edited to include the later discussion and corrected p-values:

Here are the results after 1002 rolls (batches of 6):

Observed: 420 evades, 248 focus, 334 blanks

Expected: 376 evades, 250 focus, 376 evades

Chi-statistic = 9.87

p-value = 0.00719

......

If we're strictly looking at blanks:

Observed: 668 evades/focus, 334 blanks

Expected: 626 evades/focus, 376 blanks

Chi-statistic = 7.42

p-value = 0.00645

Here are the results from the first 504 rolls (yes, I'm compulsive):

Observed: 204 evades, 137 focus, 163 blanks

Expected: 189 evades, 126 focus, 189 blanks

Chi-Squared Test: this page for reference ( http://www2.lv.psu.edu/jxm57/irp/chisquar.html )

(204-189)^2 / 189 + (137-126)^2 / 126 + (163-189) ^ / 2 = 1.190 + 0.960 + 3.577 = 5.727 so our chi^2 value = 5.727. Generally people use the p < 0.05 value for significance. Our degrees of freedom is 2 (3 possibilities - 1). So using that Table B.2 chart we are between p < 0.10 and p < 0.05. So we're close to it being significant, but we accept that it's in the 'range of acceptable deviation'. There's somewhere between a 10-5% chance of this happening 'by chance alone'. If you roll a few hundred more, it may shift a little.

Conclusion: its close to being able to be rejected as non-fair, but isn't given our picked 5% chance basis for rejecting.

Edit: The 1002 rolls, I get a chi^2 value of 9.85 -- so that puts it p < 0.01 so we can reject that as a fair die.

Yeah that 1000 rolls is way more conclusive.

Those dice are biased with 99% confidence.

I brute-forced the probability distribution at 504 rolls and 1002 rolls, looking at only the evades (counting blanks and focus as a single result).

With 504 rolls, the probability of fair dice rolling at least 204 evades is 9.15%.

With 1002 rolls, the probability of fair dice rolling at least 420 evades is 0.2274%.

This says essentially the same thing as the Chi-Squared test, but stated this way may be slightly more intuitive to understand.

Story time...

Back in December, a bunch of our local players including myself bought third-party dice from the UK. They're the translucent ones with symbols copied from official FFG dice.

They look like the 2014 Regionals dice except for two key differences:

1. No air bubbles

2. Edges and corners are more rounded

It took me 1 attempt to roll this...

My very first game with them, I rolled insanely hot. I didn't think anything of it because that's just how dice work sometimes. My opponent, clearly frustrated by my luck, jokingly says to me

"Your dice were unreal. Are you sure they're not weighted?"

he proceeds to pick up my 6 green dice

rolls 6 evades

That was the first incident that gave me an inkling of a feeling that something was wrong. My thought process at the time was that because they're perfectly translucent and have no air bubbles (inclusions), how could the dice possibly be weighted? So I continued using them for a few months, rolling really well, and brought them out to our local league's playoff match. In that one game, I rolled a ridiculous number of crits - when the video is finally posted, I can post the actual numbers.

Despite paying for them, I shelved the dice after that game. That's just how bad it was. Since December, other players with these dice have noticed the same thing. They roll insanely hot, and blanks are very uncommon. In our group, some players are now asking their opponent to share these dice or not use them at all.

So what makes these dice broken if there are no air bubbles?

It is my opinion that the lack of inclusions is exactly the problem . If you look at the 2016 white Regionals dice, you'll notice that the air bubbles tend to be towards the double-blank area of the die. I've confirmed that in 4 of 6 of my green Regionals dice, there is an increased buoyancy or decreased density specifically in the double-blank corner. I used the salt water test, kept dropping the dice straight down, letting it flip, then repeating until it no longer flipped for consecutive drops.

At first, this was pretty alarming especially since there were whispers that the 2016 Regional dice roll like crap because of all the inclusions (which seem to be much larger than the 2014 Regional dice). So I tested my core set dice too. It turns out 6 of 9 were also weighted towards the double-blank area.

