He is by far the best in all formats but there is some luck in chess and the best player doesn't always win - like in most competitive games/sports.

Luck is an interesting way of phrasing what can be simply described as pure neurological deficiencies. Your opponents brain forgot to go down a crazy sacrifice line which was actually M6. Is that luck?

Or is it a comparative grey matter evaluation in time and pressure constraints?

there is atill hidden information in chess, and thus luck when you take a guess at what it is.

you provide an example, but the luck is in guessing what the opponent would check or not check.

a clearer example is trying to play out of your opponent's prep. you dont know what lines theyve prepared, and youre taking a gamble with each move on whether theyve prepped it or not. they cant prep every possible line in the available time, regardless of how long (ding wasnt prepared for most of gukesh's attacks, with months to prepare)

theres also luck in that your opponent may not have slept well the night before because a car alarm went off at 2AM, so their comparative grey matter evaluation in time was lower than usual, or they just played a tiring long game where they lost, right before this game.

With our current understanding of biology, if I model outcomes probabilistically (luck) and you model them any other non-equivalent way then I'll be more successful predicting those outcomes. The philosophy behind it is interesting, but "luck" isn't a bad way to describe what's happening to a layman when Carlsen loses.

In classical chess, yes; in Blitz and Rapid he's still one of the best, but there's lots of good competition.

His edge in rapid/blitz is generally seen as much larger than in classical.

One of the biggest examples of this was in his title defense against Caruana. Every game of that match had been drawn, and in the final game Magnus had a very promising position where he could squeeze with basically no risk.

Instead he offered a draw which was immediately accepted. That sent the game to rapid tie breaks where he casually butchered Caruana 3-0.

That's because Caruana was a bad Blitz player though; on the elo rankings, Carlsen's lead is (and usually tends to be) smaller in Blitz.

The tie breaks were rapid, not blitz. And rapid is where Magnus' gap over #2 is the largest.

And no great player is bad at any time control - they're just 'less good'. Except Magnus - since he's #1 at everything he's just more or less dominant.

Oh boy, offering a draw so he could annihilate Caruana in the next phase is a totally gangsta move. <whew>

He is both the current rapid (5 times) and blitz (7 times) world champion. He is more than one of the best.

Sure, but he's not invincible like in Classic; those 7 wins aren't consecutive (he lost in 2021 and won 22 & 23), meanwhile he's won every classical championship since 2013 (until he stopped playing in 2023).

And his freestyle performance was clearly shoulders ahead his peers

Ahh I missed that this wasn't classical, thank you.