One way of awarding prizes in Magic Tournaments is to "rare re-draft", where you take all the higher value cards that have been opened while drafting (6-8 players, 3 packs per player, approx 1 rare per pack, so 24 rares/mythic rares (+ foils)), and the winner gets first choice of card, the player who came second gets the next choice and so on.

If I've done the maths correctly, this is appallingly bad value for weaker players, not just in terms of how it benefits stronger players, but just compared to keeping the rares they open while drafting.

Is this accurate, or have I got my maths wrong?

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    This seems trivially correct.. I would assume it's the entire reason for doing a rare re-draft; as a prize for the player who came in first. Giving away random packs would not provide an incentive to win. – GendoIkari Jun 8 '16 at 21:06
  • Well, I was arguing with someone who claimed that even for the person in 8th place, they had a chance of a good card than if you randomly opened a booster. I did the maths, and as I expected found out that, no, that's completely wrong, but I'm pseudo-humble enough to want a second opinion (if only so my percentages can be strictly accurate). Also, frankly, having an authoritative source for players who don't understand this or who aren't sure to refer to seems like a worthy addition to the site. – deworde Jun 8 '16 at 21:09
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    Do you need a calculator, or another person, to tell you that if you consistently get last pick, the average card value will be lower? Isn't that obvious? – Rainbolt Jun 8 '16 at 21:12
  • So actually it depends on a variable you didn't give in the question... how many rares is the pool of rare drafts taken from? Imagine for a moment that to make the rare draft, you took 1000 random rares and chose the best 24 of them to do the draft with. This would be very different from taking 30 random rares and taking the best 24. – GendoIkari Jun 8 '16 at 21:13
  • Or to use your analogy; why did you use "24" dice? If you used 100 dice, then the answer would be different. If you use 1 die per player, then it becomes trivially bad for weak players. – GendoIkari Jun 8 '16 at 21:20

Expected value is obviously lower, but in an 8 player draft the last place player still gets the 8th most valuable card. Imagine that the value distribution is something like this

10 most valuable cards - $50 each

14 other cards - $1 each

The total value of the cards is $514, so you could say that the EV of each card is $21, and the total EV without re-drafting is $63. With re-drafting, the value is exactly $52.

But now think about standard deviation. Without re-drafting, there is a significant chance the player ends up with a value of $3. With it, they will get $52 regardless of their performance.

The moral of the story is that if there are enough expensive cards available that even the last player gets one, re-drafting gives them a consistent value, while otherwise there is a chance that they end up with practically nothing (or possibly a jackpot).

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    As the answer says, without re-drafting, there is a significant chance the player ends up with a value of $3. There is also a significant chance the player ends up with a value of $200. Do you want to mention that too? – Rainbolt Jun 8 '16 at 22:31
  • It's a good point that the chance of a real whiff on value is lower under rare-redraft if there's a sharp plummet in value around the mid-point. – deworde Jun 8 '16 at 22:36
  • Could such an mtg set actually exist (in-print?) if opening packs on average yielded a pile of cards with wildly higher secondary market value than the cost of the packs, wouldn't people keep opening packs until the secondary market prices normalized. :) (You can see this historically with worldwake where the price of jace TM eventually became almost exactly the wholesale cost of the # of packs on average you have to open to get him while the set was still available. and maybe a bit of margin for abyssal persecutor who flopped but was sought at the time) – Affe Jun 9 '16 at 18:35
  • I'm obviously simplifying to make the math more obvious. It is certainly reasonable to assume that there might be 8 cards that are significantly more valuable than the rest. If you make it $5 instead of $50, the same conclusion applies, just to a smaller degree. – bwarner Jun 9 '16 at 21:19

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