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the drop rate is estimated between 1 and 5%, but no one actually knows
So far, of 278 players completing a tour, 62 have received a third item, of which 4 were australium. That's an observed third item chance of 22.3%, and an observed australium chance of 1.4%.
For the australium chance, using a Wilson score 99% confidence interval, range is 0.4% to 4.7%. I'll feel pretty good about my sample representing the population around n=800.
I haven't seen any evidence that drops are weighted to lower tour counts: for any particular tour count X that received a third drop/aussie drop, the count of players receiving third drops/aussies with tour <= X divided by the count of all players receiving third drops/aussies is basically equal to the count of tour-completing players with tour <= X divided by the count of all players completing tours.
Before starting this, my guess was that third drop chance was 1/5 and aussie chance was 1/100. Now I'd only say third drop is 20-25% and aussie is 1-2%.
At 2% chance for aussie, that's 35 tours to complete before you're at 50-50 odds of having gotten one. If it's 1% chance, it's closer to 70 tours. For Two Cities, $140 on tickets best case, maybe more like $280. To be just barely-more-likely-than-not to find an australium, any australium, let alone the one you want.
Extend even your 1/10 better case unlucky streak, which isn't exactly out of this world unusual, to aussies, and that's 113 tours or $452 without australium. At 2%. If aussie is 1%, it's a 229 no-aussie streak at $916.
Anyway kids, don't gamble, and certainly not on MvM. Get your australium from the market place, or better yet, remember that cosmetics are for casuals.
Interesting. I wonder if my numbers will converge as I approach n=800, or if backpack.tf users are a skewed vs. the overall MvM population. A TF2 player can have a public inventory, but if they haven't ever used backpack.tf, then their inventory statistics would not be included, correct?