Okay, this isn't really stats, but I have been wondering about this. Some dude or collection of dudes (and dudetts) was able to figure out exactly how many chess games were possible.
Is it possible to do this with MTG?
Sort of, but not really. You are right in saying that there are only a finite number of games that can be played if you
exclude conditions that repeat, loop or recur. It's perfectly ok to make that assumption, because long sequences of repetitive actions can be shortcut, usually leading to a game that ends. There might be a few fringe strategies that rely on getting the deck in a particular order via shuffling but those are usually frowned upon and either lead to a draw or a loss due to slow play.
The problem here is magnitude. While it's possible to tie up all the loose ends through rulings you can't really do anything about randomness in shuffling. Players don't have complete information about the game (unlike in chess) so they have to make assumption about the best possible play. Defining said best play is a little bit hard. Let me illustrate:
- I'll make the best play based on all games I've ever played using the previous games as an average
- I'll make the best play based on all games I've ever played with this format, using previous games as an average
- I'll make the best play based on all games I've ever played against this deck arcetype
And so on. So while it's possible to tweak the rules so that nothing is infinite* you still can't grant players full information about the game. Now, you could say that decisions must be based on your knowledge of Magic alone, in which case you can get a finite set of criteria (because you've only played a finite number of games in your lifetime) but ultimately you can't do anything about the fact that often times in multiplayer for example we assess someone to be a higher threat due to their intelligence. That's not a criterion you could conclude from any finite set of anything, really.
Now here's the asterisk. There are also a few cards that pose a real problem: cards that force you to do something that is random and you can't choose to stop doing so. In an infinite loop either you, the opponent(s) or the judge usually have a chance to react somehow and the game ends. However, there are four cards that aren't guaranteed to ever resolve:
Crazed Firecat,
Mirror March,
Okaun, Eye of Chaos and
Zndrsplt, Eye of Wisdom. If you win every flip you
have to keep flipping. These cards are truly infinite in the sense that there is no defined outcome, you cannot shortcut them and the rules don't allow you to exit the situation. The opponent could scoop but I don't know what the rules are for scooping or if you can ever justify conceding to be "best possible play". To me it sounds like the exact opposite. It'd also have to be 'faster' than instant speed because you're doing it during the resolution of another card and I'm not sure if the rules even recognise such a state. Except
Panglacial Wurm.
Panglacial Wurm is always fun at parties...
TL;DR
No. Rules, cards and criteria for decision making are too ill defined.