Alright. I think I broke Magic. Here is the scenario.

1. I am playing Doomsday Combo, utilizing the kill that works with Second Sunrise, Conjurer's Bauble, Lion's Eye Diamond, and an infinitely large Brain Freeze. Once I commit to this Brain Freeze and to a specific number, due to the nature of my combo, I will not be able to cast any more spells whatsoever. It is my turn, the turn after I have cast Doomsday, and I am fully capable of executing the combo with no setbacks.

2. I have a Cephalid Looter in play. It is untapped and capable of using its activated ability to force my opponent to draw a card.

3. My opponent has no cards in hand and no relevant permanents on the board. He also has absolutely no way to disrupt my combo, and no way to harm the Cephalid Looter.

4. My opponent has exactly 48 cards in his library, exactly 3 of which are Gaea's Blessing. No other card in his library is relevant here.

Now, here's what I understand, so correct me if I have an error here:

I have to pick a number of times I'm going to repeat my LED/Second Sunrise/Conjurer's Bauble combo, in effect setting a Storm Count, then I cast my Brain Freeze. Let's say, for example, I cast Brain Freeze as the 10,000,000th spell for the turn. This should in effect end with 10,000,000 Brain Freezes on the stack, each milling the opponent at 3 cards a shot.

Now, the second I roll a Gaea's Blessing, the trigger from Gaea's Blessing will go on top of the stack, above all remaining Brain Freezes. As my opponent has no responses and neither do I, this will result in the graveyard as it stands at that moment being shuffled back into the opponent's library.

The key factor here, however, is that eventually, with 48 cards and 3 Gaea's Blessings in my opponent's library, his library is going to be randomly shuffled to this, from top to bottom:

45 Random Cards
Gaea's Blessing
Gaea's Blessing
Gaea's Blessing

The odds of this happening are, of course, astronomically low. However, should it happen, all three Gaea's Blessings would be milled at once, resulting with a stack of all three triggers at once.

I could then kill my opponent by tapping my Cephalid Looter before those triggers resolve.

The problem is this.

Since every shuffle is completely random and every shuffle will have an insanely low chance of arranging the library in that exact stack, but that chance does exist, how do you determine whether or not that stack actually happens in the span of 10,000,000 Brain Freezes?

Regardless of what number of Brain Freezes you decide to put on the stack, there's always a chance that the exact stack of 48 cards required for me to kill my opponent won't ever happen. And there's always a chance it will.

So given that it would be absolutely impossible to actually play through 10,000,000 Brain Freezes, and given that there's no mathematical way to prove whether I win or whether I lose, but I definitely either win or lose, what happens?