Pretty sure I learned how to do these in high school, but I have since forgotten. It has been a while. Some helpful formulas and/or explanations for how to solve these would be much appreciated.

Questions:

1. If I roll 2/3/4 dice, what's the likelihood I'll get 1/2/3/4 hits/evades?

2. If I roll 1/2/3 dice, would it be better for me to take a target lock or a focus?

3. [Han Solo] If I roll 3 dice and get only 1 hit, should I reroll the dice?

4. How long is Chewbacca going to last assuming that my opponent has 2/3/4 attackers that can roll 2/3 attack dice each per turn? (So, ignore crits) - Assume Range 2 for simplicity. Also, assume naked Chewbacca without MF title, Lone Wolf, or C-3PO.

Let's assume crit = hit for sake of ease.

a red dice has 8 faces: 4 crit/hits, 2 focuses, 2 blank.

meaning: an unfocused red dice hits 4/8s of the time (1/2).

a focused red dice hits 6/8s of the time.

a green dice has 8 faces: 3 evades, 2 focuses, 3 blanks.

If I roll 3 Focused red dice, the number of hits i will generate on average is: number of dice x chance of hitting

3 x 3/4 = 9/4 = 2.25 hits. In people speak, this means you're most likely to hit twice.

Exactly how to calculate what your chances are of hitting exactly twice with 3 focused dice is beyond my statistics...

--

TL vs F: literally the same

F: # of dice x chance to hit (3/4)

TL: # of dice x chance to hit (2/4) + total remaining possibility of misses x chance to hit again on reroll (1/2)

2 dice F: 2 x 3/4 = 6/4 = 1.5

2 dice TL: 2 x 2/4 = 1 + (2-1) x 2/4 = 1.5on your first roll, you will average 1.0 hit total, and have 1.0 dice to reroll, thus you then calculate the chance of hitting again for 1.0 dice.

(2-1) means, your greatest chances of hitting are 2 hits.

same

3 dice F: 3 x 3/4 = 9/4 = 2.25

3 dice TL: 3 x 2/4 = 6/4 = 1.5 + (3-1.5) x 2/4 = 1.5 + 0.75 = 2.25

same

4 dice F: 4 x 3/4 = 3

4 dice TL: 4 x 2/4 = 2 + 2 x 2/4 = 2 + 1 = 3.

same.

1. Here's how I think about dice:

One attack die has 8 outcomes:

.CHHHffxx
.11110000

.CHHHffxx
C22221111
H22221111
H22221111
H22221111
f11110000
f11110000
x11110000
x11110000

.CHHHffxx
C22222211
H22222211
H22222211
H22222211
f22222211
f22222211
x11111100
x11111100

2. Target lock and focus both have a 50% chance to take a non-damaging result and turn it into a damaging one. The better move is entirely dependent on if you're going to be able to use a focus defensively or if you'd rather potentially have a TL next turn.

3. Probably. Expected hits is 1.5 on three dice, so you're below average. Unless you're shooting at a decimator with only one hull left.

4. Expected damage is 0.5 per die (0.75 if focused). Assuming Chewie, MF title, and C3P0, you're looking at 13/8ths of an evade per turn, plus 3/8ths per shot. Ex:

3 shooters, 3 dice, all with focus.

3 * 3 * 0.75 - 11/8 - (3*3/8) = 6.75 - 20/8 = 4.25 damage per round.

A note is that lets say you have 3 dice TL...

you roll 2 hits. and now ask whether you should use the TL. That TL literally just has a 1/2 chance of rerolling the last dice into a hit. So here you have 50% chance of getting 1 more hit.

Han Solo Q: YES. Reroll it.

3 unfocused dice: 3 x 1/2 = 1.5. Average dice roll is more than 1.

---

Chewbacca Q:

You can get an answer for this, but depending on the arc dodging and range, the real life result can be wildly different.

Assume 4 ties vs naked Chewbacca.

If we assume each tie will always have a shot.

