imping rare and probability math

[joedobo 1,187]

Based on the following, I would need to plan to do around 4000 improves to make my still rare with improvement?  First, it could happen much sooner than this, but I like to have an estimate of worst case. Second, I'm ignoring the bit about imp failures canceling the roll. I plan to improve very low ql things with 90s skill and high QL tools, so my failure chance is low.

 

• There is a 1:3600 chance each second to make a rare widow. In rare window chance: 1/3600 or 0.0278%
• In rare window chance for each roll/improve made. 100% - (100% - 0.0278%) ^30 = 0.8300%, where 30 is the lesser of improve action staggered attempt time or the rarity window length.
• Improve chance is 20%
• Rare + chance for each rarity roll. 100% - (100% - 0.0103%) * (100% - 4%) * (100% - 50%) = 52.0049%. This is for premium and it is 50.5% for F2P.
• Rare + chance for each improve done. rare+ 52.0049% * in rare window 0.83% * improve chance 20% = 0.0863%

Zero rare + items made in 3469 attempts would be the %5 confidence to reject.
Zero rare + items made in 5332 attempts would be the %1 confidence to reject.
(100% - 0.000863) ^x = 0.01
LOG 0. 01^-1 / LOG (100% - 0.000863) ^-1 = x

 

The math and model for this is based on a post by Lethyria here: https://forum.wurmonline.com/index.php?/topic/192530-testing-spamming-creation-for-items-of-rarity/&do=findComment&comment=1922922

[rangerklypf 140]

guess that makes rares pretty rare huh?  what's the math for probability you'll imp it fantastic?

[joedobo 1,187]

I'm most interested in confirmation if my math and model is right.

Although, I think blue (rare) items are easy to make most of the time. 4k improves is doable. I made 15k butcher knife blades to get a supreme. 

 

With a fantastic you'd replace that 52.0049% number with 0.0103%. It is basically impossible and not worth spending the time to do that math from my perspective.

Edited March 22, 2023 by joedobo