tgm0112

06-03-2013, 12:44 PM

(Some background, for those who care for it. If you just want data, skip the italics.)

I'm currently spending a lot of time on MatLab (math modelling software) for my research and I keep busy creating simple models for fun while my actual work does its best to overheat my CPU. This is recreational and in some ways unrealistic, as I greatly doubt most people will simply open all their multitude of booster packs at launch. Drafting is a great incentive for saving those up. Enjoy!

Assumptions and Methodology

I ignore the contributions of starter decks, since I don't know their rare ratios or potential overlap. Not a huge deviation, mind you.

Based on MTG standards for core sets, the ratio of rares to other cards is set at 15%. (round to 53 for Hex Set I)

Rares are uniformly distributed. You are just as likely to get any particular rare card.

I ignore the primal pack some tiers get from KS. Easy enough to add in if you wish.

Likelihood of a primal pack is set at 1%. Independent and identically distributed. Uniform.

Scenario presented is what will happen to 95% of people, as long as other assumptions hold.

How many rares should I expect to have if I open a bunch of boosters?

20 Boosters: Between 11 and 26 distinct rares. Four+ copies of at most one rare, likely none.

40 Boosters: Between 22 and 38 distinct rares. Four+ copies of at most 2 rares with none still likely.

60 Boosters: Between 31 and 45 distinct rares. Four+ copies of at most 6 rares, still none ~10% of the time.

100 Boosters: Between 42 and 52 distinct rares. Four+ copies of 2 to 16 distinct rares.

150 Boosters: Between 48 and 53 distinct rares. Four+ copies of 13 to 30 distinct rares.

(Let me know if you want me to do a custom trial run. I have time to kill on this program and the model is extremely simple. All assumptions malleable.)

I'm currently spending a lot of time on MatLab (math modelling software) for my research and I keep busy creating simple models for fun while my actual work does its best to overheat my CPU. This is recreational and in some ways unrealistic, as I greatly doubt most people will simply open all their multitude of booster packs at launch. Drafting is a great incentive for saving those up. Enjoy!

Assumptions and Methodology

I ignore the contributions of starter decks, since I don't know their rare ratios or potential overlap. Not a huge deviation, mind you.

Based on MTG standards for core sets, the ratio of rares to other cards is set at 15%. (round to 53 for Hex Set I)

Rares are uniformly distributed. You are just as likely to get any particular rare card.

I ignore the primal pack some tiers get from KS. Easy enough to add in if you wish.

Likelihood of a primal pack is set at 1%. Independent and identically distributed. Uniform.

Scenario presented is what will happen to 95% of people, as long as other assumptions hold.

How many rares should I expect to have if I open a bunch of boosters?

20 Boosters: Between 11 and 26 distinct rares. Four+ copies of at most one rare, likely none.

40 Boosters: Between 22 and 38 distinct rares. Four+ copies of at most 2 rares with none still likely.

60 Boosters: Between 31 and 45 distinct rares. Four+ copies of at most 6 rares, still none ~10% of the time.

100 Boosters: Between 42 and 52 distinct rares. Four+ copies of 2 to 16 distinct rares.

150 Boosters: Between 48 and 53 distinct rares. Four+ copies of 13 to 30 distinct rares.

(Let me know if you want me to do a custom trial run. I have time to kill on this program and the model is extremely simple. All assumptions malleable.)