https://imgur.com/YprsAxD

(Sorry for just the link. I'm working, and my firm has some weird stuff locked down.)

EDIT: I left off CFB , which is also only 0.5 from "average."

That's decent, thanks.

This gives a good understanding of it too X-Wing Probability

You don't understand the dice, you'll end up sacrificing your young to the Dice Gods. Not a bad option when they become teenagers to be fair.

Cheers
Baaa

21 minutes ago, Baaa said:

This gives a good understanding of it too X-Wing Probability

That was super helpful, but some people are just never gonna give up on what they think, or let go on what they believe.

For me, the logic is simpler.

On a roll of 3 attack dice, there's about a 60% chance to roll at least an eyeball. And you're going to roll 2 hits roughly on average.

And so "HFB" isn't so much a true kind of "average" so much as it represents my expectation that I will probably have a chance to spend a focus, and I'll probably get 2ish hits.

6 minutes ago, Ablazoned said:

And so "HFB" isn't so much a true kind of "average" so much as it represents my expectation that I will probably have a chance to spend a focus, and I'll probably get 2ish hits.

Agreed. I don't really have any objection to calling it an "expected" roll, or a "normal" roll. It's just that when it's referred to an "the average roll," it's misleading people who don't really understand that it's actually noticeably sub-average.

22 minutes ago, Jeff Wilder said:

That was super helpful, but some people are just never gonna give up on what they think, or let go on what they believe.

Showing your age old man.

Cheers
Baaa

I went over this on the Fly Better podcast about dice as well: the *average* is a property of a distribution of rolls. The average may not even appear in the distribution. The notion that a given sample from that distribution is "average" or something is almost always a misunderstanding. Also using any of this sort of data to try and decide if you think your rolls were "above or below average" is not meaningful outside of all of the context of the game, although I fully realize this a losing battle as no matter how well people know the math, they are going to continually find a way to blame something extrinsic for undesirable outcomes. That doesn't make it right or even a meaningful question though

I will however request we not conflate the word "average" with *most common result*. We already have a word for that: the "mode" of the distribution.

I'd also be remiss to not point out that there exists a tool that not only tells you the actual "average" number of hits for a given roll, but shows you the full distribution with fancy JavaScript interaction and everything. Feel free to use it to check your assumptions

24 minutes ago, Jeff Wilder said:

Agreed. I don't really have any objection to calling it an "expected" roll, or a "normal" roll. It's just that when it's referred to an "the average roll," it's misleading people who don't really understand that it's actually noticeably sub-average.

If your intention here is to convince people that talking about "the average roll" is nonsense in the first place, same team! If it's to instead shift the discussion to trying to argue that "no, HHB or some other result is actually the average" and thus I can feel validated complaining when I get (whatever thing I think is worse than that) then super nope - that's the same mistake about distributions everyone else is making.

Ex. the frequency of HHB and HHF is identical, and indeed that's true for any permutations of blanks and focuses obviously. Assigning focus a "higher value" from the point of view of X-Wing is not really meaningful... either you have a focus mod you are willing to spend or you don't when you roll those dice. If you do then focuses are hits and you're rolling a 6/8 die. If you don't, they're blanks. Obviously rerolls and other mods factor into this too, but that's the whole point: the only meaningful thing to measure from a roll distribution is the results *after modding*, not the "roll" itself.

None of this making up "values" for dice or results or anything else - it's a pretty simple probabilities and distributions. Usually when people get confused it's because they are asking questions or making assumptions that are fundamentally flawed. Ex. there's no such thing as an "average *roll*" (only average results), as you are pointing out here.

1 minute ago, punkUser said:

If your intention here is to convince people that talking about "the average roll" is nonsense in the first place, same team! If it's to instead shift the discussion to trying to argue that "no, HHB or some other result is actually the average" and thus I can feel validated complaining when I get (whatever thing I think is worse than that) then super nope - that's the same mistake about distributions everyone else is making.

It's the first. I don't think it's possible to stop people from calling a roll "average," so I would be a little happier if they'd expand what they call an "average" roll, though. It's really striking: you'll see a player roll HFB and hear it called "exactly average," and then the same player will roll HHB and have it called "really good." It's like ... wut? This sort of thing really is contributing to the misunderstanding of probability, and probability is already not intuitive.

1.5 hits =P with a focus token, 2.25 ;}

21 minutes ago, Jeff Wilder said:

Agreed. I don't really have any objection to calling it an "expected" roll, or a "normal" roll. It's just that when it's referred to an "the average roll," it's misleading people who don't really understand that it's actually noticeably sub-average.

The place where I think it's really lead to mistakes: evaluation of Advanced Optics on a 3-red ship. Someone will say: "Oh, but the average roll will have a hit/eye/blank, so Optics will be wasted on average." And that's just plain inaccurate. HHB will show up about 19% of the time, treating crits as hits.

