Unless you are Corran or have Gunner, this is better than Markmanship since this + Focus action gives the same results (if you have only 1 attack) for 2 less points.
No, it doesn't. Read the card - it changes one eyeball to a crit. If you roll two eyeballs on that one attack, it's only going to change one of them. So if you roll zero eyeballs, it's going to do nothing. If you roll 2 or more eyeballs, you'll be giving up damage to get that crit. I laid out the odds above - the best it gets is just under 20% of the time for a 2-dice attack.
Oh dear, it seems you've fallen into the number of arrangements trap! What you've calculated is the probability of rolling exactly one focus on one specific die of your two dice.
Flip a coin twice. What's the chance of getting a head and a tail in either order? 50%, because head tail and tail head both count. How many possible results are there for flipping a coin twice? Four, not three. HH, HT, TH, TT.
You've got a 0.25 probability of a focus, and a 0.75 probability of not getting a focus per die. To simply the mathematics we'll treat every side that's not a focus as a Not Focus result (as it doesn't matter what the other result is for the purposes of this).
Possible arrangements for a 2 dice attack?
NN, NF, FN, FF
The probability of two events both occuring is their probabilites put together. Therefore:
NN: 0.75 * 0.75 = 0.5625
NF: 0.25 * 0.75 = 0.1875
FN: 0.75 * 0.25 = 0.1875
NN: 0.25 * 0.25 = 0.0625
To get the probability of a focus you need to add every result that gives a focus up. That means the actual probability of a focus is 0.375, just under 40%. Much more respectable.
For three dice there are three arrangements with a single focus, NNF, NFN and FNN. 3(0.75 * 0.75 * 0.25). This gives a 0.42 probability! The chance of the individual arrangements has gone down but there are now three ways to get a single focus instead of two.
Remember this is still exactly one focus. At least one focus is about 0.58.
Now let's take it up to the HLC.
NNNF, NNFN, NFNN, FNNN. 4(0.75 * 0.75 * 0.75 * 0.25) = 0.42 again.
This is about the maximum. As you get to higher and higher dice and the chances of multiple foci get higher the chance of a single focus goes down. At 5 dice, you're looking at about 0.40, and it's slowly downhill after that. Such an appearance is typical of competing forces: the chance of no focus results goes down as you add more dice but the chance of multiple foci goes up.
You can always check if you've got this right by adding up all your probabilities for all possible arrangements: if you've done it right they'll always come to 1. After all, you've got a 100% chance of getting any result.
Short version, at the number of dice that usually come up your chances of one focus are actually pretty good.
Edited by TIE Pilot