Not sure why my first post got removed, but I'll try again- I've created three tables you need in order to decide how much gold you need to spend rerolling to have either a 50%, 75%, or 90% confidence of hitting a particular champion. I'd like to point out that almost every table I've seen with "average gold required" (including the heavily upvoted post here) uses improper math- in particular, using the mean from a geometric distribution (which is the distribution of number of rolls) is flawed since the graph is skewed right and thus heavily influenced by outliers. This experience is definitely felt by all of you- usually, to get that one Gnar you need for your 4 wild/sorc/drag comp, you just needed to roll like 2-5 times in most scenarios- but holy cow that one game it took 30 ROLLS. If you calculated the arithmetic mean of your experiences, that one time is going to artificially bump up your expected number of rolls, and so your result might be pretty off center from what you might expect. In other words, the mean is very susceptible to outliers, whereas the median (50th percentile result) is not, because we don’t actually care about how extreme the highs and lows are, we only care about the middle number.

To clarify how to read the table, it's saying for example that at level 7, assuming Gnar is not already in your shop, you need to spend 18 gold to get Gnar 50% of the time, 34 gold to get Gnar 75% of the time, and 56 gold to get Gnar 90% of the time! Hopefully this gives a complete picture on what you should expect while rerolling, so start spamming that button now!

EDIT: I actually messed up one of the values, tables are fixed now!

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Amount of gold needed for 50% confidence in finding a specific champ

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Amount of gold needed for 75% confidence in finding a specific champ

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Amount of gold needed for 90% confidence in finding a specific champ

Edit 2: OK so someone asked about making tables for getting 2* of a unit. Alright I did my simulations again! OK so I'm making an assumption here- I think it's actually more beneficial to assume you already have a copy of a unit (Gnar), and you're asking how much gold you need to make him a 2* (aka get 2 more copies, rather than 3). If you already have 2 copies, just use the tables above :P

Here are the tables! Notice that it's not just previous table * 2, but actually more. A little surprised but I did check my work

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Amount of gold needed for 50% confidence to find TWO copies of a specific champ

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Amount of gold needed for 75% confidence to find TWO copies of a specific champ

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Amount of gold needed for 90% confidence to find TWO copies of a specific champ

Edit 4: A lot of people are noting that it doesn't take into account champs taken out of the pool and that's correct. This is supposed to be a quick tool that you can use to have basic understanding of how much gold you should be expecting to spend. There are spreadsheets with more sophistication, thanks /u/DeepDiveLM for this one ( https://docs.google.com/spreadsheets/d/1XPeiUYjFItQoHSAPLsbsPiHSay74jbZR69LzKPY_TeU/edit#gid=638762221 ) and u/SimonMoonANR for this one ( https://docs.google.com/spreadsheets/d/12LFP7JNd45DQfzKZiIdE4IslUAtvdzzf_q2q9kNLM4A/edit#gid=1367361620 )