All ships are R2 (This usually isnt true). Also ties will get many more dice when they are R1. Although they are prone to being 1 shot.

Nvm, too hard for me. haha.

a simplified answer is possible. but not that useful =)

very interesting, I’ve done this before for the other games I play, but never really put some time to apply it on X-Wing dice, please don’t judge me (too hard) but I just realized that rolling 1 red dice against 1 green, the red has the statistic advantage

Pretty sure I learned how to do these in high school, but I have since forgotten. It has been a while. Some helpful formulas and/or explanations for how to solve these would be much appreciated.

Questions:

1. If I roll 2/3/4 dice, what's the likelihood I'll get 1/2/3/4 hits/evades?

2. If I roll 1/2/3 dice, would it be better for me to take a target lock or a focus?

3. [Han Solo] If I roll 3 dice and get only 1 hit, should I reroll the dice?

4. How long is Chewbacca going to last assuming that my opponent has 2/3/4 attackers that can roll 2/3 attack dice each per turn? (So, ignore crits) - Assume Range 2 for simplicity. Also, assume naked Chewbacca without MF title, Lone Wolf, or C-3PO.

Each time you're talking about rolling X dice in this game, the denominator is going to be 8^x. This does include re-rolls.

The way that I do it, rather than with a pure brute-force, is to make a list of each distinct combination, and also count how likely each one is, multiplied by the different ways I can re-arrange the result.

Example: on no 1. If you roll 4 dice, that is the possibility of EEEE, EEEF, EEEB, EEFF, EEFB, EEBB, EFFF, EFFB, EFBB, EBBB, FFFF, FFFB, FFBB, FBBB, BBBB. The odds of rolling an Evade on one die is 3/8. The odds of rolling 4 evades on 4 dice is (3*3*3*3 for the results and *1 for the possible arrangements)/8⁴, whereas the odds of rolling two evades and two focii are 3*3*2*2 for the results and *6 for the possible arrangements)/8⁴. Et cetera, &c. &c.

For no 2, let's actually break down the differences between the actions.

Focus allows you to alter your odds on each distinct die to go from 4 sides of Damage and 4 sides of No-Damage to 6 sides of damage.

Target lock splits the 4 sides of No-Damage in half, each having an equal chance of Damgage and No-Damage. ¹/₂ of 4 is 2, so in the simplest form, this is also 6 sides of expected damage.

However, TL has a higher variance. You could always re-roll into 0 damage, re-roll into Crits, and re-roll into more damage than expected. It is also better if your dice came up Blank rather than Eyeball, but worse if they came up Eyeball.

So: Expected damage between the two is actually equivalent, and each comes with tertiary benefits (Being able to be used defensively, vs being able to retain the action for a subsequent round).

For no 3, we're looking at that expected damage again.

The median result for attacking with 3 dice, unaltered, is going to be 1 or 2 damage rolled (a 1.5, if going indiscrete).

Han is as likely to come into 1 damage as he is at 2 if he re-rolls. Starting at 1 damage, that becomes a 50% chance of improvement (into 2 or 3 damage), with only a 12.5% chance of worsening into 0 damage.

Do the bloody re-roll.

For no 4, this is incredibly complicated. The "Assumptions" you've listed help a good deal, though.

This is a theoretical Chewbacca, so incoming Crits don't differ from incoming Hits.

However, we also don't know the Action Economy or maneuverability of the ships in question. Chewbacca evades all attacks from a ship that can't shoot at him, after all.

MajorJuggler's version of MathWing really shines here. What he does is simply calculate the Jousting value of each ship (his term), and includes variables for maneuverability and other things.

However, even though his scripts are constantly evolving, he is still forced to make assumptions, as sheer statistics cannot fully model gameplay. Yet.