Inclusions tend to be towards the double-blank corner.

So why is that? Well, I think it's because FFG is accounting for the missing material when engraving symbols and is actually trying to balance the dice with inclusions. The faces with engraved symbols on them weigh less due to the material that's missing (although the density is unchanged) relative to the blank faces, especially the double-blank side. That means in order to balance the weight of the faces , you want air bubbles to be towards the blanks.

And that's where the 3rd party dice are flawed. Lack of inclusions on solid dice weights the blanks towards the bottom. I don't know how exactly that works out on the red dice because the blanks are opposite to each other, but the green dice roll like aces for sure. To make matters worse, these dice have rounded edges and corners, making them much more susceptible to flipping.

I'm not accusing these dice of being intentionally weighted. It's just that they don't account for the weight differences due to the engravings.

Please note that these are just my opinions based on my own observations. I play a lot of X-wing, and others have noticed the same thing with these dice - but I can't scientifically prove this beyond my own salt water testing.

TL;DR - if your opponent is using third-party dice without inclusions, I would recommend asking to use his/her dice that game to be safe.

Interesting, no one here uses 3rd party dice but i will keep an eye on it.

To note my 2016 regional dice seem to roll fairly average for me.

Those dice were in sale at UK Nats. I think a lot of people were a bit miffed they bought shiny dice then walked over to the tournament and were told they couldn't use them.

Now pls calculate the force with which dice are rolled and then think about the weight difference on one of the sides with 0.0001 gramm less.

Then those people are a bit silly as there should have been no expectation those dice would be useable.

I very much doubt that the manufacturing process is accurate enough to make the dice reliably fair. If you're concerned about your opponent's dice, that's why the clause in the tourney rules exists for you both to share a set.

Now pls calculate the force with which dice are rolled and then think about the weight difference on one of the sides with 0.0001 gramm less.

When you roll a die, it doesn't just flip once and slam down on a result.

It rolls many times until the force dissipates to a level so low that it doesn't have enough to flip again.

At that stage, or where a die is on the brink of flipping; an air bubble does have a big effect.

You're not comparing the force of your arm to the air bubble. You're looking at the effect of major inclusions on a die that is on the brink of flipping on its final roll. If it's weighted away from blanks, you're not getting a blank.

I have purchased a similar set in May this year, 6 red and 6 green. I've played in several tournaments and local games. In my last 2 tournaments I specifically mentioned to players how many blanks I rolled, so much so that I actually wanted to take my original dice out to play with.

Maybe it's a batch thing but I have not had "hot" dice like you mentioned. In fact, in my opinion fairly average rolls.

I'll happily share them with anyone interested whilst playing.

You did the fair thing, choosing not to use them when you suspected they were unfair.

I am wondering if your first game was a casual one or in a tournament.

Also - did anyone at the league playoff question the dice?

I'm not sure if it is intentional weighting or adding of air pockets by FFG, since the dice I've seen rarely look exactly the same. I would be very surprised if FFG could control the process that precisely.

If there is difference in rounding of edges and corners, then that may attribute more to one side being likely to come face up than another.

You did the fair thing, choosing not to use them when you suspected they were unfair.

I am wondering if your first game was a casual one or in a tournament.

Also - did anyone at the league playoff question the dice?

I'm not sure if it is intentional weighting or adding of air pockets by FFG, since the dice I've seen rarely look exactly the same. I would be very surprised if FFG could control the process that precisely.

If there is difference in rounding of edges and corners, then that may attribute more to one side being likely to come face up than another.

The first game was at a tournament.

The dice quickly got a reputation for rolling hot, so it only took a few months and most of our league players have shelved them.

You're right that the inclusions are never the same so it's unrealistic to say that FFG's quality control is that precise. And to your point, a third of the dice weren't weighted towards

But I'm telling you, for that other 2/3 of dice... With some of the core set dice, they were so clearly less dense on the double-blank side that I only had to drop them once or twice because they flipped so hard toward the blanks.

