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Vorpal Sword

So how *exactly* do you tell whether dice are fair?

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Part 1: TL;DR



(1) DRAMA!!

So there's been a lot of DRAMA!! over the last couple of days with respect to loaded dice, in (at least) two separate threads. I don't want to partake in that here.

But the question no one seems to have answered is how you would actually go about figuring out whether a set of dice is fair. So what would it actually take to do that?
 
The short version is that it's going to take an inconvenient amount of dice rolling, and there are no good shortcuts. In fact, it takes so much die rolling that you almost certainly can't tell based on a single tournament.
 
(2) Wait, you're just telling people it's okay to cheat!
 
Don't be ridiculous. I'm telling you there's no way you can use math to tell whether your opponent is on a hot streak or playing with weighted dice without a lot of work.

The bad news is that means someone who wanted to cheat could probably get away with it for a long time. But there's an easy way to deal with that: it's already in the rules* that you can ask for you and your opponent to share a set of dice. If you're really worried about your opponent's dice, get in the habit of asking at the start of the match to share--either a set of dice or the FFG dice app.

That will prevent your opponent (and you) from cheating in his or her favor, and entirely sidesteps the issue of how to tell if they were actually doing so. An ounce of prevention is worth a pound of cure, and all that.

***

*Thanks to VanorDM: I even went and checked the rules for good measure, and just automatically lumped dice in with the other components you can request to share. It's something that probably should be added, and I think it would be good if people wrote in to Organized Play to let them know it's something they would like to see.

But I still think people should feel free to ask: I think most players wouldn't see it as unreasonable, and it makes it much clearer to any observer that the game was fair (at least as far as dice are concerned). Edited by Vorpal Sword

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Part 2: Math

 
 
(1) No, really, you can't do it by eyeball and/or memory.
 
I know that unlike the rest of us, you are a special snowflake with brilliant mathematical intuition. ;) But there are just too many different cognitive biases at work here for you (or literally anyone else) to be able to figure out whether a set of dice is performing as expected. Look at the bottom of this post, for instance: it could take thousands of rolls.
 
(2) What do you mean by "fair" or "loaded"?
 
Basically, you need to know how far off a die is from true. An attack die that always rolled crits would be very easy to detect; a die that produces an extra (say) 1 hit in every 10 rolls is pretty hard to detect.

(3) You’re going to have to roll a lot.
 
The actual number of times you need to roll depends on how different a die or set of dice is from "normal"--or, more precisely, how large of a difference you want to be able to detect. The actual answer gets into a relatively complicated branch of statistics called power analysis, and you need at least a spreadsheet and probably dedicated statistical software to figure it out.
 
But here's an example: suppose you suspect someone is using a heavily loaded die, with one particular hit face coming up literally half the time. This is actually really easy behavior to see (technically, any set of n_i that satisfy the assumptions of the chi-squared test will have sufficient power). In fact it's so easy to see that all you need to do is roll until you've seen each face of that die 5 times or so, and then do the statistical test.
 
The less heavily a die is loaded, though, the more you'll need to roll. If one hit face is twice as likely to come up as usual (and the rest of the faces are correspondingly less likely), you'd need to roll at least 69 times (under α=0.05, β=0.8).

If one face is just 10% more likely than usual to come up (that is, it comes up 13.75% of the time rather than 12.5%), you'd need to roll 6,852 times. Edited by Vorpal Sword

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Part 3: Other Stuff

 

(1) What about that thing with the salt water and the floating die?

 

Uh, what about it? It doesn't test the distribution of results on the die, except indirectly. What it does is test to see whether there's a variation in density in the die--that is, if weight is concentrated toward one side.

 

The first problem with it is that even in the best case it's not very sensitive. Unless the die is really heavily weighted or you're working as carefully as an experienced lab technician, your results are likely to be confounded by all sorts of factors you're not controlling for: air bubbles clinging to the surface of the die, salinity of the water, the temperature of the die, etc.

 

The second problem is that the physical system you're creating might have multiple equilibrium configurations--that is, you could end up with a die that floats equally happy with Face #1 up or Face #2 up.

 

The third problem is that even if you do get an unambiguous result, it can be hard to interpret. For instance, what does it mean if you have a green die that likes to float with the same point (vertex) always facing up?

