# Every Crystal Ever Bundle = Daily Crystal Bundle

Gutzdeep
Posts:

**13**
So I saw this bundle got all excited and stuff and bought it thinking finally I will get at least 1 decent 4 star... nope I was wrong out of every single crystal I got a total of four 3 stars and the rest was all 2 stars. Not a single 4 star at all. I feel like I paid $20 for a bunch of daily crystals.

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## Comments

246It is what it is. You don't get 4* just cause you buy a bunch of crystals.

587382,02713Reasonably priced... yea if you were actually awarded something... basically I paid 20 bucks for a a bunch of 24 hours crystals that aint right on any level.

216You can't really expect 5 4* for that price. The deal is reasonable, but it's good for new players to help them a bit in the catch up game. Not for the ones that are looking at 5 stars bots.

I guess you've expected a little too much for your 20 bucks.

1,70642,8532,736My work here is done.

8If you do the math on 1.5% 4* drop rates and 37 crystals, you have a 57% chance of getting no 4* bots. So almost like a coin flip... However if you pull all 2*, then we can talk complaints and lawsuits since that's a super slim 0.001% chance. If you can't do the math, consider that something very useful to learn.

44I'm not great with maths, but I'm pretty sure the odds for 37 crystals is still 1.5% for a 4*. As each crystal spin is 1.5%, the odds don't increase just because you have more crystals.

This means you don't have a 57% chance of not getting a 4* from 37 crystals, you have a 98.5%chance of not getting a 4* from 37 crystals. The odds aren't cumulative.

718This is absolutely correct, and is the primary reason statistics screws with people. Each crystal is its own event, so your odds don't change no matter how many you open.

8Let's pretend this is coin flipping so I can use outcome names T and H. T = 4* bot, H = non-4* bot, and P(T) = 0.015, P(H) = 0.985. Since each spin's outcome is independent of the next, we get total probabilities by multiplying 37 P(T)'s and P(H)'s in various combinations.

If we only had 3 spins, we have these possible results:

TTT prob = 1.5% * 1.5% * 1.5% * 1 way to get 3 T out of 3 spins

TTH, THT, HTT prob = 1.5% * 1.5% * 98.5% * 3 ways to get two T out of 3 spins

THH, HHT, HTH prob = 1.5% * 98.5% * 98.5% * 3 ways to get one T out of 3 spins

HHH prob = 98.5% * 98.5% * 98.5% * 1 way to get zero T out of 3 spins

More generally, the probability of exactly N tails is P(H)^(37-N) * P(T)^N * C(37,N) where C(37,N) is the combinatorial function that gives number of ways to choose combination of N items out of 37 ignoring ordering.

Probability of exactly 0 tails is 0.985^37 * 0.015^0 * 1 = 0.5716 (57%)

Probability of exactly 1 tail is 0.985^36 * 0.015^1 * 37 = 0.322 (32%)

Probability of exactly 2 tails is 0.985^35 * 0.015^2 * 666 = 0.088 (8.8%)

Probability of exactly 3 tails is 0.985^34 * 0.015^3 * 7770 = 0.0156 (1.6%)

Probability of exactly 4 tails is 0.985^33 * 0.015^4 * 66045 = 0.0020 (0.2%)

...

Probability of exactly 37 tails is 0.985^0 * 0.015^37 * 1 = 3.2e-68 (0.0000000000000000000000000000000000000000000000000000000000000000032%)

So your results for 37 spins are going to give you at least a 1.5% chance of getting a 4* bot, but you're leaving a lot of favorable outcomes on the table. Intuitively, if we increased the number of spins to a million, yes you still have at least a 1.5% chance to get a 4* bot, but practically speaking, you have 100% chance to get at least one 4* bot.

Sorry, could not resist bad joke - intuition and statistics don't go together. And now I'm going to have to flag all you guys for making my brain hurt so late at night when I could have been grinding raids and arena instead.