So let's say you wanted to get a FOIL tarmogoyf from the booster pack it's from. To calculuate the odds of getting it, would you be using the generalized pigeonhole principle? Could anybody show me the calculuations to getting a card like this?
Non-foil, Pre-Mythics: 1/# rares in set
Non-foil, Post-Mythics: X/(# mythics in set + 2 * # rares in set), where X = 1 if mythic, 2 if rare
For foils, multiply by foil rare ratio (which has changed several times over the years). Currently approximately 1/31 (observed, don't know if there is official word on this).
So, for foil Tarmogoyf: (1/60)*(1/31) ≈ 1/1860 packs
that's for foil cards : non-foil cards, not rare sheet foils/pack. Unfortunately, they fudge the rarities a bit for foils, making it impossible as far as I can tell to calculate the true odds of any given rarity. But when I was busting cases, I was consistently getting 7 foil rare sheet cards/case, which is what I use for now.
On MTGO they say on the boosters that the odds of getting either a foil or a mythic is 1 / 56 so the odds of a foil has to be higher than 1/56 but less than 1/112.
So what's the minimum amount of packs needed to open yourself a tarmogoyf?
Math can't answer that question. The odds for any given pack are 1/60 for non-foil, and slightly better for either version. But you could in theory open 5 in a row, or open 500 without seeing one.
The minimum amount of packs it takes to open a goyf is 1. But the minimum amount to guarantee a goyf is impossible to say.
On MTGO they say on the boosters that the odds of getting either a foil or a mythic is 1 / 56 so the odds of a foil has to be higher than 1/56 but less than 1/112.
I think you misunderstood something. The odds of getting a mythic are 15/121 or 10/80 depending on set size (not counting flip-Garruk). The odds of getting a foil are (apparently) 1/67. But the two have absolutely nothing to do with each other.
7 is about right for a box. The "normal" extremes I've seen (not counting dumb outliers like the 0 foil box) are somewhere between 5-9 foils.
I am only talking about foil rares and mythics, since that is what the TC asked about. It's also a stat I have handy. Statistically one should get a little over 8 per box, but as I said, foil rarities aren't the same 1:3:10:1 ratio that non-foils have. Which makes it impossible to calculate the exact odds to open a foil rare+mythic (or common, or uncommon for that matter).
Anyone who has opened a lot of product can tell you foil rares are a lot more common than 1/15 foils (which would be ≈ 1 per two boxes)
This graph shows the probability (as a %) of opening at least 1 foil tarmy vs the number of packs opened.
It uses a foil rare to pack ratio of 1:31 (same as what Medusas gave, and is close to what I've observed) and the tarmy:rare ratio of 1:60.
The probabilities of 25:50:75:99% are at ~500:1300:2600:8600 packs. Yes, I know the distribution of cards in packs is technically non-random, so it isn't 100% accurate.
And I honestly don't see how the pigeonhole principle could be applied here...
So let's say you wanted to get a FOIL tarmogoyf from the booster pack it's from. To calculuate the odds of getting it, would you be using the generalized pigeonhole principle? Could anybody show me the calculuations to getting a card like this?
You want to get that, from a booster..
Your odds are close to 0% then, due to actually wanting it. This is because the Vizzerdrix you don't want is increased to 80% and there is still a lot more rares in the set. however, attempting to use reverse phycolegy won't work, as the power of the secret will then take over and give you a vizzerdrix like you wanted.
Non-foil, Post-Mythics: X/(# mythics in set + 2 * # rares in set), where X = 1 if mythic, 2 if rare
For foils, multiply by foil rare ratio (which has changed several times over the years). Currently approximately 1/31 (observed, don't know if there is official word on this).
So, for foil Tarmogoyf: (1/60)*(1/31) ≈ 1/1860 packs
Math can't answer that question. The odds for any given pack are 1/60 for non-foil, and slightly better for either version. But you could in theory open 5 in a row, or open 500 without seeing one.
The minimum amount of packs it takes to open a goyf is 1. But the minimum amount to guarantee a goyf is impossible to say.
I think you misunderstood something. The odds of getting a mythic are 15/121 or 10/80 depending on set size (not counting flip-Garruk). The odds of getting a foil are (apparently) 1/67. But the two have absolutely nothing to do with each other.
I am only talking about foil rares and mythics, since that is what the TC asked about. It's also a stat I have handy. Statistically one should get a little over 8 per box, but as I said, foil rarities aren't the same 1:3:10:1 ratio that non-foils have. Which makes it impossible to calculate the exact odds to open a foil rare+mythic (or common, or uncommon for that matter).
Anyone who has opened a lot of product can tell you foil rares are a lot more common than 1/15 foils (which would be ≈ 1 per two boxes)
This graph shows the probability (as a %) of opening at least 1 foil tarmy vs the number of packs opened.
It uses a foil rare to pack ratio of 1:31 (same as what Medusas gave, and is close to what I've observed) and the tarmy:rare ratio of 1:60.
The probabilities of 25:50:75:99% are at ~500:1300:2600:8600 packs. Yes, I know the distribution of cards in packs is technically non-random, so it isn't 100% accurate.
And I honestly don't see how the pigeonhole principle could be applied here...
You want to get that, from a booster..
Your odds are close to 0% then, due to actually wanting it. This is because the Vizzerdrix you don't want is increased to 80% and there is still a lot more rares in the set. however, attempting to use reverse phycolegy won't work, as the power of the secret will then take over and give you a vizzerdrix like you wanted.
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