Quote from user_938036 »For any one mythic in a set there is two of any one rare, this is why mythics appear at an average of 1 in 8 packs.
Quote from Desolator777 »I'm pretty good at math but this particular one I can't figure out. Probability is so annoying.
Let's say a set has 5 mythics worth $15,$16,$17,$18, and $19
and it has 10 rares worth $1,$2,$3,$4,$5,$6,$7,$8,$9, and $10
If I want to calculate the estimated value of the average booster pack (disregarding foils and uncommons)
The average mythic cost would be $17 and the average rare would be $5.50. So since mythics are printed at half the amount on the sheet as rares, so the equation should be
(17 + (5.50 x 2)) / 3 so that rares are weighted double. So that'd be $9.33 average return per booster.
Except if I take the sequence of numbers 15,16,17,18,19,1,2,3,4,5,6,7,8,9,10,1,2,3,4,5,6,7,8,9,10 and average it, I get $7.80.
Both methods appear to weigh rares as double and both seem correct. Obviously the difference in numbers is because there are 10 rares and 5 mythics and it would be the same number if there were 5 rares. So that's great except which method of calculating results in the actual, true expected value of a pack? It seems to come down to what WOTC actually means by mythics are twice as rare as rares. Do they mean for every Force of Will in eternal masters, there are two Isochron scepters? Or do they mean that for every general mythic slot on the sheet there are two general rare slots regardless of the individual card. I'm leaning towards the first one from what I know about sheet printing but please, someone that's good at this type of thing let me know
Quote from user_938036 »For any one mythic in a set there is two of any one rare, this is why mythics appear at an average of 1 in 8 packs. If it was a simple 1 to 2 slot then mythics would have to show up 1 in 3 packs. The problem with your numbers is that you don't have the right balance of rares to mythics which throws off the math.
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Quote from 57messier »I think you are over complicating it. The formula would be:
(1/8) * (Average Mythic) + (7/8) * (Average Rare) = Estimated Value of Rare Slot in Booster Pack
So you would get
(1/8) * ($17) + (7/8) * ($5.5) = $6.94