 

If you have a lot of time and salt and water to spare, go ahead and try it. But it's probably not going to give you a good answer about whether the dice are fair.

 

(2) Is there anything I can do other than roll a set of dice 7,000 times?

 

Well, you can look for obvious stuff. One of the easiest ways to load a die is to add weight to one face, usually by putting something small and dense (like a piece of metal) in the face you want to have land down. So you can look for imperfections in the regularity or color of the surface, which might indicate that the face was drilled out and then patched.

 

Adding weight to a particular face will also add weight to the die overall. You might not be able to tell if you're working with just your hands, but a sufficiently precise scale might find a difference. You can also change the shape of a die to make it more or less likely that it will land on a set of faces. That means the dimensions of the dice will be different from an unaltered die, and you could use a ruler or (better) a set of calipers to check that.

 

Unfortunately, because of the way the dice are manufactured, the tolerances are going to be fairly broad--that is, two completely normal dice from a newly-unwrapped core set could have different weights and dimensions.

 

(3) I know you already went over this, but it seems like you're just telling people that no one will know if they cheat!

 

Well, that's probably true. In fact, it's perfectly possible that you've already played against a cheater, and didn't know it! But my saying so isn't going to change anything about the game, and bringing it up also gives me the chance to bring up the solution: get in the habit of asking your opponents to share a set of dice, or to share a single instance of the FFG dice app. That way you're protected from the start, and it doesn't require you to single anyone out.

Edited by Vorpal Sword

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Dice aren't fair, just like most things in life. This is just one of those things you have to accept.

Now correct me if I'm wrong but aren't you allowed to use the same dice and range ruler as your opponent in tournaments?

That seems like a perfect rule for you paranoid players out there.

Edited by jocke01

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It will be a sad day in X-wing history when my proposed solution becomes the norm... but here it is:

 

Before a game starts, the opponents agree on a set of dice that both will use during the game.  No other dice may be used other than the communal dice agreed upon. 

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I just prefer to ask to share a set of dice, that way you cancel out any advantage you or your opponent might have.

This is the 'real' solution to dice issues in this game...

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VP - So I am curious at what point official X-Wing event will start adopting policies like 40K events did to help take this out of the equation.  Its real simple, have a portion of the fee charge for the event go towards buying a new pack or two of dice which must be used for the duration of the event.  

Personally I do not know the correct answer aside from what I am suggesting here.  There would never be any questions at that point.  

The truth, is that without extensive testing, at an already timed event, there is no real true way to determine if dice are hot, cold, or baked.  

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The problem is... The rules don't actually say you can request a shared set of dice.

It seems some people are adding dice to the following rule. "Before a tournament match begins, any player may request that a single range ruler and/or set of maneuver templates be shared for the duration of the match."

But I looked at the latest PDF again and nowhere does it say you can request a shared set of dice.

It perhaps should, but the fact is that it currently doesn't actually say that, and so if someone requested it the other guy has every right to refuse.

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The sad/scary truth is that you typically cannot. 

 

Limited techniques might work, but they are not practical:

A. If the crooked dice have had metal weight inserted into them:

(0) Cutting the dice open to investigate, but it ruins the dice. Kinda like the drowning an accused witch: maybe she drowns and is cleared, but she's still dead.

(1) X-Ray Scanner: works great, but good luck getting access, especially at a tourney venue
(2) Metal detector: easier to get access too, but pending sensitivity will likely not pick up the metal
(3) Magnets: only works if the weights added were ferric, and even then unless substantial weight was added probably won't work
(4) Scientific scale: this one could work in the theory, but I've never tried.  My guess is that X-Wing dice already vary enough in mass (especially uncleaned) that you may not be able to detect added weight with certainty.  But who knows.

 

B. If the dice have been "cooked":
Sometimes, depending on the process discolors or deforms the dice a little bit, but it depends on how it is done.  There will be some cases where you'll be able to visually differentiate a cooked dice, but there will also be cases where you cannot.  This leaves you with visually indistinct cooked untrue dice.


C. If the dice are just naturally favorable due to processing imperfections:
Nothing can be done to determine this.  This leaves you with visually indistinct natural untrue dice.


