Hello, I am asking for some help from mathwingers. I will give an example of a theoretical situation and asking for the most likely outcome...

here is the challange!!!!

Lets assume.....

Quickdraw uses rage and shoots (in the activation phase) a dengar, with lone wolf, who has moved and took a focus.

Then in the combat phase, dengar uses Gliterstim and Countermeasures.

Quickdraw shoots again still has rage, possible focus.

howlrunner with crack and a focus also shoots dengar,

and 3 Black cracks with focus in range of howlrunner also shoots dengar.

How much damage will dengar take on average at range 2? range 3?

Can anyone solve?

Probably not a lot! (he's not going to use focus when he's planning to pop glitterstim, by the way?)

Quickdraw's initial shot into Dengar should put just under damage onto him (1.75) on average, when all he's got to draw on is Lone Wolf.

Once he's popped all his defensive tricks, you're looking at getting maybe one extra hit through, for a total of 2 3/4 damage.

Howlrunner and the Crack Swarm will not do too much - about 0.4 damage for howlrunner and 0.5 for the black squadron pilots for another 2.4 damage total.

That's a net impact of just over 5 damage - or enough to blow out Dengar's shields. That's assuming range 2, and that Dengar's own shots with Glitterstim and/or target lock don't kill anyone (or at least that he finishes quickdraw off after her second shot) or that he didn't use his action to barrel roll out of someone's line of sight.

http://xwingcalculator.x10host.com/diceuilm.html

It's dangerous to go alone, take this!

You should skill instead it's much more satisfying.

Okay, the inclusion of glitterstim makes this easier to calculate since it’s just the sum of each expected damage. QD has essentially 3TL+F vs. 3F w/ LW. From the X wing calculator, that comes out to be .57 damage. But it’s important to know where that comes from. The probability to roll 3 hits from QD is (15/16)^3 = 82.4% (the 15/16 comes from the combination of TL+F, each die has a 6/8 chance of rolling a hit/crit/focus, and the 2/8 that roll blank have a 6/8 chance of rerolling into hit/crit/focus, for an overall chance of 15/16). QD’s chance for 2 hits = (15/16)^2 * (1/16)^1 * 3 = 16.5% (Two dice end with a positive result, and one with a negative result. There are 3 ways for this to occur: Die 1 is negative, die 2 is negative, die 3 is negative). QD 1 hit = (15/16)^1 * (1/16)^2 * 3 = 1.1%, and QD 0 hit = .02%.

So with those chances established, they have to be compared against Dengar’s chance for getting however many evades. 3 evades can be achieved by natural rolls, or 2 + reroll. (5/8)^3 + (5/8)^2*(3/8)^1*3*(5/8) = 51.9% (5/8 chance of rolling evade/focus on each die, and if you roll 2, then you have a chance with LW to roll a 3 ^rd ). 2 evades can be achieved by 2 + failed reroll or 1 + successful reroll = (5/8)^2*(3/8)^1*3*(3/8) + (5/8)^1*(3/8)^2*3*(5/8) = 33%. 1 Evade can be achieved by 1 w/ failed reroll, or 0 w/ successful reroll = (5/8)^1*(3/8)^2*3*(3/8) + (3/8)^3*(5/8) = 13.2%. Finally, 0 evades = 0 successful with failed reroll = (3/8)^3*(3/8) = 2%.

Finally, you have to compare hit results vs. evade results to determine probability of damage. 3 damage can be achieved only via 3 hits and 0 evades = 82.4% * 2% = 1.6%, 2 damage can be from 3 hits/1evade + 2hits/0evade = 11.2%, 1 damage via 3hit/2evade + 2hit/1evade + 1hit/0evade = 29.4%, and 0 damage for all of the remaining, 57.8%. And then expected damage has to include the quantity of damage, so 3 damage * 1.6% + 2 damage * 11.2% + 1 damage * 29.4% = .566 expected damage, which aligns with the x wing calculator!

So, that QD’s expected damage, I’m not going to go through all of the math for the remaining attacks, and just use the calculator, keep in mind that with Crackshot, it becomes 2 hit vs. 2 evade = 1 damage, that’s the only special part of it.

Range 2:

QD = .566

QD#2 (w/o F, 68%) = .350

QD#2 (w/ F, 32%) = .566

HR = .654

Black = .787

Total = .566 + .350*.68 + .566*.32 + .654 + .787 *3 = 4.00 damage

At Range 3:

QD = .302

QD#2 (w/o F, 68%) = .181

QD#2 (w/ F, 32%) = .302

HR = .473

Black = .572

Total = .302 + .181*.68 + .302*.32 + .473 + .572 * 3 = 2.710 damage