Here is the dumbed down overly simplistic rules that I keep in mind while playing (using only the average hit, very basic math):

Attack dice:

Average unmodified hit: 0.5

Average hit with a focus or target lock : 0.75

Average hit with a focus and target lock : 0.94 (15/16)

So let's say you roll 3 attack dice:

Average unmodified : 1.5

Average with focus or target lock : 2.25

Average with focus and target lock : 2.81

If you have an effect like predator instead of a target lock, instead of scrambling your brain to see the average, just put in somewhere in between those lines. For example, 3 attack dice with a focus and predator falls between 2.25 and 2.81 average hits. If you want to know the average hits if you want to keep that focus to activate Rexler's ability, you know his attack would be between 1.5 and 2.25 hits (so in short, not a whole lot).

Defense dice:

Average unmodified: 3/8

Average with a focus : 5/8

Evade token: increase average by 1

So let's say 3 defense dice (tie fighter):

Average unmodified : 1.125 (9/8)

Average with focus : 1.875 (15/8)

Average unmodified with evade token : 2.125

Average with focus and evade token : 2.875

So if you make a scenario, let's say Dark Curse with stealth device and an evade token following Boba Fett. How do you find out whether to take a focus or evade as Boba Fett?

Dark Curse's average attack : 1 hit

Dark Curse's average defense : 2.25

Boba Fett's attack (cannot be modified because of Dark Curse's ability) : 1.5

Boba Fett's defense with focus : 1.25

Boba Fett's defense with evade token : 1.75

So in this case, Boba probably won't hurt Dark Curse, but if he keeps using an evade token each turn, Dark Curse probably won't hurt him either. Keep using evades until you find a good opportunity to arc dodge and then get back on Dark Curse's back

Here is the dumbed down overly simplistic rules that I keep in mind while playing (using only the average hit, very basic math):

Attack dice:

Average hit with a focus and target lock : 0.94 (15/16)

Actually, the odds of missing with F+TL is equivalent to rolling two whiffs with two dice, or 9/64. The obverse (to hit) is only 55/64.

That's appx 86% to hit, not 94%.

Here is the dumbed down overly simplistic rules that I keep in mind while playing (using only the average hit, very basic math):

Attack dice:

Average hit with a focus and target lock : 0.94 (15/16)

Actually, the odds of missing with F+TL is equivalent to rolling two whiffs with two dice, or 9/64. The obverse (to hit) is only 55/64.

That's appx 86% to hit, not 94%.

Are you sure? I take for granted that both target lock and focus are used in that scenario (with the target lock being used to reroll blanks only and the focus used afterwards). So the odds having blanks is 2/8 and having it twice are 4/64 (or 1/16).

Here is the dumbed down overly simplistic rules that I keep in mind while playing (using only the average hit, very basic math):

Attack dice:

Average hit with a focus and target lock : 0.94 (15/16)

Actually, the odds of missing with F+TL is equivalent to rolling two whiffs with two dice, or 9/64. The obverse (to hit) is only 55/64.

That's appx 86% to hit, not 94%.

Are you sure? I take for granted that both target lock and focus are used in that scenario (with the target lock being used to reroll blanks only and the focus used afterwards). So the odds having blanks is 2/8 and having it twice are 4/64 (or 1/16).

There are 3 blanks on a green die, not 2.

I am an idiot.

Here is the dumbed down overly simplistic rules that I keep in mind while playing (using only the average hit, very basic math):

Attack dice:

Average hit with a focus and target lock : 0.94 (15/16)

Actually, the odds of missing with F+TL is equivalent to rolling two whiffs with two dice, or 9/64. The obverse (to hit) is only 55/64.

That's appx 86% to hit, not 94%.

Draco, you might want to recheck math.

If you have a focus, you have a 75% to hit. Which means that 25% of the time, you will spend your TL, and will then have a 75% chance to hit. The end result, .75 + .25*.75 = .9375 = 93.75% = 15/16.

I think you're confusing the evade dice with the attack dice. The chance of not rolling a blank with a RR + F (for example, LW on a stressed Ibby w/ a Focus token or Flight Instructor) = 5/8 chance of not needing to reroll + 3/8 chance to need the reroll * 5/8 chance of getting something good = .859375 = 55/64... Which means the chance of flubbing is 1-55/64 = 9/64. This could also be calculated as the chance of rolling two blanks (3/8)^2 = 9/64.

