I use this to practice. I’m not sure if the probabilities have been confirmed. Below, whenever I say “1/2” you should interpret it as “less than 1/2, because of a chance that you get a boon that has nothing to do with your gum.” Using more gums makes this “1/2” more like 1/2 and less like 1/3.
Vansten’s method has a little less than 1/2 chance to get damage, 1/2 chance to get AoE, longevity is basically guaranteed, so you’ll try on average 4-6 times to succeed 1 time.
Orrian’s method of damage and dura first and using a transmute to guarantee the AoE means you try 2+ times (mainly on the damage step, and I assume 2 effect gums, boons, VC, 3 long gums, boons, VC) to succeed 1 time. But you spend vigour and coin and a forge slot on transmute half of the time, adding about 500c to your average hammer cost for the transmute, and more if the vigour cost requires more pastes to be used.
Cuetzpalo’s method of 1 gum Special, 2 gums Effect is interesting. Roughly 1/2-1/3 the time you succeed to find AoE, but then since you leave the special gum in, roughly 1/3 the time you succeed to find Damage. If you succeed 1/6-1/9 of the time, you have to try about 6-9 times to have a success. In the video they have 4 decon resin remaining, which means they used 7 and tried 8 times for 1 success.
The chance to fail N times in a row is (failure rate)^N. Sometimes things with 5-10% chance happen.
Vansten: (4/5)^10 ~ 10%, (4/5)^13 ~ 5%. So some of the time you’ll get 10 or 13 failures in a row.
Orrian: (1/2)^N: 3-4 failures in a row. (1/3)^N: 5-7 failures in a row.
Cuetzpalomitl: (7/8)^N: 17-22 failures in a row have a 5-10% chance of happening. RNG is not their friend ho ho ho.
Damage and Effect Adjacent is 42% each and Longevity is not guaranteed, you have a 70% chance of getting it with two gums. That makes it 0.42 * 0.42 * 0.7 = 0.12348 which is about 1 in 8 tries. That does not include the chances to fail after the initial selection process which makes it even less than 1 in 10 depending on your technique. Using protection and fate pastes until all vigor is gone makes it 1 in 13. I have gone over 30 failures in a row before on multiple occasions.
Put 3 gums on Long because you don’t want to fail after getting the .42*.42 Dmg + AoE.
I did caveat that the forge simulator numbers aren’t confirmed(?) and that my provided estimates were generous. Mainly I wanted to provide some intuition for the differences between some different methods
The simulator numbers are calculated by assigning a weighted value to each boon available. They all start with 1 and each gum adds 10 to each boon depending on the gum type used. In the case of longevity the gum only affects durability so two gums makes its weight 21 while the other nine boons are 1 each making the odds 21 / 30 or 0.7. Three gums would make it 31 / 40 or 0.775 which is certainly an increase but by no means a guarantee.
I do take your point about comparing the different methods though, I haven’t even tried using a boon transmute so I have something to look forward to next time I hit the forge.
