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4/9/2015 7:33:32 PM
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The Statistics behind a Ghallarhorn drop, and where I'm at on the curve

Sooo, I don't have a ghallarhorn. Yep, I'm in that party. Rather than whine about it (oh, I have done my share of complaining), I thought I'd break out some statistics. [b]Assumptions[/b]: RNG is in play and impartial. Perhaps I'm wrong. But that's my assumption. [u][b]Background Numbers[/b][/u] There are currently 17 exotics that can drop as a reward. My drop count is in parenthesis if I've gotten multiples. They are: Hard Light Hawkmoon (2) Mida Multi-Tool Monte Carlo (2) No Land Beyond Red Death (2) SUROS Regime The Last Word (2) Universal Remote (2) Ice Breaker Patience and Time Plan C 4th Horseman Dragon's Breath (3) Ghallarhorn Thunderlord (2) Truth (3) Excluded: Vex Mythoclast, Necrochasm. These are raid specific. Excluded: 247 Vesta Dynasty, Fate of all Fools, Lord of Wolves. These are not available. Excluded: Exotic bounties: Pocket Infinity, Thorn, Bad Juju, Invective, Super Good Advice I currently lack SUROS Regime, 4th Horseman, and Ghallarhorn. I've received (as rewards) 23 exotics. [u][b]The Statistics[/b][/u] If every weapon has the same drop rate, then the chance of receiving a Ghallarhorn as an exotic reward is 1 out of 17, or 1/17 == 0.058824 or 5.8% So, I have a 5% chance of getting a ghorn each time. To put it another way, I have a 94.11% chance of NOT receiving a ghorn each time. To determine the odds of not receiving a ghorn across multiple drops, I multiply the chance by itself each time. So, the odds of not receiving a ghorn in 3 straight exotic drops is 94.11 * 94.11 * 94.11 = 83% The odds are 83% that I will NOT receive a ghorn as the exotic in 3 straight drops. [u][b]Where I'm At[/b][/u] So when I track down the numbers, since I've received 23 exotics so far, that puts me at a 25% chance of not receiving a ghallarhorn even once during those 23 drops. 25%? Is that crazy? Insane? If someone told me, "look beaker, you're going to get 23 exotics, and there's a 1 in 4 chance you won't get a ghallarhorn", would I be upset at this point? Nah. I don't think so. Honestly, I'm not that lucky of a person. To fall in the 25% category really doesn't surprise me. [i]It's a bummer[/i], but it's not that surprising. [u][b]When do I Start Crying Foul?[/b][/u] I think when I get to the 10% point, I'll start belly aching. That's 38 exotic drops. 15 more for me. If, after 15 more exotics I still don't have a ghallarhorn, then I'll probably start complaining that something isn't fair. [u][b]What about you?[/b][/u] So what about you? If you're still lacking that one exotic you'd really like, how many exotics have you received without getting it? Where are you statistically? [u][b]The Raw Numbers[/b][/u] Exotic Drops in a row ==> Probably of Not Getting a your desired exotic even once during that time 0 ==> 100% 1 ==> 94% 2 ==> 89% 3 ==> 83% 4 ==> 78% 5 ==> 74% 6 ==> 70% 7 ==> 65% 8 ==> 62% 9 ==> 58% 10 ==> 55% 11 ==> 51% 12 ==> 48% 13 ==> 45% 14 ==> 43% 15 ==> 40% 16 ==> 38% 17 ==> 36% 18 ==> 34% 19 ==> 32% 20 ==> 30% 21 ==> 28% 22 ==> 26% [b]23 ==> 25%[/b] 24 ==> 23% 25 ==> 22% 26 ==> 21% 27 ==> 19% 28 ==> 18% 29 ==> 17% 30 ==> 16% 31 ==> 15% 32 ==> 14% 33 ==> 14% 34 ==> 13% 35 ==> 12% 36 ==> 11% 37 ==> 11% 38 ==> 10% 39 ==> 9% 40 ==> 9% 41 ==> 8% 42 ==> 8% 43 ==> 7% 44 ==> 7% 45 ==> 7% 46 ==> 6% 47 ==> 6% 48 ==> 5% 49 ==> 5%

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  • Edited by Der Sheff: 4/10/2015 8:12:52 PM
    I like the math, but can say out of experience, it is irrelevant. I have received a minimum of two of every exotic as a drop except Red Death (only one) and Hard Light (never). I am probably pushing 200 opportunities or more between Nightfalls and raid drops. I have four Ghallarhorns, three Crux and three Mythoclast. I have gotten at least six Suros, six Patience and Time and five Dragon's Breath and four Thunderlords. I bought Hard Light off of Xûr, otherwise I still wouldn't have it. Another elusive little bugger is the new raid sparrow. I cannot get one. I haven't checked my hard mode completions in a little while, but it feels like I should have one by now. Anyhow, there are some things that need to be sold by Xür because the game will not yield them for some players.

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