11 minutes ago, Jeff Wilder said:

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.

Such a thing would not be terribly hard to do FWIW and has been discussed. I do think it's not too uncommon for people to do a quick gut check while commentating a game with the calculator though. Certainly a lot of streams I've watched have checked their assumptions with it.

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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.

I think it's reasonable to expect people to only comment on the *results*, not the *roll* regardless of calculator use. Is it useful for someone to freak out when they roll 3 blanks, but then target lock it into 3 hits? Obviously not, no matter what you think of "either" "roll". This isn't just an edge case it's fundamental; the more people are thinking about "rolls" and the less about "results" the more likely they are to make largely erroneous statements and judgements. And while those sometimes benefit me on the table, they more often just turn into whining about dice which is simply tiresome.

So yeah my advice (which I consider totally practical) will continue to be: stick to talking about whether Kylo was likely to take 2 damage there or less/more. If you can talk about how much he was likely to take that *turn*, even better. You can develop a gut feeling for that kind of thing the exact same way people *think* they have a gut feeling about raw rolls. And checking your gut after the game lets you improve it over time.

19 minutes ago, punkUser said:

Sure but when you go too far down this path the question just becomes... why are you doing this in the first place?

Going a little bit down the path anyway shows to me how arbitrary it gets. The assumption that not spending a token is better than spending one seems fair. Using that to further separate the results creates 7 buckets, sorted by decreasing likelihood:

• Most frequent result is then 3 hits with a spent focus (29.6%, CCF, CHF, CFF, HHF, HFF, FFF). All of these should be treated equally because it does not matter if you spend a focus for 1 or 2 or 3 eyes (corner cases excluded, Padme...)
• Followed by 2 hits with a spent focus (23%, CFB,HFB, FFB).
• Next is 2 hits without a spent focus. That is usually more desirable as per the assumption (18.75%, CCB, CHB,HHB).
• Then 3 hits without a spent focus. Clearly the most desirable (12.5%, CCC, CCH, CHH, HHH)

Note that these 4 add up to the 84% from my previous post and make up the two modes of HH and HHH. Here I just separated them based on focus spending.
Now it gets even weirder. If I continue the pattern, I have to treat 1 hit with and without spent focus differently to stay consistent.

• 1 hit without spent focus is next most frequent (9.4%, CBB, HBB)
• 1 hit with spent focus (4.7%, FBB)
• And finally 0 hits (1.6%, BBB)

These buckets are really arbitrary though, they have no meaning because I mix focus spending and not-spending.

2 minutes ago, punkUser said:

Certainly a lot of streams I've watched have checked their assumptions with it.

Out of curiosity, which streams? I don't think I've ever heard a stream commentator do this, although Ryan often checks the calculator on Fly Better. I might enjoy those streams.

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I think it's reasonable to expect people to only comment on the *results*, not the *roll* regardless of calculator use.

Well, Rebellions are built on hope!

52 minutes ago, Baaa said:

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?

Honestly? That'd be utterly irrelevant.

• Two dice hitting each other and changing from 6/6 to 4/5 is equally likely as 4/5 changing to 6/6.
• Hitting a ship base and changing from one particular side to another single side will be, again, essentially equally likely.

Let's grant that initial position in the hand matters to the roll. If folks aren't specifically controlling the positions before the roll, if the initial positions are "something close" to random, the entire black-box system--from dice picked up to the final facing--is going to be close enough to the mathematical model over the small sample size of an X-Wing game that there'd be no reason to consider something else.

6 minutes ago, Jeff Wilder said:

Out of curiosity, which streams? I don't think I've ever heard a stream commentator do this, although Ryan often checks the calculator on Fly Better. I might enjoy those streams.

Krayt's and Fly Better folks do it frequently, but I've heard it on occasion on GSP or similar as well.

1 minute ago, theBitterFig said:

Honestly? That'd be utterly irrelevant.

