So I just defeated a weather boosted Palkia with a team of 5 players, we failed the first attempt but succeeded on the second. I got 3 charged TM's for beating the raid, I wonder what are the chances of this, seems pretty rare?
TSR has some (somewhat) outdated information on this. It has to do with how many balls you get to determine how many "packages" you get to even have a chance at any given reward set; the odds of a CTM in any given package from a 5* raid is, if I recall correctly, 1.8%ish. Roughly 1/185,000 if my percentage is correct.
Edit: 1 in 171,000.
Even if my percentage is wildly off as I'm doing it from memory, it's not until you pass 6-7% that it becomes "frequent"
Let me check my math - I probably added a digit somewhere, but the basic premise was 0.018 (first chance) x 0.018 (second chance) x 0.018 (third chance.) It's not a 1.8% chance for 3. It's per each one. Ergo the odds of getting 3 are the odds of getting a single one to the third power, as the chance is rolled individually.
Your calculation implies that the player gets only three bundles.
If the player gets 14 bundles and each bundle has a 1.8% chance to contain a Charge TM, the chance that the player will get 3 Charge TMs is 0.17% (about 1 in 588) and the chance to get more than 3 Charge TMs is 0.009% (about 1 in 11,000).
Rewards follow a binomial distribution. To find the probability if the player instead gets 10 or 12 (for example) bundles, use a binomial probability calculator such as https://stattrek.com/online-calculator/binomial.aspx.
What hkn said above. Your calculation assumes only 3 bundles are possible for the player (see TSR for further detail. You can receive 1 charged TM per bundle), but the minimum amount of bundles is 4, and goes up to 8.
Now suppose we are dealing with 4 bundles. The 'combination' part is how the rewards can be ordered. Denote the event of reward of charge TM as X and the event that something else is given other than charge TM as Y, there are 4 distinct combinations that can give OP's criteria of 3 charge TMS: namely:
YXXX
XYXX
XXYX
XXXY
There are 4 possible combinations of this to satisfy the "3 charged moves" criteria.
Given that you can receive up to 8 bundles, yet the criteria "3 charged moves" stays static, the chances are way higher than what you quoted. Even if the worst possible 4 bundle case is quoted, the odds are still much higher.
