TFT shop odds when the champion pool is shared
Your data
The percentage per level is yours to type because it changes from patch to patch and from game to game. Slots inside one shop are treated as independent, which is the usual approximation and very close at these sizes.
Results
Chance of seeing it at least once in those rolls
—
| Cards of that cost still left in the pool | — |
| Chance that one single slot is the one you want | — |
| Chance that one whole shop has it | — |
| Rolls it takes on average | — |
| Rolls that get you there half the time | — |
What other players holding copies does to you
| Copies held by others | Left for you | Chance in those rolls |
|---|
This is the table worth staring at. With none of the copies taken the odds here are one thing, and with all but two of them taken the same rolls come to a small fraction of that. Nothing about your play changed between those two rows: other people did it to you, and a calculator that treats the chance as a fixed number of the game cannot show it.
The average number of rolls is not the number to plan around either. Because the tail is long, the average sits well above the point where half the attempts have already succeeded, and that midpoint is closer to seven tenths of it. Half the time you get there sooner than the average suggests, and the other half you find out how long the tail is.
Why does this ask about other players at all?
Because the pool is shared, and that is the whole point of this page. Every copy sitting on somebody else's board is a copy your shop cannot show you, so your odds move without you doing anything different.
With twelve copies of the one you want, twelve others at that cost, a quarter chance of the cost appearing and ten rolls of five slots, the chance of seeing it is 65.1 percent. Let other people take ten of those twelve copies and the very same ten rolls come to 17.0 percent, which is barely a quarter of what it was.
How is this different from a normal drop chance calculator?
A drop chance calculator starts from a probability the game publishes and asks what happens over many tries. Here the probability is not published: it is worked out from how many copies are left, and it changes every time somebody buys one.
That is why the interesting part of this page is the table of what other players holding copies does to you, rather than the headline number.
Why type the percentages instead of having them built in?
Because they change from patch to patch and they are different in every game that uses this kind of shop. A number frozen into the page would look authoritative long after it stopped being true.
Typing them also means the page works for any game with a shared pool, not just the one it was written for.
Why show a median as well as an average?
Because for this kind of waiting the average is dragged upward by a long tail and is not the number to plan around. The point where half the attempts have already succeeded sits at about seven tenths of the average.
In the example above, the average is ten rolls but half the time it is done in under seven. The other half is where the reputation of bad luck comes from.
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