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People have gone thousands of tours without a pan (the person with the most tours, 3600+ has yet to drop a golden pan), where people have gotten a pan within their first few tours.
Australiums are far more common, but still rare, some people have gone a few hundred tours without an Australium drop (I have 90 overall completed tours, zero Australium drops), where I've seen people get an Australium on their first tour. It's also worth noting that you can't get Australiums or pans in Oil Spill.
Blood/Gold/Diamond botkillers have a chance to be dropped instead of their common counterpart (Rust/Silver/Carbonado, respectively). It is possible to get a Blood/Gold/Diamond and an Australium (and possibly a Pan) in the same tour, and it is possible to get a Pan multiple times (so far, at least two people have gotten two Pans).
Its been 4 years since that.
1 in 4000 or 0.025% chance for a Golden Frying Pan
Maths is hard :(
Ya its ♥♥♥♥♥♥♥♥ cause its not confirm. But you'll never know the Australium drop rate cause TF2 devs haven't released what it is and never will.
But mathematically speaking and after a couple months of research thats the closet percentage to a Australium drop and Golden Pan drop.
You don't need to believe it, but if you want an ideal percentage in the back of your head of an Aussie / Pan drop rate, well thats the best result you'll get.
3% is just out of nowhere, not really trustworthy source. Numbers of aussies dropped from bp.tf but they're outdated.
Maybe you'll be so good as to share your maths and research with us. I mean let's completely forget that - if there is a 'rate' at all - it's in no way 0.5% and just focus in on your numbers here.