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Odds of getting BOTH Mythic and Legendary cards

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questccg
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Rarity Card Count Booster Qty Sheet Info
Common 20 x 6 = 120 6 Sheet #1
Uncommon 16 x 6 = 96 3 Sheet #2
Rare 9 x 6 = 54 1 Sheet #3
Mythic 4 x 6 = 24 1* Sheet #2
Legendary 1 x 6 = 6 1** Sheet #3

The idea behind this distribution is as follows:

  • Sheet #1 for 120 Common cards (6 out of 120)
  • Sheet #2 for 120 Uncommon and Mythic cards (3 out of 120)
  • Sheet #3 for 120 Rare and Legendary cards (1 out of 120)

(*) Odds of getting a Mythic card is 24/120 = 20% (1 in 5). Replaces one (1) Uncommon card.

(**) Odds of getting a Legendary card 12/120 = 10% (1 in 10). Replaces the Rare card.

Question?

What are the ODDS of getting BOTH Mythic and Legendary cards?

questccg
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Removed babbling ...

Get to the point already! Sheesh.

questccg
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Am I doing the MATH correctly???

24 Mythic cards (per sheet) and we use up 2 x 24 = 48 Uncommon cards + 24 Mythic cards = 24 Mythic Boosters.

Leaving (96 - 48) = 48 Uncommon cards / 3 = 16 Uncommon ONLY Boosters.

Seems a bit lop-sided. You get 24 Mythic Booster and only 16 Uncommon Boosters...

Am I doing the MATH correctly???

That means 24 / 40 = 60% Mythic Booster chance. Meanwhile only 40% Uncommon only Booster chance.

Sheet #1 (120 cards, 20 Boosters) x 6 = 720 cards, 120 Boosters.
Sheet #2 (120 cards, 40 Boosters) x 3 = 360 cards, 120 Boosters.
Sheet #3 (120 cards, 120 Boosters) = 120 cards, 120 Boosters.

Total cards for 120 Boosters = 1,200 cards / 10 = 120 Boosters.

Which means my sheets when laid out require multiples of 120 Boosters.

If a BOX contains 30 Boosters, that's "4" Booster "BOXES". (with 10 packs per well and 3 wells: 10 x 3 = 30)

I think this is correct... But I'd still like to know the ODDS (Q? #1)...

Rick-Holzgrafe
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You might try asking your

You might try asking your question on BoardGameGeek. There's an excellent thread there for questions just like yours, and responses seem usually to be quick and thorough: Post Probability Questions Here

If you've already posted there, my apologies. I keep an eye on that thread but I don't read it religiously.

questccg
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Thanks Rick...

Because of the LENGTH of the post, I don't feel I can express myself to the BGG audience who are reviewing that thread. They said the problem must be explained in 5 sentences or less!

Update:

I've computed the sheets and 60% have a Mythic card (3 out of 5). So it's NOT 1 in 5... It's 3 out of 5!

The Legendary cards are still 12 / 120 = 10% (1 in 10).

So it's (3:5) Mythic and (1:10) Legendary.

(I hope my Mythic card calculations are correct... Please correct if I did make a mistake...)

Juzek
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In MTG, the packs are semi

In MTG, the packs are semi randomized, ensuring one rare in each. Sometimes that rare is replaced with a mythic or other better card, but they will never put more than one rare or better in a booster pack.

Jay103
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So do I understand that your

So do I understand that your sheet of uncommons is 117 unc and 3 mythic?

And you get 3 cards at random from that distribution, with replacement? (meaning it's theoretically possible to get a booster with 3 of the exact same mythic and no uncommons at all?)

questccg
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From what I have seen ... Here's my understanding

Jay103 wrote:
So do I understand that your sheet of uncommons is 117 unc and 3 mythic?

Uncommon + Mythic = 96 + 24 = 120 cards.