D. Dremel and Paint used to add symbols to the die:

An old cheat in dice games is to use dice with an inappropriate amount/arrangement of symbols.  For instance, Warhammer players using D6s with only 4,4,5,5,6,6 or D&D or HeroClix players using "spin-down" D20s that arrange the faces sequentially (for easier life-tracking in Magic) and roll them in a biased way to favor the quadrant of the die with higher numbers.  This is probably rare in X-Wing given its unique dice, but anyone with a fine dremel and a half-can of talent could add a symbol to the blank side of an X-Wing D8 then just hit it with white paint.  It would be really easy to determine upon inspection of the dice, but it's something no one ever bothers to check.  Especially if you only did it on three of your six dice or something.

 

So, how do you test dice that might be unfair due to either (B) cooking or the © manufacturing process?

I dunno, I don't think there's a realistic way to do it.  The floating in super-saturated salt water test simply does not work for D8s, despite what some might claim.  So, shy of rolling the dice in a fair test a significant number of times, there isn't much that can be done.  That presents only two solutions:


I. Serious Premiere X-Wing Events Start Using Specific Dice
Either TOs/Venues provide the shared dice for players to use at premiere events, or alternatively events provide players with a special set of dice to use that double as a participation prize.  Lost of other games do this, though for X-Wing with its unique symbols it would be harder. For instance, lots of tourneys provide dice with costs of entry, and have their special logo replace the "6" of the D6 for instance.


Otherwise, all players/TOs can hope to do is to track rolls of players with suspicious dice.  If a TO/Observer jots down the immediate result of each die everytime it is rolled (and re-rolled) you get a good sense (e.g. tick marks recorded for every Hit, Crit, Focus, and Blank symbol).  I've done this before for a player who was using third party kickstarter dice.  I wasn't a TO, but after I watched him god-roll myself and another opponent, I tracked his rolls through the Final Game. He lost, so I didn't press the issue, but he only rolled about 9% blanks on his red dice, which is less than the 25% you'd expect of true dice.  Still, it's a very small sample size, but it's a start to painting a picture, especially after witnessing his incredibly hot rolling in two earlier games as well.

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The problem is... The rules don't actually say you can request a shared set of dice.

It seems some people are adding dice to the following rule. "Before a tournament match begins, any player may request that a single range ruler and/or set of maneuver templates be shared for the duration of the match."

But I looked at the latest PDF again and nowhere does it say you can request a shared set of dice.

It perhaps should, but the fact is that it currently doesn't actually say that, and so if someone requested it the other guy has every right to refuse.

That's amazing. I know the rules fairly well, and even went to read them before I posted to make sure... and I still missed that fact that dice aren't among the components you can request to share. I updated the first post in the thread to reflect that.

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The problem is... The rules don't actually say you can request a shared set of dice.

It seems some people are adding dice to the following rule. "Before a tournament match begins, any player may request that a single range ruler and/or set of maneuver templates be shared for the duration of the match."

But I looked at the latest PDF again and nowhere does it say you can request a shared set of dice.

It perhaps should, but the fact is that it currently doesn't actually say that, and so if someone requested it the other guy has every right to refuse.

Does it explicitly say you can't ask for a shared set of dice? TO judgement required. :D

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You know what?  Thanks!

 

That was well written and thoughtful.  Your summation makes me feel better about my own dice.  I always feel like my dice hate me, but this goes a long way to alleviating that stress.  Even if my dice are poorly made it would take so much effort to discern the truth of it that it is far simpler to just roll the damned things and accept your fate.

 

Or... use communal dice.  No one seems to want to use mine though, haha!

 

Funny Story Time!

 

I played a match at the shop and my dice were just unbelievably bad.  HLC, TL & Focus, one hit.  Evaded.  Autoblasta, all crits, all evaded.  That sort of game.  So this fella comes by and says oh dude, it's just you!  You suck at dice!  He then proceeds to pick up my 6 red dice and throw them.  All blanks.  On six dice.  Red ones no less!  He's like... Oh.  Tries again.  One hit, one focus, the rest blank.  He's like, oh...  Picks up all 6 of my greens and before he throws I say FLUB!  And sure enough, one focus, five blanks.  Buddy just looks at me and says "You're cursed!".  We all laugh.  Game continues.  Buddy starts to play a game at another table and first dice roll he makes, all blanks.  He just looks at me with death in his eyes.  I was like, hey I told ya!  You should have left the devil-dice alone, now the mojo is on you.