I recommend people who are curious to try the test themselves. Make sure you use a smaller cup so you don't need a mountain of salt.

Now pls calculate the force with which dice are rolled and then think about the weight difference on one of the sides with 0.0001 gramm less.

When you roll a die, it doesn't just flip once and slam down on a result.

It rolls many times until the force dissipates to a level so low that it doesn't have enough to flip again.

At that stage, or where a die is on the brink of flipping; an air bubble does have a big effect.

You're not comparing the force of your arm to the air bubble. You're looking at the effect of major inclusions on a die that is on the brink of flipping on its final roll. If it's weighted away from blanks, you're not getting a blank.

Even if the force goes down through bumbing on the table and in the situation you are describing the orientation of the die towards the surface is very random because of those bumps/jumps of the die before the force dissipates. So while you are correct that the force gets less and less i still doubt that little off balance at the end of a roll will do much about the overall roll.

Of course i didnt calculate it. But the effect you describe is still very slim if you look at how many possible ways the die could have turned before that even coming into effect. Also i think it will effect only a tiny amount of rolls that if you take away everything else, like friction and all the other forces, exactly the amount of off weight will influence the die tipping over. Its still only one effect of many.

Now pls calculate the force with which dice are rolled and then think about the weight difference on one of the sides with 0.0001 gramm less.

When you roll a die, it doesn't just flip once and slam down on a result.

It rolls many times until the force dissipates to a level so low that it doesn't have enough to flip again.

At that stage, or where a die is on the brink of flipping; an air bubble does have a big effect.

You're not comparing the force of your arm to the air bubble. You're looking at the effect of major inclusions on a die that is on the brink of flipping on its final roll. If it's weighted away from blanks, you're not getting a blank.

Even if the force goes down through bumbing on the table and in the situation you are describing the orientation of the die towards the surface is very random because of those bumps/jumps of the die before the force dissipates. So while you are correct that the force gets less and less i still doubt that little off balance at the end of a roll will do much about the overall roll.

Of course i didnt calculate it. But the effect you describe is still very slim if you look at how many possible ways the die could have turned before that even coming into effect. Also i think it will effect only a tiny amount of rolls that if you take away everything else, like friction and all the other forces, exactly the amount of off weight will influence the die tipping over. Its still only one effect of many.

Take weighted dice to Vegas, and then use your explanation to let them allow you to use them.

If the weight only effects 1 dice per round or every 2 rounds or every 3 rounds that is huge, that could be as strong as palpatine.

Do some math! 1000 rolls!

Do some math! 1000 rolls!

Might take you up on that.

Dice in Vegas are engineered for precision, unlike X-Wing (or any other 'casual' gaming dice) - and they are very much more expensive than what we play with. Anomalies are an accepted part of the components, just like the variations in movement templates. And the rules have been adjusted to take into account any potential advantages granted by these variations by virtue of shared components.

Some official FFG out of the box dice -seem- to be better than others, but I've found (with all my dice) that luck tends to even out. Some games it seems I can't miss nor be hit, while I've had others wherein the exact opposite is true. Using both official and third party dice. And I have always offered the use of my dice to my opponent, even before the rule change. Especially if they seemed to be rolling exceptionally well for me.

Intentional manipulations is a different matter entirely, of course.

Now pls calculate the force with which dice are rolled and then think about the weight difference on one of the sides with 0.0001 gramm less.

When you roll a die, it doesn't just flip once and slam down on a result.

It rolls many times until the force dissipates to a level so low that it doesn't have enough to flip again.

At that stage, or where a die is on the brink of flipping; an air bubble does have a big effect.

You're not comparing the force of your arm to the air bubble. You're looking at the effect of major inclusions on a die that is on the brink of flipping on its final roll. If it's weighted away from blanks, you're not getting a blank.

