Post by @SnoopJ@hachyderm.io

2026-09-29 00:29 UTC

@ifixcoinops@retro.social assuming an infinite supply of jellybeans and uniform probability of any given flavor (and that the machine spits out the same number every time because fuck modeling that), the chance of drawing the same combination of m flavors in a single pull is 1/49^m (i.e. 49^m combinations, only one of which is *your* combination) So the probability of *not* getting the same combination is 1-that, and across k trials, that's (1-1/49^m)^k for the probability that you haven't drawn, which is just kinda an easier thing to work with here. EDIT: this calculation is missing the nCr factor and my estimate is excessively pessimistic, see: https://infosec.exchange/@whbboyd/117351781880656742 for m=5, after k=3 million pulls, you have about a 1% chance of having pulled the same combination. after k≈640 million pulls, you have about a 90% chance, and after k≈1.3 billion pulls you have about a 99% chance. so, let's be safe and say around £65 million. for bonus marks, the total number of flavor combinations is (49!)/(49-m)!, which for m=5 is 228,826,080 combinations. Assuming it took you the full 1.3 billion pulls, you would see repeated flavors after a bit less than 1/10th of the way into the process.

Replies (2)

@whbboyd@infosec.exchange 2026-09-29 01:41

@SnoopJ@hachyderm.io @ifixcoinops@retro.social I think the problem here is that 49^m will give you the number of combinations *including order*. I'm sure *someone* will claim to have a sufficiently discriminating palate to distinguish two Basil Pesto and three Tiramisu [1] from three Tiramisu and two Basil Pesto, but I sure can't. I think you want to divide out by m factorial here to cancel the different orderings. Given that, for m=5, you're at 1% with roughly k=24 thousand pulls; for 50% you need 1.64 million, and for 99% you need 11 million. £110 thousand. I think you need to make the same correction for total combinations, too, which makes the formula that of the binomial coefficient [2] (pronounced "49 choose m" and typeset too complicatedly to toot). 49 choose 5 is 1,906,884. Fedi Never Disappointing awaaaaaaay! [1] I have absolutely no idea what flavors Jelly Belly makes, in case you couldn't tell. [2] https://en.wikipedia.org/wiki/Binomial_coefficient

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@ifixcoinops@retro.social 2026-09-29 00:30

@SnoopJ@hachyderm.io Fedi Never Disappoints

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