Make the card or open another pack
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Nothing here is tied to one game: any game that lets you buy a random bundle or pay a fixed price for the exact thing works out the same way.
Results
| Cards like it you would have to destroy to make one | — |
| Packs whose takings pay for making it | — |
| Packs to find it by luck, on average | — |
| Packs by which half of people already have it | — |
| Packs to be nine in ten sure of having it | — |
| Chance at which chasing starts to win, in per cent | — |
What the chance per pack changes
| Chance per pack, in per cent | Packs on average | Packs for half of people | Packs to be nine in ten sure | Packs that pay for making it |
|---|
The line between the two is exact rather than a matter of taste, and it is worth memorising: chasing only wins when the chance per pack is bigger than what one pack brings in divided by what the thing costs. Everything else in the argument is noise around that one comparison.
The three columns of packs are the same situation described three ways, and the gap between them is the part that gets people. The average is not what usually happens, the middle column is, and the last column is what you should budget for if you actually need the card. At one in a hundred the average is a hundred packs, half of people are done by sixty-nine, and being nine in ten sure takes two hundred and twenty-nine.
That spread is the whole argument for paying the fixed price, because it buys away the tail rather than the average. What the page cannot weigh is the rest of what a pack contains, which is real value even when the card you wanted is not in it, so read the comparison as being about this one card rather than about whether packs are worth buying at all.
Is there a rule for when chasing it in packs is right?
Yes, and it is exact: chasing wins only when the chance per pack is bigger than what one pack brings in divided by what the card costs to make.
At sixteen hundred to make and a hundred a pack, that line sits at six and a quarter in a hundred. Below it, making the card is cheaper; above it, opening packs is.
How far apart are the average and the unlucky case?
Much further than people expect, because the average of a chase is not what usually happens to anyone. At one in a hundred per pack the average is a hundred packs, half of people are done by sixty-nine, and being nine in ten sure takes two hundred and twenty-nine.
That is the real argument for paying a fixed price: it buys away the tail, not the average.
| Chance per pack, in per cent | Packs on average | Packs for half of people | Packs to be nine in ten sure |
|---|---|---|---|
| 1 | 100,00 | 68,97 | 229,11 |
| 2 | 50,00 | 34,31 | 113,97 |
| 5 | 20,00 | 13,51 | 44,89 |
| 10 | 10,00 | 6,58 | 21,85 |
Why does destroying cards to make one lose so much?
Because what a card gives back when destroyed is a fraction of what the same card costs to make, so the exchange is lossy by design. At four hundred back against sixteen hundred to make, one card costs four of its equals.
The page shows that ratio on the first line rather than burying it, because it is the number that decides whether a collection can ever be converted into the cards you actually want.
Does this say packs are a bad buy?
No, and it cannot. A pack is full of other things that are worth something even when the card you wanted is not in it, and none of that is on this page.
Read the comparison as being about one specific card you have decided you need, which is the situation the question is usually asked in.
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