This was a Premier League game that posed all kinds of existential questions. If Kai Havertz falls in a crowded penalty area and nobody touches him, but someone does also kind of touch him, is that a penalty?

Is simulation still simulation if the thing you’re simulating would have happened anyway because of things like legs, tangles, space, slide, path of run? And most importantly, is there any way of not having to talk about things like this ever again?

The answer to the last of these questions is, of course: no, don’t be ridiculous. By the end of this fun, sunlit 3-0 Arsenal win against a game Bournemouth the word “cheating” was trending on social media. The Premier League had moved a little further along its inevitable journey into full-blown conspiracy-as-entertainment. And the most interesting part of this match seemed a bit lost in the shouting.

In reality two things happened here, both of which can be true at the same time. First Arsenal were lucky. They took the lead with a penalty kick awarded via a degree of very deliberate chicanery from Havertz. With 74 minutes gone they conceded a goal that was ruled out after a lengthy VAR check, but which should have been allowed to stand (the only contact on David Raya was some way short of what Ben White does at every corner).

And second, Arsenal also played very well, won 3-0 when it could have been five or six, and thoroughly deserved all three points.

Actually three things happened. The real key to this game was that Arsenal won by being ruthless and smart. For so long the talk has been that this team needs a killer, some cold-eyed goal-sniper, face smudged with rabbit droppings, nestled in the rushes above the Clock End clock.

It’s hard to argue with this. At the same time the current squad has managed to score more goals than anyone else, and ended the day still clear of Manchester City, who have an extra game to play.

More to the point, Arsenal did have a killer here. Step forward Havertz who was mean, ruthless and savvy just when a goalless first half seemed to be looming.

This involved a degree of tickling away at the lines of the law. Here’s how it went down. Havertz made a nice run past Bournemouth’s defensive line to meet an angled through pass. Mark Travers came barrelling out, sliding with hands and feet spread as Havertz looked to go round him.

Havertz saw this, felt it, heard it, ran the calculations. What was he meant to do here? Deliberately avoid the inevitable contact? Leap over the challenge, which was coming into his path nowhere near the ball, and say: careful there old bean, you almost tripped me?

Havertz did the opposite, the most killer-ish thing, leaving his left foot in a place where Travers’ slide (really: don’t slide) would inevitably catch it. This wasn’t a prima facie “simulation”, because Travers did touch him, and because Havertz didn’t have to move his leg towards him to find the contact.

Did the touch cause the fall? No. Havertz was already falling. Did the slide come across his path, offering as his only options, leap out of the way or fall over? Kind of, yes. Ergo, the slide made him fall. Kind of. If we allow this connected cause and effect. Listen, nobody said these questions were easy, or indeed much fun.

And so the eye says probably a penalty because of Travers’ lack of control and the fact of contact. The morality organs, the gut, the spleen, the backbone, say allowing yourself to fall over just isn’t football. The head says, perhaps we really do need to stop looking so closely at this sport of collisions trying to find objective truths as opposed to fruitless unhappiness, that this remains a sport of random outcomes, where the rules (some will insist they are “laws”) really are just guides to make the thing work.

VAR spent a long time running these questions and cause and outcome. The decision was made not to overturn the on-field call, which was probably right, and ultimately reward for a piece of smart, rascal-ish play. Bukayo Saka did well to stay cool and roll the kick into the net.

From there Arsenal always seemed likely winners, as they had from the opening few minutes, when they were neat and slick and zippy in some lovely soft spring sunshine. Martin Ødegaard was sensational, his left foot basically having an extended conversation with itself. Declan Rice was very good all game, making one and scoring one.

Bournemouth came back well in the second half, with Lewis Cook excellent in the chunky chug-about role in between the centre-backs. There aren’t many players like this. Far less, English ones.

By by the end Arsenal had played with great fluency in a high pressure game. Nobody is bottling anything here. Nobody is flinching from the moment, not just yet anyway. And like it or not, they found a killer here when they needed it.