<<Diademas> Given that Firouzja lost on time, I think it's safe to assume that <he was in time trouble.>>

I'm not so sure I had glanced at the Rules and Regulations (https://norwaychess.no/en/regulatio... ) but I had not read them in detail, and the R&Rs for Armageddon games went over my head. But they are as follows:

<Time control Armageddon game>

White has 10 minutes and Black has 7 minutes with an increment of 1 second per move, starting from move 41. <[Meaning, I think, that 1 sec is added to each player's remaining time for each move they play starting after they play their 41st move]>

I then looked at the evaluations and time per move in https://chess24.com/en/watch/live-t... and it looked as though Firouzja spend 3 mins, 1 sec on 1...Nf6. It doesn't seem reasonable that with only 7 mins for the entire game that he would spend 3 of them on 1...Nf6! So that part seems incredible to me unless he arrived 3 mins late for the game.

I then created a spreadsheet (of course!) with the data and calculated the amount of time each player had following each of their moves, given the time that they had for the game and the time they spent after each of their moves. If the <chess24.com>'s data is correct, Firouzja would have lost on time after 27...Kh8 since at that point he had 2 secs remaining and he spent 6 secs on 28...Rf4.

So I'm assuming that his 3 mins, 1 sec on 1...Nf6 is incorrect. If we assume that Firouzja spent only 1 sec on 1...Nf6 (after all, it was still book :-) ) then he had 14 secs left after 45...bxc5 taking into account a 1 sec increment per move <following> move 41and, by spending 5 secs on 46...Kxe5, he would have 10 secs left, again taking into account a 1 sec increment per move <following> move 41.

So, given that scenario and assuming that <chess24.com> Stockfish evaluations are correct (which is doubtful given that they often ha 1 – 4 secs to calculate the evaluation), then after spending 31 secs 31.Rxf3 Carlsen had 68 secs left and his position was evaluated at [-2.63], normally winning for Black in a game played at Classic time controls.

But this was effectively a Blitz game with draw odds for Black, and after spending 15 secs on 31...Nxg3, Firouzja had 121 secs left, <more time than Carlsen>. True, the position's evaluation had dropped dramatically to [-0.48], indicating that 31...Nxg3 was not the best move, but the position remained practically even. <But given that Black had draw odds, this was still effectively a winning advantage>.

After spending 4 secs on 41.Kc4 Carlsen got a 1 sec increment so he had 14 secs left with an evaluation of [-0.27] and after spending 4 secs on 41...Rg4 Firouzja had 13 secs left with an evaluation of [-1.37]. This was effectively <still a winning advantage> with only 1 sec less time than Carlsen.

After playing 46.Rf8 instantaneously (well, in less than 1 sec) Carlsen had 12 secs left with an evaluation of [0.00] after all the time increments since 41.Kc4 are taken into account, and after spending 5 secs on 46...Kxe5 Firouzja had 11 secs left with an evaluation of [+0.13] after all the time increments since 41...Rg4 are taken into account. This was effectively <still a winning advantage> with, again, only 1 sec less time than Carlsen.

Carlsen played 47.Rf7 also instantaneously giving him 13 secs left but Firouzja might have lost concentration and apparently spent more than his remaining 11 seconds on his 47th move and lost on time in an even position, effectively throwing away a likely win.

So, no, I don't think that Firouzja was in any greater time trouble than Carlsen and he had achieved a position with equal chances for both sides, <effectively a winning position given draw odds>. True, he lost on time, but I don't think that it was because he was in any more time trouble than Carlsen. Do you know if he explained what happened to him in the post-game analysis?

This all, of course, depends on <chess.com> erroneously indicating that Firouzja spent 3 mins, 1 sec on 1...Nf6 (which I think is likely) and that <chess24.com>'s position evaluations were valid (which I think is unlikely). Still, in the final position Black is a pawn up (although he will shortly lose one pawn) and Stockfish 12 at d=56 evaluates the position at [0.00] after Black's "top" 3 moves. I suspect that FinalGen would confirm this but it estimates that it will require about 4 months and would require about 1 TB of uncompressed disk space to determine that and I have neither the patience nor the disk space to let it do that.

I was wondering what you thought about these new Armageddon time controls, after all the efforts you put into analyzing the optimal ratio, and criticizing the original 5:4 time controls (justifiably IMO).

The time ratio was indeed considerably improved here, but don't you think that the fact that in absolute terms black has much more time now (+ the increments from move 40), that it compensates the reduced ratio?

I mean, black has much more time to figure out what is going on in the position, face white threats, and figure out a proper drawing (or winning) strategy.

<AylerKupp: I'm disappointed that they reduced the time increment from 3 secs/move (2019) to 1 sec/move (this year)>

I disagree on that one. I think that 3 secs incraments would have given black way to much time to figure out white's threats and defend properly, which would give him an unfair draw-odds advantage.

