1/8 * 1/6 * 2/153760 is indeed 1/3690240 (typed 2 instead of 1 and didn't re-check)... And also forgot about the double dipping thing yeah.
Your chance for getting either the Dex, Int or Str version is off though, it's simply 3x the chance to get one specific type (as the chance to get each one is of equal probability). Same thing as when you calculate the chance to get a 1, 2 or 3 on a 6-sided die (3x the individual probability).
But yes, the chance to get that perfect item with very specific affixes is outrageously small. Don't forget though that with several million players, even if each is only crafting one item once, it is expected that -some- people will end up with that perfect item. Just don't expect it to be you.
You also have to remember that we assumed here that your primary stat and MF are the optimal affixes to have, but if Blizzard balances correctly then it should be very, very difficult to determine the actual "best" stat, as these things might vary with for example crit chance (and the fact that survivability is much harder to measure than raw DPS). Don't forget that for example Str adds armour, so it might not give as much +DPS as say a pure DPS affix like +crit chance.
- 2/10/2012 11:24:05 AM Posted in: Theorycrafting and Analysis
2/10/2012 10:15:00 AM
You are almost correct in your calculations (under the assumptions that you have stated, which seem reasonable enough to me).Posted in: Theorycrafting and Analysis
First of all, the range 25-32 includes 8 integer values, not 7. You made the same error with the range 12-17, which includes 6 values. You did it correctly for the ranges 1-8 Dex and 5-9% MF, which include 8 and 5 different values respectively. This is assuming that the range is a closed interval (includes the endpoints noted), but if it is an open interval then your amount of Dex and MF values is wrong.
Furthermore, when you do the calculation for the chance to get the optimal range if you have 2 random properties you forgot about combinatorics. The chance that you get both of the desired properties (+Dex or +MF in your case) does not depend on the order in which those properties occur. An item with +8 Dex and +9% MF is just as valuable to you as an item with +9% MF and +8 Dex (other order of properties, same values). This means that the chance to get the desired combination of properties is doubled.
1/62 * 1/8 (chance to get +Dex and +8 out of 1-8 for the first property) * (and) 1/62 * 1/5 (chance to get +MF and +9% for the second property)
1/62 * 1/5 (chance to get +9% MF for the first property) * (and) 1/62 * 1/8 (chance to get +8 Dex for the second property)
This means that in the end your chance for getting the optimal armour becomes:
1/8 * 1/6 * ((1/62 * 1/8 * 1/62 * 1/5) + (1/62 * 1/8 * 1/62 * 1/5)) = 1/8 * 1/6 * 2/153760 = 2/3690240 = 1/1845120
So about 1 in 2 million. Not as bad as what you calculated, but still a hell of a lot of crafting... Take note though that the probability that you craft a "valuable" perfect item is way more than that, because you might also play other classes or like different affixes other than MF.
2/5/2012 8:08:55 AM
Good luck to everybody who entered!Posted in: Diablo III General Discussion
Really hoping that Blizzard also sends some invites to the EU as well, cause me and my friends are all dying to try out D3.
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