I am looking at getting into MTG again. Thinking about just playing pauper and maybe some EDH. However it's kind of fun opening packs. My thoughts are I buy a box at the release of a set and just use it to build play sets of the commons. Sell off everything else except perhaps a couple cards that may work with EDH or something. Not asking if this is the cheapest way, just whether or not it would be viable to get a full common play set from a single box or maybe two.
The exact value is difficult to calculate. This is due to the print runs of the cards - the 74 commons have "print runs" of 5 to make the printing easier. There are hundreds of these, but the fact that no pack contains the same cards does complicate the calculation.
I did throw together a pack simulator to test this and it ran in the background. Below is the output after 10 million trials. The highest was 200 packs and the lowest was 45. On a different run (of about 22 million trials) I was able to get a playset in only 44 trials. This run I've let go for 35 million trials and it was only able to get that 45, although eventually I got so unlucky I needed 215 packs on one of them. The last 17 million trials have not changed the min and max, though. I don't expect them to be changing any time soon.
Thus I think it's safe to say you are never going to get a playset from a single booster box.
I modified it to check the number of boxes and found a very consistent: 2 boxes were sufficient 39.2% of the time, three boxes 58.8% of the time, and four boxes sufficient 2.0% of the time. Five boxes were only necessary on 0.03% of runs but that was consistent far far into the tens of millions of trials.
If you want to play it safe, buy 3 boxes - you'll have them all 98% of the time.
new max: 72 on trial: 2 new max: 77 on trial: 3 new max: 81 on trial: 4 new low: 72 on trial: 6 new max: 87 on trial: 9 new max: 88 on trial: 10 new low: 65 on trial: 21 new max: 92 on trial: 25 new low: 64 on trial: 31 new max: 95 on trial: 42 new max: 108 on trial: 64 new low: 61 on trial: 78 new max: 115 on trial: 80 new max: 116 on trial: 110 new max: 119 on trial: 146 new low: 60 on trial: 153 new low: 59 on trial: 162 new low: 58 on trial: 222 new low: 56 on trial: 296 new low: 55 on trial: 607 new low: 53 on trial: 744 new max: 140 on trial: 2928 new low: 51 on trial: 6183 new max: 156 on trial: 9309 new low: 49 on trial: 49366 new max: 162 on trial: 60593 new max: 170 on trial: 112123 new low: 48 on trial: 117347 hit trial: 500000 new low: 47 on trial: 830525 hit trial: 1000000 new max: 186 on trial: 1307797 hit trial: 1500000 hit trial: 2000000 hit trial: 2500000 hit trial: 3000000 hit trial: 3500000 new max: 195 on trial: 3563925 hit trial: 4000000 hit trial: 4500000 hit trial: 5000000 hit trial: 5500000 hit trial: 6000000 new max: 198 on trial: 6005659 hit trial: 6500000 new low: 46 on trial: 6614767 hit trial: 7000000 hit trial: 7500000 hit trial: 8000000 new low: 45 on trial: 8015142 new max: 200 on trial: 8333263 hit trial: 8500000 hit trial: 9000000 hit trial: 9500000 hit trial: 10000000
Someone else might be able to do the math a bit better than me, but I will try to break it down for you. For this example lets use the recently released Hour of Devestation set.
Each Booster box you get will contain 36 packs.
Each Pack will normally contain 10 Commons, 3 Uncommons, 1 Rare, 1 Land.
However if you get a foil card it will take the place of one of your commons, so you may only get 9 Commons in a pack.
So one box of Magic cards will get you a bit less than 360 Commons.
In Hour of Devastation, there are 74 Commons not including Basic lands (so a full play set of Commons is 74 x 4 for 296 total cards). Since the cards you get from the packs are random it is unlikely (though I guess technically possible) for you to get a full play set of Commons from a single box.
Note: I really have no idea how to do probability calculations, so anyone who does feel free post an answer with the actual precentage chances. I am kind of intrigued by this now.
However, if you are willing to trade in your cards at your Local Game Shop, you should be able to swap any Rares or Uncommons you don't want for the Commons you are missing. As of writing the Commons in Hour of Devestation are between $0.16 and $0.11 a piece. Where as the Rares range from ~$7 to $0.30 (which you will have around 36 of) are and the Uncommonsrange from ~$2 to $0.15 (which you will have around 108 of). So you shouldn't have an issue converting any of the value you do get into a complete playset.
As a complete aside, if you do plan on doing this I would recommend getting some sort of binder or card box. There are a lot of cards in a booster box (550+ per box with tokens), and it can get pretty unwieldy pretty quick.
Many e-tailers sell preorder and post-release packs of common playsets, which will guarantee you the full playset. Coolstuffinc has a pack that you can preorder for $19.99 that includes a full playset of commons (link is for Ixalan). You can also do this through ebay vendors both before and after set release (link is for Hour of Devastation).
This solution also prevents you from having to spend a lot of time selling extra cards you don't want. Additionally, sometimes you won't make back your initial cost anyway, depending on set value and the rares you open. A listing of all expected box values can be found at mtg.dawnglare.com. If you look at Hour of Devastation, assuming you don't get an invocation, the expected value is just over $83. If you buy a box at $110 from your LGS, you probably aren't making that back by trading in cards you don't plan to use.
You best solution is probably to just buy the playset outright, and buy any uncommon or rare cards you want as singles.
The probability of getting 4 copies of each common is effectively 0.
Taking @Malco's numbers of 360 commons in a booster box and 74 commons in a set, I believe the probability can be computed as:
360 Choose 292 * (73/74)^4 * (72/74)^4 * ... (1/74)^4
(You are guaranteed to get 4 of one common, so it's not counted in the formula, so there are only 292 cards that you are trying to open).
The product of this is 2*10^-49, which is to say 0. Even though 360 Choose 292 = 3*10^74, the sum of fractions is around 10^-123.
That said, you will probably get pretty close to a complete playset, and can fairly easily trade or sell the rares to get the rest of the way.
There are many online shops that have bulk deals. Star City Games the shop I usually buy from has for 20$US the gold collection with the following.
- 865 commons/uncommons
- 25 rares
- 25 foil commons/uncommons
- 5 foil rares
- 80 basic lands
If you want to get into pauper that would probably be a much better idea than buying maybe 6-8 packs for the same money. I have only bought their rare lots but they are not charlatans. They don't actively try and con you, they are not above putting some casual goodness in their lots.