Even if the force goes down through bumbing on the table and in the situation you are describing the orientation of the die towards the surface is very random because of those bumps/jumps of the die before the force dissipates. So while you are correct that the force gets less and less i still doubt that little off balance at the end of a roll will do much about the overall roll.

Of course i didnt calculate it. But the effect you describe is still very slim if you look at how many possible ways the die could have turned before that even coming into effect. Also i think it will effect only a tiny amount of rolls that if you take away everything else, like friction and all the other forces, exactly the amount of off weight will influence the die tipping over. Its still only one effect of many.

Take weighted dice to Vegas, and then use your explanation to let them allow you to use them.

If the weight only effects 1 dice per round or every 2 rounds or every 3 rounds that is huge, that could be as strong as palpatine.

They are making money of of it so yes every little bit off statistics count. We are playing a game. and i still highly doublt it would be even one die each game.

Now pls calculate the force with which dice are rolled and then think about the weight difference on one of the sides with 0.0001 gramm less.

When you roll a die, it doesn't just flip once and slam down on a result.

It rolls many times until the force dissipates to a level so low that it doesn't have enough to flip again.

At that stage, or where a die is on the brink of flipping; an air bubble does have a big effect.

You're not comparing the force of your arm to the air bubble. You're looking at the effect of major inclusions on a die that is on the brink of flipping on its final roll. If it's weighted away from blanks, you're not getting a blank.

Even if the force goes down through bumbing on the table and in the situation you are describing the orientation of the die towards the surface is very random because of those bumps/jumps of the die before the force dissipates. So while you are correct that the force gets less and less i still doubt that little off balance at the end of a roll will do much about the overall roll.

Of course i didnt calculate it. But the effect you describe is still very slim if you look at how many possible ways the die could have turned before that even coming into effect. Also i think it will effect only a tiny amount of rolls that if you take away everything else, like friction and all the other forces, exactly the amount of off weight will influence the die tipping over. Its still only one effect of many.

Take weighted dice to Vegas, and then use your explanation to let them allow you to use them.

If the weight only effects 1 dice per round or every 2 rounds or every 3 rounds that is huge, that could be as strong as palpatine.

They are making money of of it so yes every little bit off statistics count. We are playing a game. and i still highly doublt it would be even one die each game.

Excellent we have your highly doubt to counter the OP's experience of his dice rolling extremely hot every game for several months.

Now pls calculate the force with which dice are rolled and then think about the weight difference on one of the sides with 0.0001 gramm less.

When you roll a die, it doesn't just flip once and slam down on a result.

It rolls many times until the force dissipates to a level so low that it doesn't have enough to flip again.

At that stage, or where a die is on the brink of flipping; an air bubble does have a big effect.

You're not comparing the force of your arm to the air bubble. You're looking at the effect of major inclusions on a die that is on the brink of flipping on its final roll. If it's weighted away from blanks, you're not getting a blank.

Even if the force goes down through bumbing on the table and in the situation you are describing the orientation of the die towards the surface is very random because of those bumps/jumps of the die before the force dissipates. So while you are correct that the force gets less and less i still doubt that little off balance at the end of a roll will do much about the overall roll.

Of course i didnt calculate it. But the effect you describe is still very slim if you look at how many possible ways the die could have turned before that even coming into effect. Also i think it will effect only a tiny amount of rolls that if you take away everything else, like friction and all the other forces, exactly the amount of off weight will influence the die tipping over. Its still only one effect of many.

Take weighted dice to Vegas, and then use your explanation to let them allow you to use them.

If the weight only effects 1 dice per round or every 2 rounds or every 3 rounds that is huge, that could be as strong as palpatine.

They are making money of of it so yes every little bit off statistics count. We are playing a game. and i still highly doublt it would be even one die each game.

Excellent we have your highly doubt to counter the OP's experience of his dice rolling extremely hot every game for several months.

I just state my opinion about how physics work out here. Everyone can read it or ignore it.

