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So how does dice probability work in a group of gamers? Do the rolls average out across the group, or do you get a bigger "x" amount of gamers rolling high/low?

If you use a block of chessex dice, you tend towards low-rolling.

There's an article in the wiki that explains why.

Redbeard wrote:If you use a block of chessex dice, you tend towards low-rolling.

There's an article in the wiki that explains why.

Really? I can't find a link to that.

If the dice are properly balanced then you should get the average roll working out being in the middle. If certain gamers average out rolling higher numbers something's not right. Your standard d6 should have equal odds of landing any face up, so that the mean should be 3.5, if you roll enough dice and work out the mean it should be pretty close to this. In the same way only 1/6th of your rolls should result in a 6.

Rolling with two dice has diffent odds, there are 36 permutations, only one of these is a double 6 and only one is a double 1, ie. 1/36 chance. The most common result is a total of seven, for which there are 6 possibilities, ie 6/36 or 1/6.

So based on that the difference between someone at Ld 6 with someone at 7 is much greater than between 9 and 10. To pass at Ld 6, you have to roll 6 or under, so you need any one of 15 of the 36 permutations (41%), at Ld7 you need any of 21 permutations (58%). So the probability difference between those is 17%.

But at Ld 9 you need any of 30 of the 36 permutations (83%) and at Ld 10 (92%). The difference is 9%.

So if you have a unit of Ld 6 and a unit of Ld 9 and have enough points to upgrade one unit a point of Ld, pick the one with Ld6 they make the greatest gain statistically.

Game Workshop dice roll lowest of all. They are NOT properly balanced. All non-sharp edged dice with recessed spots tend to roll lower than sharp edged casino dice.

mikeguth wrote:Game Workshop dice roll lowest of all. They are NOT properly balanced. All non-sharp edged dice with recessed spots tend to roll lower than sharp edged casino dice.

Interesting if correct. Do they have restrictions on the dice used at tournaments?

The article is available on The Google but I don;t have time to search for it now.

Basically an engineering professor made his students make an automatic dice rolling machine and check the results of thousands of rolls.

Round cornered disc (like Chessex) tend to roll low.

For full rolling accuracy you need Las Vegas casino dice.

This is why so many games are moving to D10's.

Good thing my grandfather was a dice collector. Being the only gamer in the family, I inherited his collection several years ago (never realising that this was a hobby of his) and have numerous sets of dice from Vegas - as well as authentic ivory dice. I'll make sure to use those (gently!) instead of the numerous round-edged dice I usually play with.

warpcrafter wrote:This is why so many games are moving to D10's.

Which wouldn't actually help at all, since D10s can roll just as erratically, and you can't even get perfectly-balanced ones.

I use the Vegas Casino dice. Had my fill of Chessex little dice. The ones where you get 36 on a cube.

They are pricey, $5 for 2 retired Vegas dice. I bought 10 sets.

The D10s and other dice would be studied the same way as the D6s. The trouble is, there is no Casino quality source of non-cubical dice. I suppose a market for them could be created if it was shown that the types available now are biased like D6s are.

But how many wargamers use Casino dice?

There's a reason why in Vegas you have to bank the casino dice off the opposite wall: it is way too easy to "drop" the casino dice - and they tend to drop flat and not roll.
Not saying anything about anyone in particular - but I saw lots of cupping and dropping at the LVGT with casino dice. (No one I played against.)

Casino dice are not the answer. And while Chessex dice have historically rolled slightly lower - it's not significant. Yes, in a perfect world every pip would have an equal 16.6666_% chance of hitting. With Chessex dice, the 1 has a 16.68% chance and the 6 has a 16.65% ... woohoo, big diff.

To the OP: are you asking if probability somehow changes when you change the sample size? A die roll is a discrete event with no memory, so your opponent isn't more likely to roll 1's and 2's because you've been rolling all 5's and 6's.

Why would round dice with carved out dots roll lower? Wouldn't the six weigh the least and therefore come up most often?

ShumaGorath wrote:Why would round dice with carved out dots roll lower? Wouldn't the six weigh the least and therefore come up most often?