• Two dice hitting each other and changing from 6/6 to 4/5 is equally likely as 4/5 changing to 6/6.
• Hitting a ship base and changing from one particular side to another single side will be, again, essentially equally likely.

Let's grant that initial position in the hand matters to the roll. If folks aren't specifically controlling the positions before the roll, if the initial positions are "something close" to random, the entire black-box system--from dice picked up to the final facing--is going to be close enough to the mathematical model over the small sample size of an X-Wing game that there'd be no reason to consider something else.

I disagree.

This is the pure mathematical model of die rolls in Backgammon. That model does not take into consideration other factors, i.e it is based entirely on rolls with no outside interference.

In X-Wing (and other dice games) outside interference could be die hitting each other, falling off the gaming table or being spirited away by aliens. Don't acknowledge that they exist then you're in for a fall.

Cheers
Baaa

10 minutes ago, Baaa said:

I disagree.

This is the pure mathematical model of die rolls in Backgammon. That model does not take into consideration other factors, i.e it is based entirely on rolls with no outside interference.

In X-Wing (and other dice games) outside interference could be die hitting each other, falling off the gaming table or being spirited away by aliens. Don't acknowledge that they exist then you're in for a fall.

Cheers
Baaa

If only someone had done a rigorous testing and modeling of xwing dice and dice of other types, to see how effectively random xwing dice are

Just now, Brunas said:

If only someone had done a rigorous testing and modeling of xwing dice and dice of other types, to see how effectively random xwing dice are

And that would why it would be at the end of the day, a game of chance, albeit with some added bonuses

But I'd put my money on the fact that they only used pure mathematical models to do so.

Cheers
Baaa

1 hour ago, Baaa said:

This is the pure mathematical model of die rolls in Backgammon. That model does not take into consideration other factors, i.e it is based entirely on rolls with no outside interference.

Couple of things:

First, my silly little model assumes fair dice.

Second, the study @Brunas mentioned used real "mechanical" dice rolling.

Third, these two statements appeared within two paragraphs of each other in the Backgammon link above which ... shudder .

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Finally, keep in mind that in all games of chance the "feel" of the dice must be considered. If you have ever shot crap, recall how often you have feit either your number or a seven coming up.

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To play and win at backgammon you must understand probability (i.e. the likelihood that a given event will occur).

I continue to have the weirdest feeling that you're low-key screwing with us, Baaa. I don't intend that as an insult ... if it's true, in fact, it's pretty artistic, and I respect that.

6 minutes ago, Baaa said:

And that would why it would be at the end of the day, a game of chance, albeit with some added bonuses

But I'd put my money on the fact that they only used pure mathematical models to do so.

Cheers
Baaa

You're neglecting the condition of how the dice are rolled as well any conditions that occur after hitting the table.

1 minute ago, jagsba said:

You're neglecting the condition of how the dice are rolled as well any conditions that occur after hitting the table.

Nope, that's why I asked for a 0.5 variance to be factored in, it covers a multitude of sins.

Including my cack handiidness.

Cheers
Baaa

2 minutes ago, Baaa said:

Nope, that's why I asked for a 0.5 variance to be factored in, it covers a multitude of sins.

Including my cack handiidness.

Cheers
Baaa

What's the distribution of the factors? 50/50 rolling/table bumps?

8 minutes ago, jagsba said:

What's the distribution of the factors? 50/50 rolling/table bumps?

Seriously?

Have fun.

Cheers
Baaa

16 minutes ago, Baaa said:

I disagree.

This is the pure mathematical model of die rolls in Backgammon. That model does not take into consideration other factors, i.e it is based entirely on rolls with no outside interference.

In X-Wing (and other dice games) outside interference could be die hitting each other, falling off the gaming table or being spirited away by aliens. Don't acknowledge that they exist then you're in for a fall.

Cheers
Baaa

It's not more likely that a focus falls off a table than a blank. Falling off the table is equally likely for every die facing. Falling off a table *DOES NOT MATTER* to the probabilities.

