35...Bxe2+
Psychologic (McGoohan - cobra91)

Yes, I believe so. The game probably turned at move 27, where (if my understanding of the position was correct) White missed a winning move.
I reject Kc2

That's probably a good idea, considering how complicated this variant is. Psychologic is nothing like standard chess or any other game I have previously played, and I'm still wondering whether there might have been more to that position than what I could see at the time.
Also, I think we are still on move 36, not 37.
36...Rc1+?

I give up, on the next move is white in each case checkmate:
- If I reject 36...Rc1+ follows 36...Nxb2# (reject Ke1)
- If I take the Rook, you reject Nbxc1, so I must play 37.Nexc1
- Then black play 37…Nc3# (reject bxc3) or 37…Rd2# (reject Nxd2)
Congratulations to you, you played excellently.
What were the most critical situations in your opinion?
And yes, move 27.Nd4 might have been winning.

I definitely think that move 27 is where the game was most likely decided. Nd4 was, indeed, the move I had in mind there, and apparently we agree that it seems to win the game for White.
Apart from that, the first 4 moves were especially critical. With queens on the board, this variant is just unbelievably sharp, and my opinion is that Black was very fortunate to escape from the early opening with a playable position. I'm somewhat curious - do you remember how much time you spent searching for a direct win, prior to trading queens? With a bit of precise calculation, it should be possible to refute Black's play immediately, instead of settling for a small advantage.
I'm also not sure White was completely lost until 33. Rf1? which looks like an error to me. If 33. Nd4 (again!), the position gets very messy, and even though I still prefer Black there, the end result is far from certain.

“With a bit of precise calculation, it should be possible to refute Black's play immediately, instead of settling for a small advantage.”
I thought the same thing at first, but Black has a checkmate threat with
Qxf2+, Kd1 …Qxf1…# or …Qe1#
Perhaps I had overlooked something. I had considered the following combinations:
4.QxBf8+ is certainly rejected. Then play 4. QxRh8 does not work because:
4….Qxf2+, 5.Kd1 … Qxf1…# or Qe1#
The same problem with 4.Qg4 …Qxf2+, 5.Kd1 … Qxf1…# or Qe1#
And 4. Bb5+ make no sense because …c6 or …Nc6.
Therefore trading queens seemed to me forced. Or do you see a better move?

Good game.
I believe this variant should theoretically be a win for white, but it is difficult. In the opening I think simple moves like 3.Nc3 might be better. If black then plays 3...Qf6 white has 4.Bb5+ with the intention to reject c6. 4...Nc6 and then white can play some developing move that guards f2 like 5.Nf3 or 5.Nh3.
Black has some options other than 3...Qf6. 3...c6 might be my choice. 3...Nf6 looks scary in view of 4.Qxg7.
Either way, I think you guys played a good game. 3...Qf6 was a very nice move by black.

“With a bit of precise calculation, it should be possible to refute Black's play immediately, instead of settling for a small advantage.”
I thought the same thing at first, but Black has a checkmate threat with
Qxf2+, Kd1 …Qxf1…# or …Qe1#
Perhaps I had overlooked something. I had considered the following combinations:
4.QxBf8+ is certainly rejected. Then play 4. QxRh8 does not work because:
4….Qxf2+, 5.Kd1 … Qxf1…# or Qe1#
The same problem with 4.Qg4 …Qxf2+, 5.Kd1 … Qxf1…# or Qe1#
And 4. Bb5+ make no sense because …c6 or …Nc6.
Therefore trading queens seemed to me forced. Or do you see a better move?
4. Bb5+ Bd7 (4...Nc6? 5. Bxc6+ Qxc6 6. Qxh8) 5. Bxd7+ Kxd7 6.Qxf7 seems very strong to me. With more extensive analysis, it might even be provably winning.
Of course, the above comment assumes I have not overlooked something obvious, which has also been known to happen. ;)

@cobra91 You're completely right, I've totally underestimated the possibilities and have not analyzed sufficiently before the Queen trading.
@Martin0 after 7…Nh6 Reject f3 8. Qxb7 might be better for white

true. I did not really know what whites 8th move for black to reject is there. Black can reject 8.Qxb7 instead. 8.f3 does not look that great for white anyway since black can play either 8...Qd4 or 8...Qh4+ or simply 8...Rxa8.

Right, and in this respect, I know also not sure if white instead of the Queen trading really had a better alternative.

@Martin0: Well spotted! I clearly underestimated Black's counterattacking chances in this situation. Note that on move 8, both Qxa7 and Qxb7 are playable for White, but to show a win (or even a convincing advantage) in the resulting positions is beyond me. In fact, your idea might even be refined by swapping Black's 6th and 7th moves.
For instance: 6...Nh6 7. Nh3 Nc6 8. Qg7 Qf3 9. Nc3, where it seems to me that White is only hanging on by a thread, with numerous potential oversights in my analysis which could turn this into an easy win for Black.
Of course, we're also ignoring possibilities such as 6. Qg3 or 6. Qg4+, avoiding Martin0's variation completely. What this discussion illustrates, more than anything, is that the complexity of this variant is still very far out of reach for all of us, at the moment.

When I look at it 6...Nh6 looks much cleaner. I don't even see any move black would need to reject there since f7 is protected, white needs to reject Qxf2 and the queen is trapped. Black can reject Qxh8 or Nh3, but I don't think it is necessary.

Yeah, 7. Qxh8? (in the sample line mentioned in post #157) is basically losing after the obvious 7...Qxh8. I'm pretty sure White has to play Nf3 or Nh3, but if there is an immediate forced win for Black, it's in one of my blind spots.

I give up, on the next move is white in each case checkmate:
If I reject 36.Rc1+ follows 36...Nxb2# (reject Ke1) If I take the Rook, you reject Nbxc1, so I must play 37.Nexc1 Then black play 37…Nc3# (reject bxc3) or 37…Rd2# (reject Nxd2)Congratulations to you, you played excellently.
What were the most critical situations in your opinion?
And yes, move 27.Nd4 might have been winning.
I think you meant If I reject 36 ....Rc1+
For me, as a first time looker at this interesting thread, I had great trouble following your post. Sorry to appear pedantic, but my correction may help others, who come late on the scene like me, to understand your reasoning there.
A small quibble:
It would have enhanced the thread a great deal had more diagrams of the then current position in the course of the game.
To conclude, I must praise the efforts of both of the players, and Game_Designer, along with others, who have made this thread pleasurable to read even for latecomers like me.

@camter
I thought that v2 was officially ended, but I may be wrong, I think that it may still be possible to use v2.
It seems like, if I am correct that @McGoohan may still be using v2 and that is why there is a problem with the diagram above.
I have seen this problem before between v2 and v3, I assume that you are using v3.
Otherwise if both of you are using v3 then it is just a technical glitch.
I am using v3, perhaps both of you are using v2.
I reject Rxe2