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Many people wonder how many vouchers you need to get a spin hero. There's no universal answer to that question since there's a bit of chance involved. However it is possible to say "with X vouchers, you have y% chance".

Assumption: The odds of getting a Hero piece from Destiny Spin are 1 in 45.

There is no way of knowing if this is accurate. It's an educated guess based on anecdotal evidence (Many people report needing 8,000-9,000 vouchers, some report needing 9,000-10,000, and a rare few report an even higher or lower number). If this is wildly incorrect, then this chart will be wildly incorrect, but it's the best we can do and I believe it's close enough to the true odds.

Assumption: That the wheel is fair -- that each outcome has a defined chance that doesn't change, and there isn't some convoluted coding changing the odds based on previous spins.

I mean, the latter wouldn't make any sense. What programmer would go to such lengths, and why? A lot of people believe it however (in such nonsense that opening chests in specific bunches gives them better results or that you should always do 10x or 100x spin) -- while the simplest explanation is that those people are just completely ignorant about probability and putting far too much faith in an insignificant sample size, it is true that it is impossible to disprove that possibility.

Methodology: For each amount of spins n, we calculate standard deviation with the formula sqrt(npq), where p is the probability of getting a hero piece (1/45) and q is the probability of not getting a hero piece (44/45). Then we find the z-score by subtracting the average expected number of hero pieces (which would be spins/45) from the number of hero pieces required (20) and dividing by the standard deviation. The z-score is how many standard deviations above or below the mean a value is. Then you plug the z-score into a calculator that tells you how likely a given z-score is in a normal binomial distribution.

Probability of rolling 20 Hero pieces with X vouchers
Vouchers Chance
5,000 0.35%
5,500 1.22%
6,000 3.24%
6,500 6.97%
7,000 12.72%
7,500 20.45%
8,000 29.70%
8,500 39.80%
9,000 50.00%
9,500 59.66%
10,000 68.32%
10,500 75.74%
11,000 81.84%
11,500 86.68%
12,000 90.42%
12,500 93.22%
13,000 95.28%
13,500 96.76%
14,000 97.80%

Notes

  • One of the rewards from Destiny Spin is booster gems. This means that when you spin you actually get some more vouchers back. In my one attempt, I spent 8,600 vouchers and got 600 back. This isn't enough data to say anything with certainty but it's possible you can expect to get at least 5% of the vouchers you spend back. If you're between two levels in this chart you can probably round up.
  • 70%, 86%, heck even 96% doesn't mean it's a sure thing. The chart isn't wrong if you're unlucky.
  • These are only the odds for when you have 0 pieces and need 20. If you have 9,000 vouchers, spend 1,000 and don't get any pieces, your odds are no longer 50%, they are now 29.70%. Your past failure does not make future success more likely.
  • These odds are probably not accurate to two decimal points. Remember, they're based on an assumption (that hero pieces are 1/45 odds) and we have no idea how far off that is. It's an approximation, nothing more (Also it demonstrates how stupid you'd have to be to try with 5,000 vouchers)
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