I really shoulld have paid attention when all of my math teachers said this would one day be relevant
I don't think you missed much
.
That aside, JDizzle has reiterated my point earlier that there's more to it than just FoW or no i.e. another Blue card is needed to go with it, and mana as well. For example, below this thread is a thread for a Control Slaver primer. Following through to the decklist (available at
SCG), we get a reasonably typical sort of Type 1 deck that actually runs FoW.
This deck has 23 Blue cards, of which 4 are FoW, and 25 mana sources, of which 15 produce Blue (+ Lotus, but it's a one-shot). We might reasonably assume that a hand with fewer than 2 mana sources (or one Blue source and Brainstorm) is a mulligan, as is any hand without permanent Blue mana). I realise there will be some exceptions (mainly involving Lotus + some other combination of cards), but I'm going to ignore those, as this is getting difficult enough as it is. What follows is a statement of some probabilities from that decklist, regarding the likely mulligans i.e. The approximate 7 card odds of:
Not drawing a permanent Blue source + a second mana source/Brainstorm – 12.4% (actually quite significant)
Not drawing any Blue cards at all – 2.7%
Not drawing FoW – 60%
Not drawing FoW + another Blue card – 61.6% (1.6% is small, but it's definitely not insignificant)
Putting those together, if we want to have FoW, another Blue card and 2+ mana sources/Brainstorm, one of which is a permanent Blue source, and we're not worried about the other cards, we say we get FoW + Blue card 38.4% of the time, and of those, 12.6% are useless for mana reasons i.e. only 87.4% of the 38.4% are viable, so we end up with 33.6%. By definition of what we're looking at, we don't have to worry about mulligans for too much mana (6+ mana sources), since 2 cards are spells, leaving 5 mana cards at most. If we're willing to mulligan to at least 6 to get a good hand, the odds of drawing FoW + Blue card are 32.7%, while the odds of viable mana are 82.3%, so the odds of the 6 card hand being viable are 26.9%. For a 5 card hand, the odds of FoW + Blue card are 26.4%, while the odds of viable mana are 74.6%, giving us 19.7%.
Putting the whole thing together now, I will now modify the original pre-game statement to say "I want a hand with FoW + Blue card + Blue mana source + some other mana source/Brainstorm, and I will mulligan to 6 to get it". 33.6% of the time, I will be successful on the first 7. Of the other 66.4% which mulligan to 6, 26.9% (of 66.4%) will be viable i.e. 17.9%, which takes us up to 51.5% (note that this is substantially lower than the 61% we were looking at above). If we are willing to mulligan to 5 in our pre-game statement, then of the remaining 48.5%, we will score 19.7%, which gives us 9.6% to add on, leaving a final total of 61.1%, for this particular deck.
This ignores any other possibilities of playable hands (Lotus-based or Welder-based, I'm guessing), as well as the possibility of the second Blue card and the second Mana source being Brainstorm (quite low, fortunately), so it's not exactly perfect, but it's somewhat more accurate than just looking at FoW, or, as JD put it, ignoring the real world. I can analyse other decks in the same way, but it gives us some idea to work with. I looked at some other decks, and a lot of the FoW decks had similar or fewer Blue cards (e.g. 3CC, Gifts were similar, TPS and Dragon were fewer), although a few were more (some Oath lists, counter-control e.g. mono-U, Tog). In any case, if desired, I can run the numbers over other Blue (Drain)-based decks, or over hypothetical sets of numbers for such decks – just post some numbers.