Edit: And go go coming home from work and not realizing that you already fixed your mistake

Google dice calculator. Pick the Casio link. Profit?

The calculations get very dicey (har har har) once you start making decisions (han reroll, etc). As there really aren't that many outcomes, it is actually easier to enumerate all possible outcomes. You can use excel if you're crafty, I use matlab

Or, like MajorJuggler, you can write your own scripts

Oh, the one notion that you lear in statistics that's worth remembering: past results mean absolutely nothing when calculating current odds. This means that:

1) The odds of rolling 3 blanks are rare.

2) The odds of rolling 3 blanks twice in a row are rarer still (roll + reroll with a target lock).

3) The odds of re-rolling 3 blanks after having just rolled 3 blanks... are exactly the same as number 1. Dices really don't care whether you rolled well or not 2 minutes ago ^{(unless you belong to a religion that believes in dice gods... in which case, I'll walk away slowly now)}

^{(unless you belong to a religion that believes in dice gods... in which case, I'll walk away slowly now)}

DICE FOR THE DICE GOD

Here is the dumbed down overly simplistic rules that I keep in mind while playing (using only the average hit, very basic math):

Attack dice:

Average unmodified hit: 0.5

Average hit with a focus or target lock : 0.75

Average hit with a focus and target lock : 0.94 (15/16)

So let's say you roll 3 attack dice:

Average unmodified : 1.5

Average with focus or target lock : 2.25

Average with focus and target lock : 2.81

If you have an effect like predator instead of a target lock, instead of scrambling your brain to see the average, just put in somewhere in between those lines. For example, 3 attack dice with a focus and predator falls between 2.25 and 2.81 average hits. If you want to know the average hits if you want to keep that focus to activate Rexler's ability, you know his attack would be between 1.5 and 2.25 hits (so in short, not a whole lot).

Defense dice:

Average unmodified: 3/8

Average with a focus : 5/8

Evade token: increase average by 1

So let's say 3 defense dice (tie fighter):

Average unmodified : 1.125 (9/8)

Average with focus : 1.875 (15/8)

Average unmodified with evade token : 2.125

Average with focus and evade token : 2.875

So if you make a scenario, let's say Dark Curse with stealth device and an evade token following Boba Fett. How do you find out whether to take a focus or evade as Boba Fett?

Dark Curse's average attack : 1 hit

Dark Curse's average defense : 2.25

Boba Fett's attack (cannot be modified because of Dark Curse's ability) : 1.5

Boba Fett's defense with focus : 1.25

Boba Fett's defense with evade token : 1.75

So in this case, Boba probably won't hurt Dark Curse, but if he keeps using an evade token each turn, Dark Curse probably won't hurt him either. Keep using evades until you find a good opportunity to arc dodge and then get back on Dark Curse's back

Thanks.

How would I go about calculating the average # of hits/evades with the following abilities in play?

Single terols simply mean you add 1 x chance of hitting if your miss total is more than 1.

Ex for 3 unfocused dice

3 x 1/2 = 1.5 + 1 x 1/2 = 2

This makes sense as 3 dice TL is equal to 2.25

You can do the same for evade dice

Defense dice with auto is pretty simple too. Calculate as normal. Add one evade result up to the maximum you could have.

Just to provide some more general advice- because I assume that while you are keen to see specific examples, being able to work out new situations is more helpful- the field of mathematics we are looking at is combinatorics. In xwing, the maths is relatively simple because all of the probabilities are simple, known fractions. It is simply a case of mulitplying the relevant fractions together.

For example:

The chances of rolling two hits (I'm including crits as hits, because it is simpler and in many cases the result is the same) on two dice is 4/8 x 4/8 = 1/2 x 1/2 = 1/4.

