McMillan TAC-50 – ★★★★★ Rifle
Welp this is it. The big mamma of all bamboo rifles. I was trying very hard to make a Canadian joke except she beat me to the punch on all of them. She is OFFENSIVELY Canadian (despite being a US product, the rifle is more famous for Canadian use).
As far as Bamboo rifles go, she is THE big stick, delivering sweet, maple syrup flavoured death to all comers. Initial startup similar to small bamboo, but with damage equivalent to multiple big bamboo rifles combined when used properly. Don't let the lower multiplier fool you - what sets her apart is the fact she can crit. This is massive, as it opens up extra layers of multipliers simply not available to any other bamboo rifle. How much damage? Well on KR, with her full posse and a maxed out command fairy, she can spike vs 320k HP bosses, so yeah.
An (kind of) unfortunate trait is that due to her funny timings, it is not possible to efficiently use her with other bamboo rifles, as she has different aim times from any other one (she's faster than small bamboos).
Yes bamboo is niche, but if you really cbf to "fight" a boss and would rather just skip the fact they exist, here you go.
Nothing much I want to say, but here are some numbers while using her with Px4.
Each shot of Tac-50's skill has an independent chance of critting. If your crit rate is not 100%, there is a definite chance for some of the 5 hits of a 5 linked Tac-50 to not crit.
This is more obvious when using Px4, and getting multiple stacks of Px4 buffs. Each stack of Px4 buff reduces the crit rate and increases the chance for this effect.
Px4 not critting one of her 3 skill shots. Note to self that it really doesn't appear that much with 88% crit rate, so next time maybe use a crap crit scope or none.
With the crit rate of X, the chance get at least Y crits in 5 rolls = (5 choose Y) * X^Y + (1-X)^(5-Y) + chance to get at least Y+1 crits in 5 rolls
|Y||5 choose Y|
Credits to corsage#0001 (discord) for showing me that my maths is actually terrible.
Without Px4, with Command Fairy, your crit damage multiplier is 1.75*1.36, which is 2.38x
At 1 stacks, your crit rate is 70.40%
Chance to get at least 5 crits = 1 * 0.7040^5 * 0.296^0 = 0.1729, or 17.29%
Chance to get at least 4 crits = [5 * 0.7040^4 * 0.296^1] + 0.1729 = 0.5365 or 53.65%
Chance to get at least 3 crits = [10 * 0.7040^3 * 0.296^2] + 0.5365 = 0.8422 or 84.22%
Chance to get at least 2 crits = [10 * 0.7040^2 * 0.296^3] + 0.8422 = 0.9707 or 97.07%
Chance to get at least 1 crits = [5 * 0.7040^1 * 0.296^4] + 0.9707 = 0.9977 or 99.77%
Chance to get at least 0 crits = [1 * 0.7040^0 * 0.296^5] + 0.9977 = 0.9999 or basically 100%
Each crit gives you a crit damage multiplier of 3.57. (Each non-crit gives you a crit damage multiplier of 1x)
With 1 stack and 5 crits, your total crit damage multiplier is 3.57*5, or 17.85.
At 2 stacks, your crit rate is 56.32%
Chance to get at least 5 crits = 1 * 0.5632^5 * 0.4368^0 = 0.0567, or 5.67%
Chance to get at least 4 crits = [5 * 0.5632^4 * 0.4368^1] + 0.0567 = 0.2764 or 27.64%
Chance to get at least 3 crits = [10 * 0.5632^3 * 0.4368^2] + 0.2764 = 0.6172 or 61.72%
Each crit gives you a crit damage multiplier of 5.355x.
With 2 stacks and 5 crits, your total crit damage multiplier is 5.355*5, or 26.775.
At 3 stacks, your crit rate is 45.05%
Chance to get at least 5 crits = 1 * 0.4505^5 * 0.5495^0 = 0.0186, or 1.86%
Chance to get at least 4 crits = [5 * 0.4505^4 * 0.5495^1] + 0.0186 = 0.1318 or 13.18%
Chance to get at least 3 crits = [10 * 0.4505^3 * 0.5495^2] + 0.1318 = 0.4079 or 40.79%
Each crit with 3 stacks gives you 8.0325 crit damage multiplier.
With 3 stacks and 5 crits, your total crit damage multiplier is 8.0325*5, or 40.1625.
Now that that's established....
At 3 crits with 2 stacks, your crit damage mult is 18.065, which is higher than 5 crits of 1 stack, but you have a 60% chance of activating 3 crits with 2 stacks of Px4's buff, instead of 17% to get 5 crits with 1 stack.
At 3 crits with 3 stacks, your crit damage mult is 26.0975, which is slightly lower than 5 crits of 2 stacks. However, you have a 40% chance of activating 3 crits with 3 stacks of Px4's buff instead of 5% chance to get 5 crits with 2 stacks.
This means that, for the sake of less rerolls for a higher final crit damage, it is better to try to get more stacks of Px4 buffs. Unfortunately, it is also exponentially harder to get 3 stacks over 2, while not losing on other tile stacks you may perform, such as K5 or possibly Howa64 if you're stupid.
In the end, though, you should make your own decision on how many stacks you want to go with.
I might make a total damage potential of Px4 calculation but I lost my notes so I'll redo them later.