66.66% Solved Endgame

UPDATE AFTER 10 COMMENTS: Black can actually win 75% of the time.

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66... Black to play: Does Black win 66.66% of the time with best play from both sides? https://www.chess.com/variants/fog-of-war/game/71542170/131/1

Or does the possibility of black going for Kxd3 change things? (I don't think it does, since I don't think black wins >66% of the time in Kxd3 endgames.)

White has to survive two "50/50" guesses to win. If black wins either, then black wins the game.
Therefore, black plays the first "50/50" (69.... Kxf6) 1/3 of the time, and the safer option (69... g5) 2/3 of the time.

If black goes for 69.... Kxf6 and white doesn't counter 69. Kxf6 with 68...Kg6, then black wins, otherwise white wins.

If black goes for 69...g5 and white doesn't counter 69... g5 (with 68... Kh6 or another king move that allows 70. Kxg5), then black wins. If white does counter it, then black wins 50% of the time, with the next 50/50 that happens over the fight for white trying to win the e5 pawn.

Meta comment: Chess.com ought to allow adding comments to positions/moves in analyses like the above, like Lichess does.

Chess.com should also add FoW vision to analysis.

Actually, I think it might be more complicated than my above analysis suggests since black can play 68...Kd7! instead of 68... Ke6, followed by 69... g5, and if 70. Kxg5 then black is winning due to 70...Ke6 71...Kxf6 being unstoppable.

I saw you playing this endgame recently, I forgot against whom, but i saw you playing Kh7 first and then Kg7. That was cool. You won his king after Kxf6, right? But i see now that black can play ...g5

It was against JackAce027, see the first link: https://www.chess.com/variants/fog-of-war/game/71542170/131/1

> You won his king after Kxf6, right? But i see now that black can play ...g5

Yes, but as noted above, ...g5 isn't winning by force unless white actually played Kh6-Kh7-Kg7. If white skips Kh7 and plays Kh6-Kh7-Kh6, then ...g5 there is only a 50% win for black only after Kxg5.

I think black is winning more than 2/3rd of the time due to this, but I don't know precisely. I'll calculate it another time unless someone else wants to calculate it first?

Thinking about this more while hiking today, black can actually win 75% of the time.

How?

By playing 3...Ke6 75% of the time and 3...Kd7 25% of the time in the above diagram.

Then 25% of the time black plays 4...Kxf6 (which wins or loses on the spot depending on whether 4. Kg7 was played to defend it), and the other 75% of the time black plays 4...g5.

After 4...g5, if white plays 5. Kxg5, then in the 25% of scenarios that black played 3...Kd7 black wins due to 5...Ke6 Zugzwang, with 6...Kxf6 next move. And in the 50% of scenarios that went 3...Ke6 4... g5 5. Kxg5 black has a 50/50 with either 5...Kd6 6...Ke6 7...Kxf6 or 5...Kd6 6...Kd7 7...Ke6 8... Kxf6.

So black has three routes to winning, and regardless of which white tries to prevent, black wins 75% of the time.