Ok here we go, I have built that fun deck that everyone loves to hate, Hulk/Flash. I believe that Flash is restricted now, if not banned, but future incarnations of the deck will surely benefit from this analysis. You can surely net-deck plenty of different deck varieties, utilizing Protean Hulk, so I see no need in posting a list. Just know that the purpose behind any Hulk/(whatever) deck is to put your Protean hulk in play by turns 1, 2, or 3, have it immediately die, via Flash, or whatever else is legal now, and use the Hulk's leaves play ability to pull the combo pieces strait out of your library, pulling off an infinite damage combo, FTW. I have highlighted the key phrase in the previous sentence, as it is important; I need at least one copy of each of the key pieces to stay in my deck, so I don't want to draw into them. I will have 3 or 4 Hulks, doesn't really matter for this study. But the combo pieces in question are the Body Double and Revilark. The other two peices in my deck are Carrion Feeder and Mogg Fanatic, but they can be hard cast before the combo goes off, so they aren't in question. I can either run the two key sets as one-of's, or two-of's. I am assuming, and this is not a horrible set of assumptions, that my opponent will not remove any of my key pieces from my library, on turns one or two. I am assuming that the deck is sixty cards. I am assuming that as the bulk of the deck is geared around drawing/tutoring into Protean Hulk and Flash, I will have these cards in hand by turn three. Lastly I am assuming that I am opting to play first. So how do I find the probability of having at least one card of each of my key sets in my library on turn three?
Let's first assume that they are one-of sets, one Body Double and one Revilark. The probability of not drawing into a card from a one-of set by turn 3 is found by using the HYPGEOMDIST function on a spread sheet. Go to any cell on a spread sheet, let's assume cell A1, and type =HYPGEOMDIST(0,9,1,60). 0 is for drawing 0 of the set in question, 9 is for the number of cards you draw into by turn 3, 1 is the number of cards in the set, and 60 is your deck size. Hit enter and you have 0.85, or an 85% chance of failing to draw into a card from a one-of set on turn 3. Copy and paste the value to cell A2 and this will represent the same probability for the other one of set. As you must have at least one copy of each set for the combo to go off, both failures must occur. So we take the product of both probabilities. Type =PRODUCT(A1,A2) in cell A3, hit enter, and we get .7225. The chance of not drawing into the Body Double and Revilark on turn three is 72.25%.
Now lets make these sets two-of's. Go to cell B1 and type HYPGEOMDIST(0,9,2,60), hit enter and we have a 72.03% chance of failing to draw into a single copy in a two-of set on turn three. Now because we can still pull off the combo by drawing into a single copy, but leaving the other copy in the library, go to cell B2 and type =SUM(B1,HYPGEOMDIST(1,9,2,60)). Hit enter and we have a 97.97% chance of failing to draw into both copies from a two-of set by turn three. Copy the value to cell B3, and in cell B4 type =PRODUCT(B2,B3). Remember that we are looking for two failures of drawing into both cards from the two-of sets, thats why we take the product. Hitting enter in cell B4 we come up with 95.57%. Soooooo, be playing our key pieces as two-of's instead of one-of's, our chances of pulling of our combo on turn three increases from 72.25% to 95.57%.