tvvt-infinite
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Here are the odds of winning. Sort of. —March 11, 2020
So I playtested 100 times, getting the score for each time. The score is the turn number that the infinite is guranteed on.
Strategy was to mulligan until I found one of the required cards for the infinite (Time Vault or Voltaic Key), or until I had one card left in hand. Then take turns until I can achieve the infinite.
Assume no card draw on Turn 1
Summary: Percentage; turn infinite was guranteed by.
10%; Turn 2
37%; Turn 3
43%; Turn 4
48%; Turn 5
69%; Turn 10
Longest it ever took was 38 turns.
In other words, if your opponent can't kill you on their 4th turn, you'll win almost half the time. With a meme deck. That is hella unoptimized. With no tutors. There's a reason these cards are banned. Granted this doesn't take into account counterplay, but still.
Data for the strat is here: 2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,7,7,7,7,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,11,11,11,12,12,14,14,14,14,14,15,15,15,16,16,16,17,18,18,19,20,21,22,23,23,24,31,31,31,32,38
Data for 33 runs of no mulligans is here: 2,2,2,2,3,3,3,3,3,5,5,6,6,7,9,10,10,11,11,12,13,17,17,17,18,18,21,23,24,25,28,33,40
Data for 33 runs of {Mulligan if 5 cards or more in hand, don't have both combo cards} OR {Mulligan if >1 card in hand, don't have one of the combo cards} is here: 2,2,3,3,3,3,3,3,3,3,3,3,3,4,4,6,6,8,9,10,10,11,12,14,14,15,15,16,17,18,29,31,33
Additional note: You could theoretically get the infinite on turn 1 with time vault, voltaic key, and 3 sol rings, but that's pretty unlikely.