<AylerKupp: So, no, I don't think that Firouzja was in any greater time trouble than Carlsen and he had achieved a position with equal chances for both sides, <effectively a winning position given draw odds>>

I thought they were an improvement but I still don't think that we know what a truly "fair" (in the sense that it gives both player an equal opportunity to win) White Time Control Ratio (WCTR) is. Simply not enough data. And these Armageddon time controls are not really new, they were the same as used in Norway 2019 except that the increment was decreased from 3 secs/move to 1 sec/move.

<but don't you think that the fact that in absolute terms black has much more time now (+ the increments from move 40), that it compensates the reduced ratio?>

Probably. Again, I don't really know; not enough data. I just intuitively think that if we think it necessary to give White more time before the time control to balance Black's draw advantage that White should also get more time for his increments for the same reason, maybe with the same WCTR or a different one. But that depends on the quality of my intuition which is not always reliable, as much as I would like to believe that it is.

<I think that 3 secs increments would have given black way to much time to figure out white's threats and defend properly, which would give him an unfair draw-odds advantage.>

Yes. If you remember I also advocated for a smaller increment for Black, possibly in the same ratio as for the game. So if White got a +3 sec increment, Black should only get about a +2 sec increment (actually +2.1 secs) based on a 10:7 WCTR. But I don't know if today's chess clock allow for different increments for each player, much less fractional ones, so this may not be possible with today's technology. Does anyone know?

<The engines say the position has equal chances, but in practice, Carlsen being Carlsen, managed to create pressure on Firouzja out of nothing>

Yes, that's because (1) At this point in time he's the better player and (2) He's Carlsen.

All that a fair WCTR should provide is equality of <opportunity>, not equality of <results>. The better player should still win if they played a sufficiently large number of games, although the normal (no pun intended) fluctuations in a player's performance result in the better player not always winning a given game, or even a relatively short match. If we wanted equality of <results>, then an additional handicap in terms of material, time, or other factors could be implemented based on, say, rating differential. But that would be based on the presumed playing strength of the players and not by the color of the pieces they were playing with, so it would be somewhat different, even though on the surface they look similar.

Again, perhaps. But the truth (or as close as we can get to it based on chess engine analysis) is that the position after 47.Rf7 was evaluated at d=59 by Stockfish 12 at [0.00] for what it considered each of its top 5 moves. Its line with 48.Rxa7 after either 47...Kd5 or 47...Kd6 was 48...Kc6 49.Rd7 (perhaps unnecessarily showy, either 49.Re7 or 49.Rf7 would have been equally effective in getting the White rook out of the way of the advancing a-pawn and Carlsen would have probably played one of these 2 moves, I don't think that he has as good a sense of humor as Stockfish. But 49.Rd7 provides the best practical chances since it eliminates one of Black's drawing lines, see below.) 49...c4+ 50.Kc3 cxb3 51.Kxb3 Kb5 52.a7 Rb4+ 53.Kc3 Ra4 54.Rxg7 Kb6 55.a8Q Rxa8 56.Kc4 Ra4+ 57.Kd5 Rxh4

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And this position is clearly a draw; i.e. a win for Black in an Armageddon game. But, yes, the onus was on Firouzja to figure out how to get his rook on the a-file to prevent Carlsen's a-pawn from queening without being captured without adequate compensation and that would have required him to see some "interesting" moves such as 49...c4+. Carlsen then had to see that 50.bxc4 would have allowed the Black rook to get to the a-file after 50...Rxh4 (Firouzja actually had time for this <and> needed to do it, if 51.a7 Rh3+ and 52...Ra3) 51.Kc3 Rh1 52.Kb2 Rd1 53.a7 Rd8 54.Kc3 h4 (now the h-pawn distracts Black's rook) 55.Rxg7 h3 56.Kb4 h2 57.Rh7 Kb6 58.c5+ Ka6 59.a8Q+ Rxa8 60.Rxh2

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47.Rd7 would actually have been Carlsen's best move since it would have eliminated an additional chance for Firouzja to draw. After 47.Re7 or 47.Rf7 according to Stockfish 12 Firouzja apparently also had a draw with 47...Kd5 (or 47...Kd6 48.Rxa7 Kc6 49.49.Re7 (or 49.Rf7) 49...Rxh4 50.a7 Rd4+ (47.Rd7 would have eliminated this possibility) 51.Kc3 Rd8 52.Rxg7 Kb6 53.Rh7 h4 54.a8R (Stockfish likes to underpromote whenever possible when there are no adverse effects, either with pre-Stockfish 12 hand crafted evaluation function of Stockfish 12's NNUE-based evaluation function) 54...Rxa8 55.Rxh4 c4 (I guess just to rub it in that the game is a draw, don't mess around with Stockfish!) 56.Kxc4

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This position is clearly a draw; effectively a loss for Carlsen under Armageddon game rules.

Would Carlsen have been able to figure all this out in the time he had available? Who knows? After all, he's superhuman, no more.

Could be. Not being a top player I don't know what their motivation would have been. Perhaps they already thought that a 10:7 WTCR provided White with a sufficiently "fair" advantage to compensate for Black's draw odds. And they could be right, I just don't know. I don't think that there's enough data about Armageddon games to determine that with a high degree of statistical significance.