Let’s take your example and assume that your opponent only draws one card a turn, and that the game lasts n more turns. n<=20 because we’re assuming the traumatize wasn’t going to mill you out. That means that the opponent was never going to draw their wincon if you didn’t traumatize them and it was in the bottom half. So 50% chance to get rid of their wincon, but 50% chance to give them access to a wincon they didn’t have otherwise. However, you’re probably right in practice. If you take into account draw spells you can go through your whole deck and still have more draws available to you and not get milled out, which means the mill card removed access to cards in your deck without directly killing you.

Note that in hearthstone it’s different because a) you have a smaller deck, so you’re more likely to go through the whole thing and b) you don’t lose when you run out of cards in deck, so removing cards from an opponent’s library is relevant in more situations where decking is not.

The chances of milling your opponent’s wincon is equal to the chance that they draw the wincon because you milled them (i.e. their wincon would’ve been too far into their deck if you didn’t mill them). This means that non-game-winning mill is only useful if:

a. They see their whole deck but don’t mill out (possible with cards like preordain and dig)

b. They’re playing tutors

I’m not sure what the right answer is, but that’s important to consider.

That’s true, I was thinking more if they fixed the bugs in MODO. It would still enter into an infinite loop if someone played animate dead with worldgorger as the only creature in their graveyard, but only because the gamestate entered a loop. Is this the only place it would run into problems? Was that even addressed by the article?

Why doesn’t a theoretical perfect version of MODO count? Because it enters infinite loops?

-2 Tundra

-2 Underground Sea

+1 Hallowed Fountain

+1 Watery Grave

+1 Seachrome Coast

+1 Darkslick Shores

It's perfect

One consideration with respect to the possibility of the “magic” k is that there are diminishing returns in terms of the the probability of seeing a leyline in your opener when you add more leylines to your deck. The magic k may be the point at which the increasing likelihood of drawing 2 outweighs the increasing likelihood of getting 1 in your opener.

Thanks.

An example situation I came across where I wasn't sure what to do:

Do I get rootwallas + hollow one here or just leovold? Would it be different if my opponent didn't have the voltaic key?

I'm not finding very many situations to use elvish spirit guide in. Are there important cases where you tutor for her with survival besides exactly GG available and 2 creatures in hand?

There are casual and practice queues that you can use to get used to MTGO. Not sure how active the vintage ones are, but you should be able to find someone to play against.