PDA

View Full Version : How many rares can I expect to get?



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.)

MugenMusou
06-03-2013, 01:04 PM
i like these types of analysis but there are too many factors yet to be revealed including number and ratio of legendary to rares. But once those factors are officially announced i d like to see how much will ppl need to spend on average to complete a playset.

Daer
06-03-2013, 01:15 PM
http://hextcg.franciscabral.net/

shocker455
06-03-2013, 01:22 PM
How does someone get 26 rares out of 20 packs when you ignore primals...

larryhl
06-03-2013, 01:23 PM
How does someone get 26 rares out of 20 packs when you ignore primals...

He's ignoring the guaranteed primals from KS tiers. Not the random chance of getting primals in our booster pack allotment.

tgm0112
06-03-2013, 01:23 PM
http://hextcg.franciscabral.net/

That does a single trial. I'm relying on large numbers and CLT, not the anecdote of a single datum. Cool link, though, thanks!


How does someone get 26 rares out of 20 packs when you ignore primals...

I ignored KS primals, not the chance of a given booster being primal. Not all the tiers get that assured primal.


i like these types of analysis but there are too many factors yet to be revealed. But once those factors are officially announced i d like to see how much will ppl need to spend on average to complete a playset.

I hear ya. That's why I made my assumptions known. The most volatile variables in this model are the chance of a primal pack and the actual number of rares. Here's the output if there are only 50 rares (~14%) in the first set.


20 Boosters: Between 11 and 26 distinct rares. Four+ copies of at most 1 rare, none likely.
40 Boosters: Between 22 and 37 distinct rares. Four+ copies of at most 3 distinct rares.
60 Boosters: Between 31 and 44 distinct rares. Four+ copies of at most 6 distinct rares (<10% none).
100 Boosters: Between 40 and 49 distinct rares. Four+ copies of 3 to 17 distinct rares.
150 Boosters: Between 46 and 50 distinct rares. Four+ copies of 14 to 31 distinct rares.



EDIT: Doesn't really change matters too terribly.

dogmod
06-03-2013, 01:25 PM
How does someone get 26 rares out of 20 packs when you ignore primals...

Read the rest..

And also it would be interesting if the #was closer to 1/3 which is their WoW TCG #s I believe..

Erebus
06-03-2013, 01:28 PM
He said ignoring free primals.

He stated that he gave each pack a 1% chance to be primal.

houjix
06-03-2013, 01:29 PM
Try the number with about 80 rares, 15 legendaries and legendary replacing a rare about 1 in evey 10 packs and see what you get. Those will be a lot closer to what current sets of WoW have for ratios.

tgm0112
06-03-2013, 01:30 PM
Read the rest..

And also it would be interesting if the #was closer to 1/3 which is their WoW TCG #s I believe..

Is that the primals chance or rare ratio? Never played it, myself.

dogmod
06-03-2013, 01:38 PM
Is that the primals chance or rare ratio? Never played it, myself.

Rare ratio

Niedar
06-03-2013, 01:40 PM
One of your assumptions is wrong, looks like you are looking at the probability of a rare on each card in a pack while there is always one and only one rare guaranteed in each pack. Its impossible to end up with less rares than the number of packs you get.

Edit: Actually nvm I did not read the distinct rares part.

houjix
06-03-2013, 01:41 PM
One of your assumptions is wrong, looks like you are looking at the probability of a rare on each card in a pack while there is always one and only one rare guaranteed in each pack. Its impossible to end up with less rares than the number of packs you get.

The number of rares isn't less than the packs, he's accounting for doubles.

dogmod
06-03-2013, 01:44 PM
The number of rares isn't less than the packs, he's accounting for doubles.

accounting for primals

edit- you were right ;o

tgm0112
06-03-2013, 01:56 PM
Try the number with about 80 rares, 15 legendaries and legendary replacing a rare about 1 in evey 10 packs and see what you get. Those will be a lot closer to what current sets of WoW have for ratios.

Hehe, that was fun. Here are the results using your numbers precisely:


20 Boosters: Between 9 and 27 distinct rares, 0 to 7 distinct legendaries. Four+ copies of none.

40 Boosters: Between 22 and 42 distinct rares, 2 to 10 distinct legendaries. Four+ copies of at most 1 distinct rare and no legendaries.

60 Boosters: Between 33 and 53 distinct rares, 4 to 12 distinct legendaries. Four+ copies of at most 2 distinct rares and 1 legendary (none likely).

100 Boosters: Between 49 and 67 distinct rares, 7 to 14 distinct legendaries. Four+ copies of at most 7 distinct rares and 2 legendaries.

150 Boosters: Between 61 and 75 distinct rares, 10 to 15 distinct legendaries. Four+ copies of 3-17 distinct rares and at most 5 distinct legendaries.



Cheers


EDIT: Still open to more options. I have to admit, this last run was the most encouraging. I hope it's something like that, so I still have to wait/trade for cards I want even with all the KS packs.