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Note that sharing dice is not a true solution to this.  Dice Cheats could still bias the results if their dice are used for the match.  If I'm flying dual aggressors or a TIE Swarm, I'd just bring untrue Green dice that favored Evades.  If I'm flying Y-Wings or B-Wings or a Ghost or something, I'd just bring untrue green dice that favor blanks.  I'm still them imparting a huge advantage to myself, and at worst it's a wash if my opponent is also flying low/high agility ships.

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Note that sharing dice is not a true solution to this.  Dice Cheats could still bias the results if their dice are used for the match.  If I'm flying dual aggressors or a TIE Swarm, I'd just bring untrue Green dice that favored Evades.  If I'm flying Y-Wings or B-Wings or a Ghost or something, I'd just bring untrue green dice that favor blanks.  I'm still them imparting a huge advantage to myself, and at worst it's a wash if my opponent is also flying low/high agility ships.

Assuming you get to use your cheater dice... if they request that you use their own (not modified dice), then no advantage to you.

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Note that sharing dice is not a true solution to this.  Dice Cheats could still bias the results if their dice are used for the match.  If I'm flying dual aggressors or a TIE Swarm, I'd just bring untrue Green dice that favored Evades.  If I'm flying Y-Wings or B-Wings or a Ghost or something, I'd just bring untrue green dice that favor blanks.  I'm still them imparting a huge advantage to myself, and at worst it's a wash if my opponent is also flying low/high agility ships.

Assuming you get to use your cheater dice... if they request that you use their own (not modified dice), then no advantage to you.

 

Alternatively, there could be a set of dice that the TO brings to a disputed table and both players need to use the TO's dice set.

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Note that sharing dice is not a true solution to this.  Dice Cheats could still bias the results if their dice are used for the match.  If I'm flying dual aggressors or a TIE Swarm, I'd just bring untrue Green dice that favored Evades.  If I'm flying Y-Wings or B-Wings or a Ghost or something, I'd just bring untrue green dice that favor blanks.  I'm still them imparting a huge advantage to myself, and at worst it's a wash if my opponent is also flying low/high agility ships.

Assuming you get to use your cheater dice... if they request that you use their own (not modified dice), then no advantage to you.

 

Right, but what if each player wants their dice to be the set that is used?  (Presumably honest players will always want this: I know my dice aren't rigged, but I don't know yours are not, so let's use mine).  This means dice sharing would need to be determined by a coin toss every time, which still means a cheater's dice could enter the shared pool 50% of the games.

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Does it explicitly say you can't ask for a shared set of dice? TO judgement required. :D

It doesn't say anything. Although the TO of course has the final say. But the rules explicitly say you can request a shared set of templates, so everyone has the 'right' to do so. It does not say anything about dice, so the other guy has the 'right' to refuse. So you could end up getting the TO involved.

But speaking as a sometimes TO. I'd not be included to force someone to use a shared set of dice unless there was a good reason. "He may be cheating" is not a good reason.

Edit: Point is this. If I sit down at the table I can ask for a shared set of templates and the only thing the other person can do is pick which set we'll use. They can't actually refuse to use a shared set.

The TO only gets involved if we can't agree on which set to use.

But with dice I don't have that same 'right', if I ask and there's of course no harm in asking, the other guy can in fact refuse and at that point the only way I could force the issue is if the TO got involved.

Edited by VanorDM

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Saw a guy buy 10 packs of dice and sit their rolling each one 10 times to finally come up with a set that rolled many hits and many evades.

Then started rolling blanks at the very next event.

8 sided dice are funny that way. Even if they are weighted, they are such a weird shape the weighting does not help that much. The floating trick works great for 20 sided since its almost a sphere and will tend towards heavy side down naturally.

In the end however, cheaters always get caught. Even when they try to palm and extra card several times while video is running.

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Ok, here is the answer.

 

Tournament dice, 100% clear acrylic material tinted red or green.  Only dice without visible occlusions pass QA.  Dice are supplied by FFG to the TO's for all official tournaments and available for purchase for community events as desired.