3 minutes ago, theBitterFig said:

The place where I think it's really lead to mistakes: evaluation of Advanced Optics on a 3-red ship. Someone will say: "Oh, but the average roll will have a hit/eye/blank, so Optics will be wasted on average." And that's just plain inaccurate. HHB will show up about 19% of the time, treating crits as hits.

Yep but it's worth noting that that applies to *every* case, not just specific mods. You can't pick a value that you consider representative out of the distribution of rolls then mod *that* and claim it is representative of the distribution of *results*. You have to apply your mods to *every* possible roll separately and then combine those *results* based on the probabilities of those rolls. Yes it gets tedious for anything beyond the simple cases. If only someone wrote a tool to automate it... (or is that too close to "advertising" on these forums)

6 minutes ago, punkUser said:

I went over this on the Fly Better podcast about dice as well: the *average* is a property of a distribution of rolls. The average may not even appear in the distribution. The notion that a given sample from that distribution is "average" or something is almost always a misunderstanding. Also using any of this sort of data to try and decide if you think your rolls were "above or below average" is not meaningful outside of all of the context of the game, although I fully realize this a loosing battle as no matter how well people know the math, they are going to continually find a way to blame something extrinsic for undesirable outcomes. That doesn't make it right or even a meaningful question though

I will however request we not conflate the word "average" with *most common result*. We already have a word for that: the "mode" of the distribution.

I'd also be remiss to not point out that there exists a tool that not only tells you the actual "average" number of hits for a given roll, but shows you the full distribution with fancy JavaScript interaction and everything. Feel free to use it to check your assumptions

I think that the problem with any game that involves dice and trying to figure out the probability of outcomes is that they are nearly always based on models which use "clean" results.
Now, whilst these outcomes may be nearly close to the actual dice rolls that players hit, they invariably don't don't include conditions.

A model that included some form of Bayesian updating would be slightly more accurate.

Cheers
Baaa

@punkUser - Personally speaking, I'd like you to advertise whatever calculator you're talking about more explicitly.

This is good stuff.

4 minutes ago, Jeff Wilder said:

@punkUser - Personally speaking, I'd like you to advertise whatever calculator you're talking about more explicitly.

This is good stuff.

http://xwing.gateofstorms.net/2/multi_preset/

the thread got removed for advertising (???????????)

meanwhile, things that are actual patreons, actually infringe copyright, etc are around. Was pretty dank, would recommend.

2 minutes ago, Jeff Wilder said:

It's really striking: you'll see a player roll HFB and hear it called "exactly average," and then the same player will roll HHB and have it called "really good." It's like ... wut? This sort of thing really is contributing to the misunderstanding of probability, and probability is already not intuitive.

If we're treating Crits and Hits identically... So much nicer for fast math...

HHF = 0.5 * 0.5 * 0.25 * 3 = 0.1875

HHB = 0.5 * 0.5 * 0.25 * 3 = 0.1875

HFB = 0.5 * 0.25 * 0.25 * 6 = 0.1875

All equally likely outcomes.

1 minute ago, punkUser said:

Yep but it's worth noting that that applies to *every* case, not just specific mods. You can't pick a value that you consider representative out of the distribution of rolls then mod *that* and claim it is representative of the distribution of *results*. You have to apply your mods to *every* possible roll separately and then combine those *results* based on the probabilities of those rolls. Yes it gets tedious for anything beyond the simple cases. If only someone wrote a tool to automate it... (or is that too close to "advertising" on these forums)

Indeed. I'm loading up stuff on the calculator ( http://xwing.gateofstorms.net/2/multi_preset/ ) all the time, since that's really the most accurate way to evaluate stuff.*

I still think Advanced Optics is kind of a special case of the HFB mental trap. With something like Predator or Howlrunner, someone mired in HFB will think "Oh, I'll reroll the blank, and can still spend my focus," and while their process will be entirely wrong, their final destination won't be as far distant.

* I only wish it could model the Autoblasters effect...

6 minutes ago, theBitterFig said:

If we're treating Crits and Hits identically... So much nicer for fast math...

HHF = 0.5 * 0.5 * 0.25 * 3 = 0.1875

HHB = 0.5 * 0.5 * 0.25 * 3 = 0.1875

HFB = 0.5 * 0.25 * 0.25 * 6 = 0.1875

All equally likely outcomes.

Indeed. I'm loading up stuff on the calculator ( http://xwing.gateofstorms.net/2/multi_preset/ ) all the time, since that's really the most accurate way to evaluate stuff.*

I still think Advanced Optics is kind of a special case of the HFB mental trap. With something like Predator or Howlrunner, someone mired in HFB will think "Oh, I'll reroll the blank, and can still spend my focus," and while their process will be entirely wrong, their final destination won't be as far distant.

