Box or singles: why the average box and the typical box are not the same
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The pull rate is a field because it is printed on the product or published by the maker, and because it changes with every set. Nothing here is stored or assumed on your behalf.
Results
| What the average box is worth | — |
| Profit on the average box | — |
| What the middling box is worth | — |
| Profit on the middling box | — |
| Boxes with none of the card, in per cent | — |
| Boxes that lose money, in per cent | — |
| What one copy costs if you buy boxes | — |
Those first four rows are the page. The average and the middle are different numbers describing the same box, and the gap between them is not a rounding detail: with the starting figures the average is more than ten times the middle. The average is being carried by the rare box that opens two or three of the card, and you are unlikely to be holding that one.
What a box actually opens
| Copies opened | Chance of that, in per cent | What the box is worth | Profit |
|---|
Read the value column and something odd appears: it climbs in steps rather than smoothly, because a box either found another copy or it did not. That is why the chance of losing money does not respond gently to the price. Raising the price within a step changes the risk not at all, and the moment it crosses a step the risk jumps, so fifty more can cost you nothing and the next fifty can double your chance of ending behind.
The last row of the results is the honest comparison with buying the card outright. It divides the price of the box by the copies a box brings on average, which is what a copy costs you through the box, and the rest of the packs is what you get for the difference. If that figure is above the price of the single, the box is only worth it for the rest.
Everything here treats the packs as independent, which is the assumption the published rates describe and not always what a sealed box does: some products guarantee one of a kind per box, and a guarantee removes exactly the outcome this page finds most often. It also cannot know that the price of the card is the price you would actually get for it after fees, or that it will still be that price when you decide to sell.
Why is the average box worth so much more than the typical one?
Because the average is dragged upwards by the rare box that opens two or three copies, and you are unlikely to be holding that one. With the starting figures the average box profits more than ten times what the middling box does.
The distribution is the honest picture: the single most likely result is one copy, and the second most likely is none at all.
| Copies opened | Chance, in per cent | Box is worth | Profit |
|---|---|---|---|
| 0 | 21,6069 | 108,00 | -192,00 |
| 1 | 33,8197 | 308,00 | 8,00 |
| 2 | 25,7326 | 508,00 | 208,00 |
| 3 | 12,6799 | 708,00 | 408,00 |
| 4 | 4,5483 | 908,00 | 608,00 |
Why does paying a bit more sometimes change nothing?
Because a box either found another copy or it did not, so its value climbs in steps rather than smoothly. Any price inside the same step meets exactly the same set of losing outcomes.
With the starting figures, a box at two hundred, two hundred and fifty or three hundred all carry the same risk of losing money, and a box at three hundred and fifty carries more than twice as much. The risk does not respond gently to the price, it responds in jumps.
How do I compare a box against just buying the card?
Divide the price of the box by the copies a box brings on average. That is what a copy costs you through the box, and everything else in the packs is what you get for the difference.
If that figure sits above the price of the single, the box is only worth opening for the rest of its contents, and the card you were after is cheaper bought directly.
What is the model not seeing?
It treats the packs as independent, which is what published rates describe and not always what a sealed box does. Some products guarantee one of a kind per box, and a guarantee removes exactly the outcome this page finds most often.
It also takes the price of the card at face value, and cannot know what you would actually receive after fees, or whether it will still be that price when you decide to sell.
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