On the other hand, if we want to know the chances of rolling one or more hits on two dice, it's simpler to work out the inverse of the probability of rolling no hits (because all of the probabilities will total to 1). The chance of no hits with no focus is 1 - (1/2 x1/2) = 1 - 1/4 = 3/4. With focus, the chance is 1 - (1/4 x 1/4) = 15/16.

More complex situations are just a case of breaking it down into simple sections and totalling the results.

If you are just looking at how many of X result you should expect from a number of dice, you can instead simply multiply the chance of that result by the number of dice. So for the Han Solo example, you have 3 dice with an expectation of 1/2 a hit per die; 3 x 1/2 = 1.5; you would expect to improve on your 1 hit, but if you had 2 hits you are above the average (though you can still gamble for more ).

Now let's assume you are trying to work out something different- say, what are the possible results with three attack dice?

Let's break it down:

3 crits = 1/8 x 1/8 x 1/8 = 1/512. Pretty simple.

2 crits + 1 hit is slightly more tricky: 1/8 x 1/8 x 3/8 = 3/512 BUT that tells us the chance of getting crit, crit, hit. We could get hit, crit, crit or crit, hit, crit; and we don't care what order they are in so the actual result is 3 x 3/512 (as there are three ways to get the result) = 9/512.

2 crits + 1 focus = 3(1/8 x 1/8 x 1/4) = 3/256

2 crits + 1 blank = 3(1/8 x 1/8 x 1/4) = 3/256

1 crit + 2 hits = 3(1/8 x 3/8 x 3/8) = 27/512

1 crit + 1 hit + 1 focus is more complex again; if the first die is a crit, we could get crit, hit, focus or crit, focus, hit so there are twice as many options. This time the calculation is 3 x 2(1/8 x 3/8 x 1/4) = 18/256 = 9/128

And so on. Once you know how to work it out, it's pretty straight forward.

If you want to know how to know what all the possible combinations are (not the probabilities, just the posible combinations so you can work out the calculations) the simplest way is to use punnet squares (which you can google easier than I can type it out ).

Or just learn to use Wolfram Alpha

(...)

Thanks.

How would I go about calculating the average # of hits/evades with the following abilities in play?

Attack dice with Howlrunner

Defense dice with Serissu/Lone Wolf (similar to the Howlrunner scenario but with Defense dice)

Defense dice with Autothrusters

Some of those calculations, because they involve onlyl a single dice being rerolled, are more complex than they seem and each scenario depends on how many focus or evade tokens that a ship has. The problem is that I have forgotten most of those more complex calculations, which is why I have the rule of thumb part (like predator is a partilar target lock, so it falls somewhere in between). One scenario that is easy(er) to calculate, however, is the autothruster in specific circumstances:

Soontir, with autothruster, is pursuing Han at range 2, with at least a focus an evade token in hand. Han has C3PO and R2-D2 (no gunner). What are the odds of Han landing a hit? The best that Han can do is land 3 hits, so what are the odds of Soontir evading all 3?

The evade token handles one hit and since Soontir has a focus, all focus rolls can be turned to evades. Considering that 1 blank will be turned into an evade automatically, this means that the only way for him to be hit is to roll 3 blanks. The odds are that are: (3/8)^3 = 27 / 512 or 5%. If you add a stealth device, those odds are 1.9%. Now keep in mind that a Falcon does not systematically roll 3 hits every single time and if the Falcon rolls 2 hits or less, it simply cannot hit Soontir while he has a focus and evade token. The best that the Falcon can do in this case is to lower the amount of tokens that Soontir has.

They are not impossible odds, but let's just say that it will take the Falcon a heck of a long time to kill Soontir if he simply runs away in a straight line. So this means that in order to win, the Falcon might have to get in range 1, get Soontir in its main firing arc or somehow prevent him from getting a focus and evade token. All of those options require good piloting skills or taking chances which put the Falcon at risk.

Naturally, in a competition, the Falcon will probably win by time in such a scenario, but if it is facing 2 ships with autothrusters and push the limit then suddenly its a whole different ball game.

Well done everyone, you've just taken the fun out of X-Wing