It's really just a myth, I suspect the margin of error on the study was much larger than the 0.02% difference in 1 vs. 6 rolls

Actually no. IIRC, there was this guy on Warseer who actually tested this out. He rolled a standard GW dice (with pips and curved edges) and then he done the same with a casino dice (pipless & square).
to explain Shuma's question... Standard GW dice have pips - wholes drilled out in them to indicate numbers. Now imagine you roll a dice. You let it go and when you do, it picks up the air and traps it in the pips. Now, don't forget about curved edges - they make the dice spin, jump and do all sorts of gymnastics. Which leads to the air not being able to leave the pips, as there's moving air all around it. Almost like you not being able to drive onto the main road because of traffic. Now, some people already could've worked it out. think you're not cheating? Well, the Dice Gods are. Why? Because they're weighing down each side. And since air does have weight, it weighs the side with the "6" on it the most. And what's on the other end of the 6? 1...which is also the lightest side, and therefore comes up most often.
Another thing I didn't mention, is that stjon said, in a perfect world every side would have a 16.666% chance of rolling. In GW dice, 1 has an AVERAGE 30% chance of rolling. And Casino dice, have an avergage 16% chance. why 16% and not 16.666%? Because Casino dice are fragile, and the sharp bits in the corners often snap off, making slight imperfections. So it's not exactly a pink world.
So, to sum up. Pips are bad. Curves aren't that bad, but pips + curves = very bad. Which also makes Casino dice most fair dice in the world - no pips means no weighing down, and no curves - no rolling of the table .



P.S. Please realise, that the "technical data" I'm putting down is what I can remember from the thread on Warseer.

Here is the study. The difference between a result of 1 and a result of 6 is not only .02%, as claimed by Mike McSomething. The probability of rolling a 1 is also not a dramatic 30%, as claimed by NoobLord. The study found it to be about 19%. [edit: Sorry, I'm wrong, the GW dice did have a 29% chance of rolling a 1. Square dice with pips had a 19% chance. Sorry for misreading.]

http://www.dakkadakka.com/wiki/en/That%27s_How_I_Roll_-_A_Scientific_Analysis_of_Dice

stjohn70 is right about casino dice rolling badly. However, it is possible to get smaller precision dice with rounded corners that roll better on small surfaces. Dice of this kind are made for backgammon and are typically even more expensive than casino dice.

take this for what its worth. for my birthday my brother bought me the BIG GUNS DICE (GW style) for my renegades. they are massive dice. we have both noticed that if those dont get a long roll, they tend to roll super low all the time. so throwing them on our game table i almost always miss and die lol. but the odd thing is if i toss them on the floor and they are allowed to actually roll alot then the outcome is normal.
also we use alot of little die for tons of attacks and whatnot. those work opposite of the big ones. if they roll only a couple times you usually like the outcome. where as if they roll a bunch of times over then you end up cursing them :S

Without any sort of analysis of margin of error or deviation then the study is lacking is anything that makes it really usable - if anyone wants to plot a geometric distribution of his numbers vs. the expected results or something to get the actual probability of experiencing his results vs. the probability of that happening on hypothetical "Perfect 16.6666%" dice then that would be much more useful.

I should also note that my .02% number was taken from the post above mine.

It's ALSO important to note that saying "If I get 1000 dice and roll them, 1000x16.666% of them will come up as each number." is a common fallacy - that is the median expectation, such that roughly 50% of the time you will have higher results, and roughly 50% of the time you will have lower results.

I'm no expert but there's no way such a huge discrepancy from the expected results isn't significant when the sample size is in the tens of thousands.

It's less than a 3% difference, and we don't even know if dice position pre-roll and the strength/direction of the roll itself were even properly controlled for.

I was wrong about the 3% difference, I misread. The expectation of rolling a 1 was found to be about 29%, not 19%.

With n trials, each of which has a probability p of success, the probability of getting exactly m successes is

P = C(n,m) p^m (1-p)^n

where C(n,m) = n! / [m! (n-m)! ] is the binomial coefficient.

With 1000 rolls of a fair dice, the probability of rolling 29% or more 1s is of the order 10^-22. This is found by computing P for n = 1000, p = 1/6 and summing over m = {290, 291, 292, ... 1000}.

So the probability that a fair dice will yield at least 29% 1s in 1000 rolls is negligible. The study used not 1000 rolls, but 144000 rolls. I don't feel like waiting for my computer to calculate the sum with n = 144000, but at this point it's clear that the result is statistically significant and we can draw at least one simple conclusion: GW dice are not fair dice.

And like I said, 'median expectation' is not 'expected results' it's 'predicted results that will be too low half the time and too short half the time'

shirou wrote:I was wrong about the 3% difference, I misread. The expectation of rolling a 1 was found to be about 29%, not 19%.

With n trials, each of which has a probability p of success, the probability of getting exactly m successes is

P = C(n,m) p^m (1-p)^n

where C(n,m) = n! / [m! (n-m)! ] is the binomial coefficient.

With 1000 rolls of a fair dice, the probability of rolling 29% or more 1s is of the order 10^-22. This is found by computing P for n = 1000, p = 1/6 and summing over m = {290, 291, 292, ... 1000}.

So the probability that a fair dice will yield at least 29% 1s in 1000 rolls is negligible. The study used not 1000 rolls, but 144000 rolls. I don't feel like waiting for my computer to calculate the sum with n = 144000, but at this point it's clear that the result is statistically significant and we can draw at least one simple conclusion: GW dice are not fair dice.