Let's suppose that hitting a ship base with a die side has an understandable effect. For sake of argument, let's say that it can't land on the side that was showing when it struck the base, and let's assume that landing on the exact opposite side is twice as likely as any remaining results. Does this impact the odds? Not in the least. Each side hitting the ship base was equally likely, so the impact of hitting a ship base applies equally to each side, and it all comes out in the wash.

Unless you can point to an outside factor that only applies to certain dice facing and not others, it's all irrelevant.

11 minutes ago, Brunas said:

If only someone had done a rigorous testing and modeling of xwing dice and dice of other types, to see how effectively random xwing dice are

Well now, that's something completely different.

Some dice are untrue, with faces not being equally likely. I'd say untrue instead of unfair, to avoid conferring a value judgement. IIRC, the untrueness wasn't uniform, with some dice favoring any of the results, and it could have been good or bad.

If folks are close-enough-to-randomly selecting different dice from the pool, and the pool averages are close to the theoretical averages, it ought to mostly balance out, but yeah, this could actually matter.

15 minutes ago, Baaa said:

Nope, that's why I asked for a 0.5 variance to be factored in, it covers a multitude of sins.

Including my cack handiidness.

Cheers
Baaa

0.5 seems like a massive margin of variance. That’s big enough to be reasonably testable with just a few hundred recorded throws. (Noisy, but detectable.) Are you just arbitrarily picking this number because it swamps out everything else?

1 minute ago, theBitterFig said:

It's not more likely that a focus falls off a table than a blank. Falling off the table is equally likely for every die facing. Falling off a table *DOES NOT MATTER* to the probabilities.

Let's suppose that hitting a ship base with a die side has an understandable effect. For sake of argument, let's say that it can't land on the side that was showing when it struck the base, and let's assume that landing on the exact opposite side is twice as likely as any remaining results. Does this impact the odds? Not in the least. Each side hitting the ship base was equally likely, so the impact of hitting a ship base applies equally to each side, and it all comes out in the wash.

Unless you can point to an outside factor that only applies to certain dice facing and not others, it's all irrelevant.

Well now, that's something completely different...

I would argue that anything that affects the mathematical models on which we generally base our dice games on matters, and for those mathematical models to be effective and as true as we can can get them to be how many rolls do we have to make?

Personally, whatever dice game I play I acknowledge the mathematical model then forget about it as I sacrifice something to the Dice Gods.

Cheers
Baaa

6 minutes ago, PaulRuddSays said:

0.5 seems like a massive margin of variance. That’s big enough to be reasonably testable with just a few hundred recorded throws. (Noisy, but detectable.) Are you just arbitrarily picking this number because it swamps out everything else?

No, I said it's the initial number.

0.5 is neither negative or positive it is the median. It will also change up towards 1 or down towards 0 as data comes in.

Cheers
Baaa

32 minutes ago, Baaa said:

But I'd put my money on the fact that they only used pure mathematical models to do so.

No, it was a physical experiment. A machine (well, a few different machines) to roll dice lots and lots and lots of times.

2 minutes ago, Baaa said:

I would argue that anything that affects the mathematical models on which we generally base our dice games on matters, and for those mathematical models to be effective and as true as we can can get them to be how many rolls do we have to make?

Personally, whatever dice game I play I acknowledge the mathematical model then forget about it as I sacrifice something to the Dice Gods.

OK, so magic?

Small sample size, so my results in any turn, in any game, won't match the theoretical averages. But that doesn't mean that the theoretical likelyhoods of the different outcomes are somehow inaccurate.

That's just small sample size.

2 minutes ago, Baaa said:

0.5 is neither negative or positive it is the median. It will also change up towards 1 or down towards 0 as data comes in.

I thought you said variance and not median. Those are very different things.

There are different types of averages. What Jeff has explained is the Mode - the most common roll. Similar in craps with two six sided die, the most common sum of two six sided die is 7. So if someone where to ask me to bet on the roll of the next 3 red die attack in xwing, I would put my money on HHB.

