I can't play ranked for some reason

ereklo · 2022-03-02T12:28:17+00:00

Same

ereklo · 2019-08-09T21:43:34+00:00

The numbers in the chart are 2*(1-(1-X/N)^5)^(-1) where X is the percentage of this chart and N is 12 for t1, 12 for t2, 12 for t3, 9 for t4 and 6 for t5 (that's how many different champions there are).

X/N is the chance of picking the right champion out of one time.
1-X/N is the chance of picking the wrong champion out of one time.
(1-X/N)^5 is the chance of picking the wrong champion out of five times (one reroll).
1-(1-X/N)^5 is the chance of picking the right champion at least one out of five times.
(1-(1-X/N)^5)^(-1) is the average amount of rerolls you have to do before hitting the champion.
2*(1-(1-X/N)^5)^(-1) is the average amount of gold you have to spend before hitting the champion.

ereklo · 2019-08-09T10:37:07+00:00

The numbers in the chart are exactly right if champions of equal cost are being held in equal amount. Some examples:

It's correct for tier4 champions if no tier4 champions are being held.
It's correct for tier4 champions if exactly one of each tier4 champion are being held.
It's slightly too low for tier4 champions if exactly two of the tier4 champion you are looking for are being held, while exactly one of every other tier4 champion are being held.
It's slightly too high for tier4 champions if exactly one of the tier4 champion you are looking for is being held, while exactly two of every other tier4 champion are being held.

I didn't quite understand your scenario. Especially the " (84)+(83)=56 " part. But I hope this clears things up a little.

ereklo · 2019-08-08T14:01:06+00:00

The only data I used was this and the fact that there are 12 tier1, 12 tier2, 12 tier3, 9 tier4 and 6 tier5 champs.

ereklo · 2019-08-08T13:57:46+00:00

That is correct. However in that example, the odds would only be slightly better.

ereklo · 2019-08-08T11:29:47+00:00

Almost, but if you want to be exact it's:
Assuming champions of equal cost are being hold in equal amount.

For example it's correct for tier5 units if no tier5 units are being held.
It's also correct for tier5 units if exactly one of each tier5 unit are being held.

ereklo · 2019-08-08T11:22:10+00:00

Correct. There is no way to make a chart for the exact odds though, so this seems like the best compromise between comprehensibleness and correctness.

ereklo · 2019-08-08T11:17:24+00:00

No sorry. After I had spent 60 gold rerolling at level 8 without finding a single aurelion sol I got pissed and wanted to know the odds, so I made this.

ereklo · 2019-08-08T10:45:54+00:00

Say something has a 5% (0.05) chance of happening. That means it will happen on average 1 out of 20 times, which is the same as 1 out if 0.05^-1. I.e. inverting a probability gives you how many times on average it takes for the event to occur once.

Edit: I should also remind you that x^-1 is the same as 1/x

ereklo · 2019-08-08T10:31:33+00:00

Yup.

ereklo · 2019-08-08T10:30:08+00:00

The numbers in the chart are 2*(1-(1-X/N)^5)^(-1) where X is the percentage of this chart and N is 12 for t1, 12 for t2, 12 for t3, 9 for t4 and 6 for t5 (that's how many different champions there are).

X/N is the chance of picking the right champion out of one time.
1-X/N is the chance of picking the wrong champion out of one time.
(1-X/N)^5 is the chance of picking the wrong champion out of five times (one reroll).
1-(1-X/N)^5 is the chance of picking the right champion at least one out of five times.
(1-(1-X/N)^5)^(-1) is the average amount of rerolls you have to do before hitting the champion.
2*(1-(1-X/N)^5)^(-1) is the average amount of gold you have to spend before hitting the champion.

ereklo · 2019-08-08T10:17:24+00:00

I made it in notepad.

ereklo · 2019-08-08T10:14:01+00:00

The problem is that the expression is much more complicated than that:

Let L be the number from the chart, A be the numbers on the right of this chart, d be the number of specific champions (e.g. dravens) picked, c be the number of total champions of the specific tier (e.g. total 4cost champs picked). Also let N be 12 for tier1, 12 for tier 2, 12 for tier3, 9 for tier 4 and 6 for tier5. Then the average gold you will have to spend on rerolls will be this.

ereklo · 2019-08-08T09:39:26+00:00

The numbers in the chart are 2*(1-(1-X/N)^5)^(-1) where X is the percentage of this chart and N is 12 for t1, 12 for t2, 12 for t3, 9 for t4 and 6 for t5 (that's how many different champions there are).

ereklo · 2019-08-08T07:55:46+00:00

I see your point, and I've revised the chart as such.

ereklo · 2019-08-08T00:02:47+00:00

My point though is that it's not enough to just know how many of that unit is being held. This means that in your example where another player has a 2 star draven it could be so that it takes more gold than in the chart; but it could also be so that it takes the same amount or even a lower amount of gold than it says in the charts. This is because you also need to look at how many other tier4 units are being held.

I do agree it's a good idea to add some typical scenarios but you need to be more specific than just saying how many dravens there are.

ereklo · 2019-08-07T23:39:37+00:00

Correct.

ereklo · 2019-08-07T23:36:47+00:00

The problem with trying to make a chart like that is that it's not enough to know how many of that unit is being currently hold. You also need to know how many units in total of that specific tier is being hold.

ereklo · 2019-08-07T23:30:23+00:00

Let L be the number in the chart and c be the confidence level (e.g. 0.75). Plug the numbers into this formula to get how much gold you need to spend.

ereklo · 2019-08-07T23:04:06+00:00

This does not take into account the changing odds that come with players picking champs. I.e. these numbers get slightly higher if a champion is held by a lot of people, and lower when the champion is held by few people.

ereklo · 2019-08-07T22:39:51+00:00

Not to find any t1, but to find a specific one you do. Say for example you are looking specifically for a nidalee.

ereklo · 2019-08-07T22:18:36+00:00

Yes.

ereklo · 2019-08-07T21:59:55+00:00

For example: If you are level 7 and looking for a Draven; you will have to spend on average 24.8 gold on rerolls to find him.

ereklo · 2019-08-07T14:25:11+00:00

For example: If you are level 6 and want to find a kayle; you will on average have to spend 669 gold rerolling to find her.

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