His observation has nothing to do with the facts of if this minor difference in dice actually has any effect. You can believe it or and you can think about what i wrote or let it be. Saying that his observations even if its over several month is the better truth just isnt correct.

Here are the results from the first 504 rolls (yes, I'm compulsive):

Observed: 204 evades, 137 focus, 163 blanks

Expected: 189 evades, 126 focus, 189 blanks

Anyone do this test on that data?

https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test

Now pls calculate the force with which dice are rolled and then think about the weight difference on one of the sides with 0.0001 gramm less.

When you roll a die, it doesn't just flip once and slam down on a result.

It rolls many times until the force dissipates to a level so low that it doesn't have enough to flip again.

At that stage, or where a die is on the brink of flipping; an air bubble does have a big effect.

You're not comparing the force of your arm to the air bubble. You're looking at the effect of major inclusions on a die that is on the brink of flipping on its final roll. If it's weighted away from blanks, you're not getting a blank.

Even if the force goes down through bumbing on the table and in the situation you are describing the orientation of the die towards the surface is very random because of those bumps/jumps of the die before the force dissipates. So while you are correct that the force gets less and less i still doubt that little off balance at the end of a roll will do much about the overall roll.

Of course i didnt calculate it. But the effect you describe is still very slim if you look at how many possible ways the die could have turned before that even coming into effect. Also i think it will effect only a tiny amount of rolls that if you take away everything else, like friction and all the other forces, exactly the amount of off weight will influence the die tipping over. Its still only one effect of many.

Take weighted dice to Vegas, and then use your explanation to let them allow you to use them.

If the weight only effects 1 dice per round or every 2 rounds or every 3 rounds that is huge, that could be as strong as palpatine.

They are making money of of it so yes every little bit off statistics count. We are playing a game. and i still highly doublt it would be even one die each game.

Excellent we have your highly doubt to counter the OP's experience of his dice rolling extremely hot every game for several months.

I just state my opinion about how physics work out here. Everyone can read it or ignore it.

His observation has nothing to do with the facts of if this minor difference in dice actually has any effect. You can believe it or and you can think about what i wrote or let it be. Saying that his observations even if its over several month is the better truth just isnt correct.

What have you done to verify your theory on his dice?

I believe taking his actual experience over your theory is indeed correct.

While i was posting this he showed actual data showing the dice are indeed hot and would indeed effect the game.

Now pls calculate the force with which dice are rolled and then think about the weight difference on one of the sides with 0.0001 gramm less.

When you roll a die, it doesn't just flip once and slam down on a result.

It rolls many times until the force dissipates to a level so low that it doesn't have enough to flip again.

At that stage, or where a die is on the brink of flipping; an air bubble does have a big effect.

You're not comparing the force of your arm to the air bubble. You're looking at the effect of major inclusions on a die that is on the brink of flipping on its final roll. If it's weighted away from blanks, you're not getting a blank.

Even if the force goes down through bumbing on the table and in the situation you are describing the orientation of the die towards the surface is very random because of those bumps/jumps of the die before the force dissipates. So while you are correct that the force gets less and less i still doubt that little off balance at the end of a roll will do much about the overall roll.

Of course i didnt calculate it. But the effect you describe is still very slim if you look at how many possible ways the die could have turned before that even coming into effect. Also i think it will effect only a tiny amount of rolls that if you take away everything else, like friction and all the other forces, exactly the amount of off weight will influence the die tipping over. Its still only one effect of many.

Take weighted dice to Vegas, and then use your explanation to let them allow you to use them.

If the weight only effects 1 dice per round or every 2 rounds or every 3 rounds that is huge, that could be as strong as palpatine.

They are making money of of it so yes every little bit off statistics count. We are playing a game. and i still highly doublt it would be even one die each game.

Excellent we have your highly doubt to counter the OP's experience of his dice rolling extremely hot every game for several months.

I just state my opinion about how physics work out here. Everyone can read it or ignore it.

