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Here is how you really model flurry uptime and why 1-(1-c)^x is only a gross over simplification of what statistics really are.
Let's say that we want to calculate uptime for a fight that will last 10 white swings. If our crit % is 30% that mean that over a long enough period, any 10 swings portion of a fight will have 3 crits, leading to 3 flurry. Sometime less then 3, sometime more then 3, but that's why we take the average.
The best case scneario is that we crit on the first hit, getting flurry for hit 2, 3, 4, then criting again on hit 4, flurry up for 5, 6, 7, crit on 7, flurry up on 8, 9, 10 and our 10 hits are done. Uptime of 100%. That's with 30% crit and this got a very low % of happening. Our worse case scenario is not criting before the 8th hit, then criting on the 9th and 10th hit, flurry uptime of 20% since the last hit is "out of bound". This also got a low chance of happening.
You have to calculate the probability of each and all permutations of 3 crits in a 10 hit period and add the uptime for each value. You will probably need to change the model if you want an "unlimited" fight somehow at the end of the serie. I'm not saying that the 1-(1-c)^x formula cannot be a decent enough estimate but if you want a model that really take into account overlap and give you the real number, you will have to program something like this above in mathlab and add the hundreds of numbers this will give you.
Statistics are alot more complex then what people generally give them credit for.
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