* I only wish it could model the Autoblasters effect...

Pretty good but all based on pure mathematical models.

I play a lot of Backgammon and Yahtzee and it's pretty easy to find the probabilities of the dice rolls on either by doing a simple search on Google.

However, none of these models include conditions. So what is a condition?
Two die hitting each other and changing to a four and five when the mathematical model would show sixes?
A die hitting the base of a ship and flipping to Focus when you were sure you were getting a Crit?

And those conditions get a lot more complicated when we start adding in upgrades.

As an aside, tokens don't change the dice probabilities, they change the outcome of those probabilities and can in some cases be counteracted by an upgrade or pilot ability.

Cheers
Baaa

I try to simplify this for myself here (consistently treating H=C for number of hits, and when I say combinations, I ignore order and treat all 6 way to get HFB as the same) because I really don't understand your table Jeff.

• If I have a focus then the two modes are
  • 3 hits (because there are actually 10 different combinations that lead to that outcome)
  • and 2 hits (because there are 6 different combinations for this outcome).
• Without a focus, the two modes are
  • 2 hits (because there are 6 different combinations)
  • and 1 hit (because there are 6 different combinations).

The individually most frequent dice roll result is indeed HFB at 14%, followed by HHB and HHF at 10.5% each, but that is entirely irrelevant because we care about the number of hits. So we should treat them as HHB or HBB, depending on availability and willingness to spend focus tokens. Is that fair to say @punkUser ?

4 minutes ago, GreenDragoon said:

... but that is entirely irrelevant because we care about the number of hits. So we should treat them as HHB or HBB, depending on availability and willingness to spend focus tokens. Is that fair to say @punkUser ?

Yeah, or just "HH" vs "H" even since how many blanks you have doesn't matter. i.e. you're counting results not looking at die permutations.

Just to add a little bit of context:

I am addressing the tendency of X-Wing players and commentators to talk about rolls , whether "good," "average" or "bad." And they usually do that without regard for dice modifications available: i.e., they are usually strictly talking about what shows on the dice.

For reasons discussed, that is a problematic way of looking at things, in a strict sense, but there is some validity in ranking rolls from "phenomenal" to "abysmal," right? I mean, in the absence of corner cases, CCC is better than HHH. Without other information, does anybody disagree? And HHH is better than FFF, and FFF is better than BBB? (Yes, I know that in the absence of a way to modify your focus results, they are effectively the same result, but without knowledge of whether a ship has the ability to modify focus results, does anybody disagree that FFF is a better roll than BBB?)

That's the reason that I assigned values to results, and thus values to the full roll, to get a spectrum of roll values to look at (albeit, again, without regard to dice modifications available). I couldn't really think of another way to do it, if in fact we can all agree that CCC (or even CHH) is a "better" roll than HHH.

Really, without consideration of dice modification, players and commentators should consider every HMM and HHM raw roll as equally worthy of calling "average," if they're (we're) going to call rolls average at all.

1 minute ago, Jeff Wilder said:

Just to add a little bit of context:

I am addressing the tendency of X-Wing players and commentators to talk about rolls , whether "good," "average" or "bad." And they usually do that without regard for dice modifications available: i.e., they are usually strictly talking about what shows on the dice.

For reasons discussed, that is a problematic way of looking at things, in a strict sense, but there is some validity in ranking rolls from "phenomenal" to "abysmal," right? I mean, in the absence of corner cases, CCC is better than HHH. Without other information, does anybody disagree? And HHH is better than FFF, and FFF is better than BBB? (Yes, I know that in the absence of a way to modify your focus results, they are effectively the same result, but without knowledge of whether a ship has the ability to modify focus results, does anybody disagree that FFF is a better roll than BBB?)

That's the reason that I assigned values to results, and thus values to the full roll, to get a spectrum of roll values to look at (albeit, again, without regard to dice modifications available). I couldn't really think of another way to do it, if in fact we can all agree that CCC (or even CHH) is a "better" roll than HHH.

Really, without consideration of dice modification, players and commentators should consider every HMM and HHM raw roll as equally worthy of calling "average," if they're (we're) going to call rolls average at all.

Pretty sound basis, but try modelling again with a probability of 0.5 as an outside factor and see what your results are.

It's the basis of how intelligent systems are built.

Cheers
Baaa

1 minute ago, Baaa said:

Pretty sound basis, but try modelling again with a probability of 0.5 as an outside factor and see what your results are.

I have to admit, I'm not sure what you mean here. (Oddly, it almost feels like a low-key joke.) My understanding of probability, while better than most X-Wing and poker players, is still very basic. I have no formal training in it (nor any math class past my sophomore year in high school) ... I was just born lucky with a better-than-average instinctive feel for it. I end up brute-forcing a huge number of combo/permutation problems that would be pretty simple to calculate if I learned how.

