The basic effect of "two-shot": Increase overall damage by 25% by firing 2 shots that each do 62.5%
Thought I'd list some cases where the "two-shot" prefix acts differently:
Shotguns: Does not double pellet count but only adds 1 pellet to the burst.(Theoretically, the effect should be lowering the overall damage). I believe the harpoon gun's flechette rounds work the same way. Disclaimer: I'm having trouble testing the damage because the only TS shotgun I currently have is a TSE and I can't seem to find another explosive combat shotgun or TS shotgun on any of my characters. From tests, my TSE gets very similar numbers to a regular combat shotgun but does slightly more damage due to the additional pellet.
Heavy explosives: Doubles the explosives fired and essentially doubles damage. I believe this is because the damage reduction is applied to the initial impact damage(that I believe only ever does 1 damage) and not the explosion itself. So a MIRV for example will fire two mini-nukes that both split. The listed damage when viewing the TS weapons shows to have about a 126% increase(so total of 226% to be clear). Testing is a bit tough but I generally get at least double damage.
Gamma gun: The ballistic damage is affected the same as most weapons but the radiation damage per shot remains unaffected by legendary prefixes including bloodied and such. In this case, two-shot doubles radiation damage dealt. So with a deep dish, you'll be doing 250 rads per shot. Radium rifles seem to work the same way.
Cryolator: Like the gamma gun, TS seems to only affect ballistic and energy damage so the cryo damage and freezing effect should be doubled.(I don't have a TS flamer but I have a feeling that it may have gotten double damage ever since it was changed from energy to fire damage.)
Laser gun: Still increases overall damage by 25% but I wanted to point out that the beam splitter specifically just does as it is called and divides the damage evenly between each laser. With a two-shot laser, a beam splitter splits the total 125% damage between 6 shots(regular splits between 5).
(if anyone has a TS shotgun/harpoon gun/flamer and would be willing to test out the damage, it would be a great help. For testing, I'd recommend going using things like sneak/headshot if possible because a higher damage would let you see a more noticeable difference. An example would be testing a 20% damage bonus when you're only doing 1 damage/shot. It may still be doing 1 damage, maybe two, but the only observable change is either no change or a double in damage.)
TL;DR Shotguns get an extra pellet to spread, heavy explosives double damage, and only ballistic/energy damage seems to be directly affected by the TS damage reduction so other damage types are doubled.
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