Jay103 wrote:
And you get 3 cards at random from that distribution, with replacement? (meaning it's theoretically possible to get a booster with 3 of the exact same mythic and no uncommons at all?)

What I was favoring was all Uncommon cards in one SLOT #1 and then all Mythic one is another SLOT #2 (distribution machinery).

What I would have is 2 from SLOT #1 and 1 from SLOT #2 for a total of 24 Boosters with a Mythic. And then the remainder be 3 from SLOT #1 which is equal to 96 - 48 = 48 / 3 = 16 Boosters with 3 Uncommon.

So it would be AT MOST ONE (1) Mythic ... According to the odds of the SLOTs... so 24 Boosters with a Mythic and 16 Booster with 3 Uncommon for one Sheet. So 40 Boosters. To make this 120 Boosters, you would need to print 3x this sheet (so 120 cards) in total...

(I'm still trying to figure all of this out...) I just researched Pokemon's distribution which is similar to my own. Magic is different.

questccg
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I'm trying to do my best

But what this means is that IF you DON'T get a "Mythic" card... Then you've gotten a LAME booster. Because 3 out of 5 Boosters WILL have a Mythic card instead of a 3rd Uncommon card. It makes the boosters a bit more EXCITING!

24 / 40 = 0.6 = 60% = 6 out of 10 or 3 out of 5!

Jay103
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Just to make things more

Just to make things more coarse..

Half the boosters will have a mythic and half won't. That simultaneously makes mythics less "rare" to get, AND makes it more frustrating to be one of the ones who doesn't get one.

I'd think either you want everyone to get one mythic, or you want fewer people to get one..

questccg
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Ugh... I wish I knew what I was doing!

This is my NEW distribution... I'm have difficulties getting the final Sheet counts... So I'm not sure it's 100% yet.

Rarity Count Per Booster Sheet #
Common 120 6 Sheet #1
Uncommon 120 3 Sheet #2
Rare 42 1 Sheet #3
Mythic 12 1* Sheet #3
Legendary 6 1** Sheet #3

300 cards in Total...

Rare = 42 / 60 = 70%
Mythic = 12 / 60 = 20%
Legendary = 6 / 60 = 10%

Tell me if this sounds MORE reasonable. More Uncommon cards, less Rare ... And Rare, Mythic and Legendary are all cut off the same Sheet (#3).

The distribution goes as follow:

  • 6x Sheet #1 for 720 Common cards
  • 3x Sheet #2 for 360 Uncommon cards
  • 1x Sheet #3 for 120 Rare/Mythic/Legendary cards

Does all of this seem to COMPUTE???

questccg
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I understood ... I have revised my attempt

Juzek wrote:
In MTG, the packs are semi randomized, ensuring one rare in each. Sometimes that rare is replaced with a mythic or other better card, but they will never put more than one rare or better in a booster pack.

Thank you for your insight. I did the same: only one (1) rare or better.

Rare/Mythic/Legendary are all cut off the SAME sheet. The cards can simply all be Randomized and collated the right way.

But yeah, much simpler even if it was HARDER to figure out (myself). The thing which is complicated was figuring out the Sheet count. But I think I managed to get the correct result.

For now, I'm waiting back for an e-mail from a Manufacturer to get a QUOTE and see if this is realistic or not!

questccg
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My boosters are closer to Pokemon than Magic

Magic's booster card count is 15 cards per pack. Pokemon's booster card count is 10 cards per pack. So I naturally felt like Pokemon would be the best example to follow. But I could only get the booster pack distribution not the sheet count. On the flip side, Magic had the sheet count and it was pretty easy to find. So it was a challenge to go from 15 cards to 10 cards and then to figure out the sheet distribution.

My boosters are like in Pokemon:

  • 6 Common cards
  • 3 Uncommon cards
  • 1 Rare/Mythic/Legendary card

But my sheet distribution is my own... Based on trial and error. I posted the data here (in this thread) in the event anyone wants or needs this information.

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