The typical "average" roll used in Xwing is the Mean average over a long period (infinity) of time represented visually with hit,focus,blank assuming you only have a focus (50% of the time on offense, again over infinity). Its not the most common roll, but its the most visually represented mathematical mean average. I dont think its wrong to call it average roll on streams without going all mathematical on the viewers.

51 minutes ago, Jeff Wilder said:

Couple of things:

First, my silly little model assumes fair dice.

Second, the study @Brunas mentioned used real "mechanical" dice rolling.

Third, these two statements appeared within two paragraphs of each other in the Backgammon link above which ... shudder .

I continue to have the weirdest feeling that you're low-key screwing with us, Baaa. I don't intend that as an insult ... if it's true, in fact, it's pretty artistic, and I respect that.

I'm definitely not low-key screwing with anyone.

The bits you've quoted are saying exactly what I've been trying to say all along, there is always a variance outside of the mathematical model. So why not factor it into your calculations?

I would argue that mechanical dice rolling mitigates variance as there is less chance of it being different.

I used 0.5 as it is the median of 0 and 1. It is the figure used by Hopgood in his book to introduce variance. It is neither positive nor negative, it is simply the middle number (or median) with which to start.

At the end of the day, in any dice game you either go with the averages and curse the dice when they don't come up (you can always console yourself with the thought that over a thousand dice rolls it would have been came up the way you wanted them to) or you accept that there are factors which the mathematical models don't take into consideration.

I choose the latter.

Cheers
Baaa

2 hours ago, Baaa said:

But I'd put my money on the fact that they only used pure mathematical models to do so.

How much money? Asking for a friend.

1 hour ago, wurms said:

The typical "average" roll used in Xwing is the Mean average over a long period (infinity) of time represented visually with hit,focus,blank assuming you only have a focus (50% of the time on offense, again over infinity).

What does this even mean? The mean of "what" distribution and how is that distribution being "visually represented" by - presumably - one sample from it? Why not HBB or HFF or any other individual result?

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Its not the most common roll, but its the most visually represented mathematical mean average. I dont think its wrong to call it average roll on streams without going all mathematical on the viewers.

But it *is* wrong and misleading, hence this thread. If you don't want to go "all mathematical" on streams that's great, but then don't make claims like your rolls are above or below "average" or this specific roll is "average". If people say things that are pretty wrong in ways that consistently cause folks to make bad decisions and rationalizations, I think we're well into the territory of where we're allowed to call them out on it

To put it another way, if you say "my dice are bad" I'm definitely allowed to tell you "no they aren't" or at the very least "prove it"

12 minutes ago, punkUser said:

What does this even mean? The mean of "what" distribution and how is that distribution being "visually represented" by - presumably - one sample from it? Why not HBB or HFF or any other individual result?

I think wurms is restating what I hypothesized in my original post as the reason people like to call HFB the "average" roll: it "visually represents" every face of the attack die ... as long as you don't count crits. It's just one of those fuzzy things that folks strangely consider relevant.

3 minutes ago, Jeff Wilder said:

I think wurms is restating what I hypothesized in my original post as the reason people like to call HFB the "average" roll: it "visually represents" every face of the attack die ... as long as you don't count crits. It's just one of those fuzzy things that folks strangely consider relevant.

So like... what do you do for 2 die attacks? Pick your favorite die faces?

32 minutes ago, punkUser said:

So like... what do you do for 2 die attacks? Pick your favorite die faces?

What do I do? I don't talk about rolls in this way, and I wish folks wouldn't. As far as I'm concerned, HHM and HMM are just expected rolls in the mass of 75% of all three-die rolls, and HM (at 50%) is the same for two-die rolls. (On the other hand, I'll seethe pretty hard at my fifth FB in a row with Optics RZ-2s.)

How other people decide? Beats me, really, but I could guess. CB is 9.5 points in the table in my original post, and HF is 9.5 points. HF seems more "visually representative," so my guess is that more people would call that an "average" roll.