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In a hypothetical minor variant, could White's first-move advantage be compensated for by Black's right to last move?

Normally, White wins have White play N+1 plies to Black's N. How would the game change if Black had a N+1st "revenge move", that bypasses check rules, and draws the game if it immediately checkmates White?

To be specific, in this variant:

  • Rule 5.1a would be amended to "The game is won by the player who has checkmated his opponent’s king, unless their own king is checkmated at any time during the same game. If the white king is checkmated, this immediately ends the game. If the black king is checkmated, black is permitted, but not required, to make one additional revenge move."
  • Rule 5.2f would be added, as "The game is drawn if both kings have been checkmated at any point in the game. This immediately ends the game."
  • Rule 3.9 would be amended to "No piece can be moved that will expose the king of the same colour to check. No piece can be moved that will leave that king in check, except during the revenge move."

The reason it's a draw is that in 5.2f both players have reached a mating position in an equal number of moves. "At any point" is added in case black's revenge move gets them out of checkmate. That's still only a draw.

There are good reasons these aren't the rules (who wants more draws?), but what I'm wondering is:

  1. Does it balance the game, or does it make Black even stronger than White?
  2. Would it only affect scoring, or also lead to different optimal play?
  3. In existing GM games, how often would this even be applicable? Would any well-known matches end differently?

The third part could probably be answered with analyzing a few games.

Own research:

  • I've checked chessvariants to look if this has already been tried, but it's too minor for a variant. There have been other balance attempts that work through move order, but they affect the openings.

  • This rule breaks some puzzles, which use a mate-in-one threat to enforce forcing moves. Under new rules, removing the M1 threat before checkmating is more valuable than checkmating ASAP. All win puzzles still work the same if the player is black, and all draw puzzles if white. Some draw puzzles might get alternate solutions.

  • The wording of the check rule) has implications. Can the player expose a double-checked king to a triple check, or even replace one check with another? Under this ultra-conservative wording, they can't. If designing this rule into a variant, I'd certainly prefer "go wild" for the revenge move.

Therac
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  • How would you rule a situation like this, where Black has just been checkmated by White? Is a draw with 1...Kg2# allowed? (since Black uses a King sacrificing move to checkmate White) If yes, would this also be a draw without the black pawn on f3? (since under normal chess rules Kings are not captured, so there might technically be no necessity for the Black King being guarded on g2) – Andreas Tsevas Jul 24 '23 at 09:13
  • Also, it is possible that the checkmated Black player cannot make any moves, not even self-mating ones, like this. Would this be checkmate or a stalemate? – Andreas Tsevas Jul 24 '23 at 09:30
  • @AndreasTsevas I suppose not, the king definitely can't check the other king. The question is regarding moves that are normally legal. I guess one point of contention is whether moving a pinned piece should be legal. As for not being able to make any moves, that's a draw either way (per current rules). – Therac Jul 24 '23 at 12:39
  • It's not a "draw either way". The "stalemate" I posted in my second comment would be a checkmate under normal rules, but it becomes ambiguous under the requirement of a post-mate move. To your first point, yes, there would need to be a formal definition of which "illegal moves" are allowed and which ones are not. But I feel like not being able to move the king into check or not being able to move a pinned piece would defeat the entire purpose of "post-mate moves" (since you are already ignoring a checkmate to your king either way.) – Andreas Tsevas Jul 24 '23 at 13:12
  • @AndreasTsevas The concept of post-mate move for Black is that the position is only evaluated after both sides made an equal number of moves (stalemate excepted; I suppose it would be more consistent to make it a loss under this rule). As if the moves were almost simultaneous. I'm wondering if it would balance the game, or make Black overpowered similar to the last-move advantage in poker instead. – Therac Jul 24 '23 at 13:58
  • I suppose you have to adjust the rules so you have to capture the King. However that leads to the situation where a player doesn't 'see' the check. So perhaps better is to add the rule of 'regular mate followed by K capture on the next move'? Whoever captures the K first wins. In the situation of @AndreasTsevas Black would win because it will capture the K (who can move everywhere he wants (the necessity of preventing checking the opponent when you're in check seems unneeded?) after which Black captures the K first). – IT M Jul 25 '23 at 14:19
  • @ITM That's the "eat the king" variant. It doesn't change the white/black balance, though. It plays exactly the same as normal chess, unless a player misreads the board. The check/checkmate system is essentially a built-in safeguard against blundering the king. In this question, the substantive difference is that a mutual checkmate is one more possible outcome of the game. – Therac Jul 25 '23 at 20:29
  • @Therac That is incorrect. The "stalemate position" I posted earlier is an explicit counterexample to the idea that capturing the king is effectively the same as checkmating him a move earlier. In that position with Black to move, there is no way to continue the game until that the Black King is captured, even though the position is a checkmate under normal chess rules. Generally, there are some intricacies with changing the rules of checkmate, which is why I posed you these questions in the beginning. Any rule change has to be thought out really well. – Andreas Tsevas Jul 26 '23 at 08:10
  • @AndreasTsevas I see your point now, you're right - that's a stalemate under "eat the king", but a checkmate under normal rules. I guess, if going for the best game, with one more way to draw, it makes sense to go back to stalemate=loss. For the question, I'd consider it a checkmate: Black can only claim a draw, if they can instantly mate the White king, temporarily suspending the check rule. – Therac Jul 28 '23 at 04:15
  • @AndreasTsevas I see your point now, you're right - that's a stalemate under "eat the king", but a checkmate under normal rules. I guess, if going for the best game, with one more way to draw, it makes sense to go back to stalemate=loss. For the question, I'd consider it a checkmate: Black can only claim a draw, if they can instantly mate the White king, temporarily suspending the check rule. – Therac Jul 28 '23 at 04:15

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