If I'm attacking with 3-7 dice with a lock and focus (actually Saw crew but whatever), how to I calculate the average expected hits+crits? How does a tool like this do it? (and is there an update to that tool for 2nd edition? I'd like to see the simulation with Saw crew instead of a focus token, since it does correctly distinguish crits)

Does it require building a large table with all the possible combinations of the path of rolling, optionally spending a lock, then focusing? Doing it by hand is prohibitively large, and I am a very lazy person. Or is there a clean formulaic way to do it?

As you may have guessed, my math skills in this area are heavily lacking; I'm not formally taught in probability, I've just picked stuff up here and there. I only know how to do some simple probability stuff, such as calculating the odds that you'll roll all blanks or all not blanks on the initial roll, etc. I don't know the right way to handle multiple steps like rerolling only blanks and then focusing, etc. I know the problem is simpler if you treat focuses, hits, and crits as the same thing (since the focus later is a given), so you're only working with the 1/4 chance of blanks per roll and reroll, but I'm uncertain where to go from there with so many dice. Easy with a single die, but not with many.

35 minutes ago, Wazat said:

If I'm attacking with 3-7 dice with a lock and focus (actually Saw crew but whatever), how to I calculate the average expected hits+crits? How does a tool like this do it? (and is there an update to that tool for 2nd edition? I'd like to see the simulation with Saw crew instead of a focus token, since it does correctly distinguish crits)

Does it require building a large table with all the possible combinations of the path of rolling, optionally spending a lock, then focusing? Doing it by hand is prohibitively large, and I am a very lazy person. Or is there a clean formulaic way to do it?

As you may have guessed, my math skills in this area are heavily lacking; I'm not formally taught in probability, I've just picked stuff up here and there. I only know how to do some simple probability stuff, such as calculating the odds that you'll roll all blanks or all not blanks on the initial roll, etc. I don't know the right way to handle multiple steps like rerolling only blanks and then focusing, etc. I know the problem is simpler if you treat focuses, hits, and crits as the same thing (since the focus later is a given), so you're only working with the 1/4 chance of blanks per roll and reroll, but I'm uncertain where to go from there with so many dice. Easy with a single die, but not with many.

So that actually is a 2.0 calculator but it looks like Saw (Crew) is just missing; weird!

Nearest you can get is to set your # of dice, focus, and lock.

Each die has a 75 per cent chance of being a hit or crit with lock focus. If you care about crit rate it's a little more complex.

Assuming that you are always prepared to use Saw, the odds of rolling a crit on a given dice are 3/8 (Crit face + 2 focus faces). Rolling 6 dice with just Saw would yield, on average, 2.25 crits, 2.25 hits, and 1.5 blanks.

If you have a lock as well, you effectively reduce the chance of rolling blanks to 25% of what it would normally be (because if you roll a blank you can re-roll, and you have a 75% chance to land on a hit, crit or focus result). So you'd roll 0.375 blanks on average, 2.8125 hits and 2.8125 crits.

Or, to do it another way: If you're using Saw, your odds of crits and hits are the same (3/8). So if you just take the "expected total hits" from X-Wing Probability Calculator, half of those hits will be normal hits, and the other half will be crits (you'll see that for your setup the average is 5.625, which comes out to 2x2.8125, the same as I got above).

If you want to something like "I'll only use Saw if I have 2 or more focus results" it becomes more complex and you probably want to go into combinatorics stuff. You can do it via the "Giant table" route but that's usually going to be very time-consuming. Khan Academy has some free learning materials on combinatorics and probability if you're keen.

Attack Die

Adding a Focus = 37.5 (3 Hits) + 12.5 (1 Crit) + 25 (2 Eyeballs) = 75% chance of a hit

Defense Die

Adding a Focus = 37.5 (3 Evades) + 25% (2 Eyeballs) = 62.5% chance of an evade

Awesome, thank you!

Just rolling naked red die. there is 1 crit and 7 non-crits. Therefore getting at least 1 crit rolling three red die:

1-(non-crits/total sides of die) to power of #-of-dice-thrown = probability of at least 1 crit

1-(7/8)^3 = 33.01%

Assuming you are always using Saw. The expected crits sides of each die is 3 (one crit and two focus). The number of not crits is 5 (3 hits and 2 blanks). So probability of getting at least one crit with 3 sides of an 8 sided die is:

1 - (not crits)^3

1-(5/8)^3 = 75.6%