 

As an aside I would like to know if anyone has actually ever been caught with modded dice.  It seems like very high effort and risk for minimal reward.

Edited by Jetfire

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As an aside I would like to know if anyone has actually ever been caught with modded dice.  It seems like very high effort and risk for minimal reward.

 

Yes, dozens and dozens of times in other games like Warhammer 40k/Fantasy, HeroClix, etc.  As competitive X-Wing continues to grow in size, poplularity, and recognition and as it continues to draw players from those other games, it is wise to be mindful of maintaining a fun and fair community.

In X-Wing, we have at least one recent account of a group stealing someone's dice and replacing them with standard dice so that one of the members could check the dice with an X-Ray machine at work.  Allegedly, the dice had weights sunk into them.  So, it depends on if you trust the word of this group.

Outside of dice, X-Wing has a sorry set of known cheaters, sadly, though the other stories that come to mind involve altering damage decks (remember when multiple players using TIE Swarms were busted for taking all the Direct Hits out of their damage decks at Regionals two years ago?) or lying about / altering dials or using intentionally sloppy maneuver toll execution to "avoid" asteroids or collisions, for instance.  They are certainly a minority, but one is too many for a community to tolerate, and a lone cheater can tarnish and ruin the effort and enjoyment of an entire community.

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Part 3: Other Stuff

 

 

(1) What about that thing with the salt water and the floating die?

 

Uh, what about it? It doesn't test the distribution of results on the die, except indirectly. What it does is test to see whether there's a variation in density in the die--that is, if weight is concentrated toward one side.

 

The first problem with it is that even in the best case it's not very sensitive. Unless the die is really heavily weighted or you're working as carefully as an experienced lab technician, your results are likely to be confounded by all sorts of factors you're not controlling for: air bubbles clinging to the surface of the die, salinity of the water, the temperature of the die, etc.

 

The second problem is that the physical system you're creating might have multiple equilibrium configurations--that is, you could end up with a die that floats equally happy with Face #1 up or Face #2 up.

 

The third problem is that even if you do get an unambiguous result, it can be hard to interpret. For instance, what does it mean if you have a green die that likes to float with the same point (vertex) always facing up?

 

If you have a lot of time and salt and water to spare, go ahead and try it. But it's probably not going to give you a good answer about whether the dice are fair.

 

(2) Is there anything I can do other than roll a set of dice 7,000 times?

 

Well, you can look for obvious stuff. One of the easiest ways to load a die is to add weight to one face, usually by putting something small and dense (like a piece of metal) in the face you want to have land down. So you can look for imperfections in the regularity or color of the surface, which might indicate that the face was drilled out and then patched.

 

Adding weight to a particular face will also add weight to the die overall. You might not be able to tell if you're working with just your hands, but a sufficiently precise scale might find a difference. You can also change the shape of a die to make it more or less likely that it will land on a set of faces. That means the dimensions of the dice will be different from an unaltered die, and you could use a ruler or (better) a set of calipers to check that.

 

Unfortunately, because of the way the dice are manufactured, the tolerances are going to be fairly broad--that is, two completely normal dice from a newly-unwrapped core set could have different weights and dimensions.

 

(3) I know you already went over this, but it seems like you're just telling people that no one will know if they cheat!

 

Well, that's probably true. In fact, it's perfectly possible that you've already played against a cheater, and didn't know it! But my saying so isn't going to change anything about the game, and bringing it up also gives me the chance to bring up the solution: get in the habit of asking your opponents to share a set of dice, or to share a single instance of the FFG dice app. That way you're protected from the start, and it doesn't require you to single anyone out.

Salt water floating the dice will not work to prove anything.  Someone on here x-rayed or mri'd their dice and there were bubbles in different spots.  The spot that floats to the top will always be where the air bubble is closest to the edge.  You can also see this from the transparent dice ffg gave out.  They are not perfect.  I would even go so far as to say that even weighing the dice would not be truly accurate to indicate anything other than a wide variance in manufacturing of said dice.

 

I believe I have seen "cooked" dice in that they were deformed on one of the sides with a hit on it(not smooth).  These dice didn't provide the player with any perceived advantage anyway over the course of numerous games with them.

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