18 minutes ago, Jeff Wilder said:

(Yes, I know that in the absence of a way to modify your focus results, they are effectively the same result, but without knowledge of whether a ship has the ability to modify focus results, does anybody disagree that FFF is a better roll than BBB?)

Sure but when you go too far down this path the question just becomes... why are you doing this in the first place? In what situation are you trying to put some sort of "value" on a roll outside of the context of modifications available? Obviously there *are* cases where these things are not true and we can call them 'corner cases', but why are we even making all of these assumptions in the first place? What's the *actual* question being asked on specific terms?

Usually when people go down paths like this it's because they have some sort of agenda and they want some sort of validation of Steps 1-3 of their process so that they can claim that their broad conclusions and statements they draw from Steps 4-10 are "mathematically valid". If you want a mathematically valid answer you first need to ask a mathematically valid question.

Quote

That's the reason that I assigned values to results, and thus values to the full roll, to get a spectrum of roll values to look at (albeit, again, without regard to dice modifications available). I couldn't really think of another way to do it, if in fact we can all agree that CCC (or even CHH) is a "better" roll than HHH.

Right but as you probably noticed when doing the exercise, the specific values you assign for these affects your conclusions, even if you maintain the ordering you defined above. I'm sure you agree this is a bit of a red flag and leads back to the question... what are we even trying to do in the first place?

Quote

Really, without consideration of dice modification, players and commentators should consider every HMM and HHM raw roll as equally worthy of calling "average," if they're (we're) going to call rolls average at all.

I'm being pedantic because this really needs to go a step further: players and commentators *should not be considering or commenting on the 'averageness' of raw rolls in the first place*, because that is precisely the misunderstanding that is leading to incorrect statements being made. It's not that we need to "fix" the specifics of how they are doing that, we need to correct the fundamental idea that "rolls" can be "average". So not to put too fine a point on it, but only results after modding can be "average" in this context, and in determining that you absolutely should incorporate *as much* information about the game context as possible (mods at a minimum, but even doing it across multiple attacks is more useful where no player agency would cause problems).

It's tempting to try and generalize and simplify this in ones mind but seriously it's already quite simple: put the exact situation you are facing/that happened into the calculator with as much detail as possible. Look at where the result you got landed in the distribution of results and decide whether it was a reasonable expectation or not and whether [the player] should modify their decision making next time. That's basically it.

1 minute ago, Jeff Wilder said:

I have to admit, I'm not sure what you mean here. (Oddly, it almost feels like a low-key joke.) My understanding of probability, while better than most X-Wing and poker players, is still very basic. I have no formal training in it (nor any math class past my sophomore year in high school) ... I was just born lucky with a better-than-average instinctive feel for it. I end up brute-forcing a huge number of combo/permutation problems that would be pretty simple to calculate if I learned how.

You've done the maths, so just add an outside factor in (a condition) which initially will be 0.5.

There's a book on my bookshelf which I dip into now and then not a Rick Roll honest which would explain it better. The problem with the vast majority of dice games (and I include X-Wing as a dice game) is that players (me) go for the easy pure mathematical model.

Nothing wrong with that in the grand scheme of things but it's not entirely accurate.

Cheers
Baaa

2 minutes ago, punkUser said:

It's tempting to try and generalize and simplify this in ones mind but seriously it's already quite simple: put the exact situation you are facing/that happened into the calculator with as much detail as possible. Look at where the result you got landed in the distribution of results and decide whether it was a reasonable expectation or not and whether [the player] should modify their decision making next time. That's basically it.

The problem is that, in a practical sense, that is not a feasible thing to do when commentating on a game or when participating in a game. It's not really even feasible when commenting on a recorded game, though (speaking as a huge nerd) I would enjoy seeing some gateofstorms pop-ups added by content providers on some of the more unusual occurrences. Similarly, it's not a practical suggestion that commentators and players stop making judgments about the value of rolls standing alone.

Your suggestion is a perfect suggestion, but it's not a workable suggestion. I'm trying to make a workable suggestion that, while not perfect, is at least "less wrong," given that the activity is -- with a probability of 1.00, BTW -- going to continue. I think I've been pretty clear -- in the original post and in subsequent replies -- that I don't have any expectation that it's perfect.

13 minutes ago, Jeff Wilder said:

I have to admit, I'm not sure what you mean here. (Oddly, it almost feels like a low-key joke.) My understanding of probability, while better than most X-Wing and poker players, is still very basic. I have no formal training in it (nor any math class past my sophomore year in high school) ... I was just born lucky with a better-than-average instinctive feel for it. I end up brute-forcing a huge number of combo/permutation problems that would be pretty simple to calculate if I learned how.

The 0.5 factors in physical interactions with the rolling environment and the other dice during a roll if I'm understanding @Baaa 's posts in this thread correctly. Those would be the outside factor.