There is a higher entry price than most other games of skill, yes.
However, "pay to win" is generally understood to mean that there are significant marginal returns to spending thousands of dollars past the entry price paid by the typical player. This isn't really true of Magic: the Gathering.
I've never seen a game where, assuming everyone had unlimited funds and was able to buy anything, that skill didn't then come into play to decide who was the best player.
"Pay-to-win" is one of those weasel phrases that doesn't really mean anything specifically.
What is a game that represents "pay-to-win" in your mind? I think the definition you're using might be "generally understood" but it also might be generally understood that "pay-to-win" means "high[1] cost of entry"
[1]-high cost is relative to each person. could be 10 bucks, could be $1,000
""Pay-to-win" is one of those weasel phrases that doesn't really mean anything specifically."
I can't answer your question because I tend to stay far away from "collectible" games.
But, if 13-year-old you scrapes together your lunch money and buys a "Magic: The Gathering Spellslinger Starter Kit Core Set 2020" (https://www.amazon.com/Magic-Gathering-Spellslinger-Starter-...), are they going to be routinely beaten by someone who spends $100 on booster packs? Assuming roughly similar skill levels, that is?
Magic can be money-positive for decent players (ignoring opportunity cost). I don't mean pros - if you're just good enough to win prizes at local tournaments and you keep abreast of card prices the hobby can more or less finance itself.
I'm just going to keep spamming this: Can someone name a "Pay-to-win" game for me? A game where money, and not skill, is what wins you the game? I think the greater point I'm going for here is that if magic isn't pay-to-win, then there's no such thing as a pay-to-win game.
Yes, there are lots of freemium mobile games which satisfy the "pay-to-win" definition I gave in a way that Magic: the Gathering does not. (Clash of Clans and Clash Royale are two very popular examples that I'm aware of.)
The two examples you gave don't prove your point. If you want to play those games at a high level, you need a good account with access to the good game pieces. Technically, you can acquire those pieces entirely for free by investing lots of time into the games (something that's entirely impossible with paper M:tG). This is literally the same as saying "to play high level Magic you need to have a good deck, but that's just the cost of playing the game".
If Magic =/= pay-to-win then neither do those 2 specific examples you just gave.
I don't believe there is a competitive (read: >2 players) game that is "pay-to-win" if you feel that magic isn't pay-to-win
At least the last time I checked, most Clash Royale and Clash of Clans players don't play with the best game pieces, because too much grinding or money is required for it to be worthwhile. In contrast, a much larger fraction of M:tG players (though still small in absolute terms) play with all the game pieces they want, and are only idea- and skill-limited.
Yes, in some sense the difference between M:tG's "~$50-500 for the best game pieces, or to enter major Limited tourneys where everyone is forced to start from scratch, for a year; only skill matters from there" and Clash Royale's "~$5000, or an amount of time and attention worth >$5000, for the best game pieces, otherwise you're strictly behind someone with higher-level versions of your pieces" is only one of degree. But again, a far larger fraction of M:tG games involve both players playing with what they consider the best pieces. I don't believe I'm the only one who sees this as amounting in practice to a difference in kind.
However, "pay to win" is generally understood to mean that there are significant marginal returns to spending thousands of dollars past the entry price paid by the typical player. This isn't really true of Magic: the Gathering.