His observation has nothing to do with the facts of if this minor difference in dice actually has any effect. You can believe it or and you can think about what i wrote or let it be. Saying that his observations even if its over several month is the better truth just isnt correct.

What have you done to verify your theory on his dice?

I believe taking his actual experience over your theory is indeed correct.

While i was posting this he showed actual data showing the dice are indeed hot and would indeed effect the game.

I would bet with you that if 100 random ppl would also note their dice results over the next 500 rolls that his actual results he posted above are indeed above avarage but a lot of ppl wuld have similar results while most would be closer to the average and several would be as much lower as he is above the average.

Sry its not a prove of his theory. of course i also dont prove my theory because i cant prove it. I neither have the equipment nor the kowledge of the exact physical calculation. Thats why i said my theory is about my knowledge of physics, i didnt even claim to prove it.

I did the test. There is insufficient evidence to say the die is biased at the 95% confidence level.

The chi-squared statistic was 5.72.

It had to be greater than 5.99.

It is biased at a 90% confidence level.

Here are the results after 1002 rolls (batches of 6):

Observed: 420 evades, 248 focus, 334 blanks

Expected: 376 evades, 250 focus, 376 evades

Chi-statistic = 9.87

p-value = 0.00719

If we're strictly looking at blanks:

Observed: 668 evades/focus, 334 blanks

Expected: 626 evades/focus, 376 blanks

Chi-statistic = 7.42

p-value = 0.00645

edit: corrected Chi-square results

Now pls calculate the force with which dice are rolled and then think about the weight difference on one of the sides with 0.0001 gramm less.

When you roll a die, it doesn't just flip once and slam down on a result.

It rolls many times until the force dissipates to a level so low that it doesn't have enough to flip again.

At that stage, or where a die is on the brink of flipping; an air bubble does have a big effect.

You're not comparing the force of your arm to the air bubble. You're looking at the effect of major inclusions on a die that is on the brink of flipping on its final roll. If it's weighted away from blanks, you're not getting a blank.

Even if the force goes down through bumbing on the table and in the situation you are describing the orientation of the die towards the surface is very random because of those bumps/jumps of the die before the force dissipates. So while you are correct that the force gets less and less i still doubt that little off balance at the end of a roll will do much about the overall roll.

Of course i didnt calculate it. But the effect you describe is still very slim if you look at how many possible ways the die could have turned before that even coming into effect. Also i think it will effect only a tiny amount of rolls that if you take away everything else, like friction and all the other forces, exactly the amount of off weight will influence the die tipping over. Its still only one effect of many.

Take weighted dice to Vegas, and then use your explanation to let them allow you to use them.

If the weight only effects 1 dice per round or every 2 rounds or every 3 rounds that is huge, that could be as strong as palpatine.

They are making money of of it so yes every little bit off statistics count. We are playing a game. and i still highly doublt it would be even one die each game.

Excellent we have your highly doubt to counter the OP's experience of his dice rolling extremely hot every game for several months.

I just state my opinion about how physics work out here. Everyone can read it or ignore it.

His observation has nothing to do with the facts of if this minor difference in dice actually has any effect. You can believe it or and you can think about what i wrote or let it be. Saying that his observations even if its over several month is the better truth just isnt correct.

What have you done to verify your theory on his dice?

I believe taking his actual experience over your theory is indeed correct.

While i was posting this he showed actual data showing the dice are indeed hot and would indeed effect the game.

I would bet with you that if 100 random ppl would also note their dice results over the next 500 rolls that his actual results he posted above are indeed above avarage but a lot of ppl wuld have similar results while most would be closer to the average and several would be as much lower as he is above the average.

Sry its not a prove of his theory. of course i also dont prove my theory because i cant prove it. I neither have the equipment nor the kowledge of the exact physical calculation. Thats why i said my theory is about my knowledge of physics, i didnt even claim to prove it.

yes that is how variance works... thanks?

The point is his dice are rolling above average, they should not be used. why are you against this?