkmate the opponent’s king with any series of legal moves.
That requirement is satisfied in #345.
Now we move on to a real answer. Under both USCF and FIDE the game is not automatically drawn until the full 75-move rule has actually kicked in. Until then a player may flag or resign. The dead position rule does not mention the 75-move rule and only says that checkmate must be reachable via legal moves [No see above]. So using the 75-move rule is overreaching when trying to declare a dead position in advance of actually reaching 75.
The dead position rule doesn't have to mention the 75-move. It's part of the game rules if competition rules are in effect. The game rules affect whether a player can checkmate his opponent with a given sequence of legal moves hence whether a position is dead. In the position in #345 White can checkmate his opponent with the sequence of legal moves I gave under basic rules, but not with that or any other sequence under competition rules. The position is therefore dead under competition rules but not under basic rules.
The dead position rule also doesn't mention
1.2 The player with the light-coloured pieces (White) makes the first move, then the players move alternately, with the player with the dark-coloured pieces (Black) making the next move.
Again it doesn't have to. It's part of the game rules (whichever set).
The sequence 1.Ng8 2.Nf6 3.Ne8 4.Nc7# (all White moves) is a sequence of legal moves terminating in checkmate. (You can check that these are legal moves in accordance with art 3. which defines "legal move" only as a mapping from board layout to board layout).
You can't then decide that the position is not dead. White can't checkmate with that sequence because he has to play in turn. It's precisely analagous to the situation with the 75M/5R rules except that those only apply when competition rules are in force.
MARattigan, in a few weeks I'll be working a tournament along with a few IA-C arbiters and an IA-B (the USA has no IA-A and only one IA-B). I'll bounce your interpretation off of them. Your interpretation seems to b dependent on deeming any moves after the 75-move threshold as not being legal moves.
Copied from the arbiter's handbook:
5.2.2 The game is drawn when a position has arisen in which neither player can checkmate the opponent’s king with any series of legal moves. The game is said to end in a ‘dead position’. This immediately ends the game, provided that the move producing the position was in accordance with Article 3 and Articles 4.2 – 4.7.
Good luck. Try and apply it correctly. It's correct in the handbook.
And no - legal moves are legal moves whether they're in a game of chess or not, played out of turn, after the game compltes - whatever. They're defined in section 3 merely as mappings from one diagram to another.
What I'm saying is the players can't checkmate with any sequence of legal moves that exceeds the 75 move threshold. That's the criterion in 5.2.2. Similarly they can't checkmate with any sequence of legal moves that are not played in turn.
Who came up with 75? Why not just make it an even 100 full moves?
It was thought to be sufficient in all cases (which weren't at that time computer generated).