You can't draw that one simple conclusion at all - You're only correct as long as we assume he properly controlled for the conditions of the 144,000 dice pre-roll and the way they were rolled. Without seeing any peer review, and his methodology being explained as "We kept the dice seperate and had the students roll them alot", and the study failing to point out anything other than "I got this and I assumed I should have gotten the median expectation" I'm going to make the likely assumption and not use this study to prop up my dice superstition.

This isn't to say that 30% isn't extremely significant, but anyone doing rigorous testing would look at that and immediately ask why the deviation is so large, and upon discovering such a massive divergence from expectations it isn't unreasonable to assume that repeating the trial more than once with multiple controls would be appropriate.

NoobLord wrote:Actually no. IIRC, there was this guy on Warseer who actually tested this out. He rolled a standard GW dice (with pips and curved edges) and then he done the same with a casino dice (pipless & square).
to explain Shuma's question... Standard GW dice have pips - wholes drilled out in them to indicate numbers. Now imagine you roll a dice. You let it go and when you do, it picks up the air and traps it in the pips. Now, don't forget about curved edges - they make the dice spin, jump and do all sorts of gymnastics. Which leads to the air not being able to leave the pips, as there's moving air all around it. Almost like you not being able to drive onto the main road because of traffic. Now, some people already could've worked it out. think you're not cheating? Well, the Dice Gods are. Why? Because they're weighing down each side. And since air does have weight, it weighs the side with the "6" on it the most. And what's on the other end of the 6? 1...which is also the lightest side, and therefore comes up most often.
Another thing I didn't mention, is that stjon said, in a perfect world every side would have a 16.666% chance of rolling. In GW dice, 1 has an AVERAGE 30% chance of rolling. And Casino dice, have an avergage 16% chance. why 16% and not 16.666%? Because Casino dice are fragile, and the sharp bits in the corners often snap off, making slight imperfections. So it's not exactly a pink world.
So, to sum up. Pips are bad. Curves aren't that bad, but pips + curves = very bad. Which also makes Casino dice most fair dice in the world - no pips means no weighing down, and no curves - no rolling of the table .



P.S. Please realise, that the "technical data" I'm putting down is what I can remember from the thread on Warseer.

Doesn't that imply that air is heavier than the plastic used in these dice? An air pocket will not increase the weight of whatever surrounds it unless the air itself is somehow more dense than the surrounding atmosphere (pressurized or cold air). If the study was accounting for drag coefficients and not weight than I can wrap my head around it, though the math would be highly suspect. However the mass of the air within the sixes pips is not logically dense enough to cause the six to orient itself downwards. This still doesn't make a whole lot of sense to me.

MikeMcSomething wrote:You can't draw that one simple conclusion at all - You're only correct as long as we assume he properly controlled for the conditions of the 144,000 dice pre-roll and the way they were rolled. Without seeing any peer review, and his methodology being explained as "We kept the dice seperate and had the students roll them alot", and the study failing to point out anything other than "I got this and I assumed I should have gotten the median expectation" I'm going to make the likely assumption and not use this study to prop up my dice superstition.

I don't know what this "median expectation" you keep talking about is. There's the median, and there's the expected result, but I don't think there is such a thing as a median expectation. Seriously, mathworld doesn't have a definition for this term. It doesn't exist.

The person conducting the study did not assume he should have gotten anything; he simply recorded what he did get. My calculation above shows that the result he got would be ridiculously improbable with fair dice. Simplest conclusion: the dice aren't fair.

And no, he did not take special measures to control for the various forces that act on a dice as it is being rolled. He just rolled them (or rather, his students rolled them), much like we do when we play a game. That is the condition under which the results are most relevant.

shirou wrote:I don't know what this "median expectation" you keep talking about is. There's the median, and there's the expected result, but I don't think there is such a thing as a median expectation. Seriously, mathworld doesn't have a definition for this term. It doesn't exist.

The person conducting the study did not assume he should have gotten anything; he simply recorded what he did get. My calculation above shows that the result he got would be ridiculously improbable with fair dice. Simplest conclusion: the dice aren't fair.

And no, he did not take special measures to control for the various forces that act on a dice as it is being rolled. He just rolled them (or rather, his students rolled them), much like we do when we play a game. That is the condition under which the results are most relevant.

They aren't the most relevant to his study, since his study isn't "Which rolls do players at a 40k table probably get more" it's "Which dice are/aren't more likely to roll certain numbers, and if they are what combination of gravity, force, and manufacturing defects gets them to behave in that manner" - if your study is taking into account things like miniscule air pockets but not the condition of the die before it was rolled there is a problem.

"Median expectation" in that post is a big error from my proofing the post, it should read "I got this and expected to get the median"