I think all 3 are important.
The mathematical and possibilities options are the main ones.
Skill is also very important.
Luck happens in that by having a hand x that you go there and see the cards of your opponent who has more possibilities than you, you can win it with an inferior hand.
Luck is essential, especially to win a tournament.
I recently won a $2 entry tournament in GG poker, in which in 2 very important moments of the MTT I had 2 fairly lucky hands.
One was to enter ITM and I had 8 BB left and in SB I wanted to steal with A5o and I went all in and my opponent had AJs, he beat me preflop but in my favor the 5 came out on the flop and I won the hand.
And being 15 of 23 players in BN I make a reraise with QQ, the BB that beat me in the blinds goes there and the UTG that I had opened also called there. The decision was mine to call or not call, and I thought that the pot was too big not to call and that it could take me to the final table. I called and BB had AA and UTG had AKs and I hit the QQQ set on the turn.
So I reached the final table where after a great monster hand I placed myself in 1st place until last.
With that I want to tell you that the luck factor is also very important, it is not all skill, strategy and other virtues, because otherwise it would become a game like chess.
Greetings