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[lawastooshort]

Hello! I wondered if anyone could help (also hello, this is my debut thread in general discussion!)


This is a simple question I think, but I’m having trouble working it out through a sleepy haze, and the poorly remembered maths of my youth is not helping.

I want to know how to work out if a series of d6 dice rolls is really worse than the expected results.

Particularly, I want to know how many times you have to roll a d6 to be able to say that, e.g. getting an average of 2.5 is definitely unlucky, and isn’t just happening because you haven’t rolled enough dice to get to the average.

Does that make sense? I’m having doubts.


This is all because of Bloodbowl.

Say I rolled 100d6 with an average of 3.6, that’s very reasonable. But if my opponent rolls 25d6 with an average of 2.5, have they been unfairly treated by the dice? Or is it not enough dice to be able to say.


(Really what I want is a formula or something  where I can put in the number of dice rolled and the results and press a button and go, aha! it was all nice and fair! Or not. With, say, a 95% confidence interval.)

(should this count as Life Advice?)

[Reelya]

Luck isn't a thing. It's just a name we give to the unknown. So there's no way to answer the question. What is luck even? If we can't answer that then how can we begin to quantify how lucky someone is? If you roll one dice and it's 1-3 you were unlucky, and the guy who rolled 4-6 was lucky. Per roll. Each roll's odds are independent of the last one. So having a bad streak does not change the odds of subsequently having a good or bad streak again.

If you think that the dice are somehow discriminating lucky vs unlucky people, well nobody has ever been able to prove anything like that in any controlled situations, and there has been plenty of research. Nobody has ever shown that specific people having a good or bad streak affects their subsequent dice rolls. And if you could prove that (the existence of an unknown luck force), well you'd probably get a Nobel Prize.

People believe in good or bad streaks, but this is probably confirmation bias. We remember the times we kept winning, and the times we kept losing, but we forget the times that we won a bit and lost a bit. Again, nobody has ever shown any existence of lucky or unlucky streaks in any lab setting testing probabilities. If one person rolls an average of 3.6 and the other person rolls an average of 2.5, this does not change the odds of them rolling high or low in subsequent rolls. Hence, you cannot say the 2.5 guy is provably unlucky. If you wrote down every single dice roll for both players you'd probably find that they're not as far apart over many rolls as you think.

If you want to quantify how good/bad you rolled then you need to work out the odds of rolling what you got. You're best off doing this with a computer for large amounts of dice.

[Frumple]

... pretty sure the OP isn't aiming for anything as fancy as that, ree. Sounds like they just want to know how you check if (/to what extent) a RNG is biased or not. Which computer RNGs often are, just as dice can be loaded or whatev'.

Far as I can tell, OP, your answer depends on the RNG that's being used. 25d6 or 100d6 might not be a big enough sample size to be able to tell if the RNG the game's using has gone wonky or not.

In any case, there's apparently resources online that could help you look into the question, OP. I'd start with google and check stuff like this (which I've only skimmed, and it being a quarter till five int the morning and me not really being a math person, can't tell you how good an overview it is), which links a .pdf that gives a bit of an overview for some methods of RNG testing. Then you'd probably have a go with calculator or spreadsheet or somethin'.

[Reelya]

I thought we were talking Bloodbowl the board-game. Presumably people are rolling the same dice that came with the set. OP was specifically asking about one specific person the dice were unfair to, not that a specific set of dice were wonky.

Either way, computer game RNGs could be broken, but should not be any different for each player.

[Frumple]

With real dice, you'd just check to see how biased the dice are (which they all are, it's just a matter of how much -- the good ones take many hundreds of rolls before the bias becomes evident, and aren't terrible biased anyway) and how many rolls it takes to determine that bias, and then see if either person is out of line, so far as I can tell.

Stuff online about loaded dice'll give most of the resources someone needs to work out how to do that, it would seem.

As to the RNG giving different results for different people, screwed up RNG code can definitely do that and pretty trivially. S'as simple a matter of some nitwit including player number in the formula, or something as silly as that. Is one of the reasons people check to make sure :V

[Tack]

Luck isn't a thing -snip-

I dunno. I have a friend who consistently rolls under the curve.
He uses the same dice as I, so it can't be a weight thing. Therefore the only other impact on the fall of the dice is the throw.
I'd wager that a good physics AI could throw a die to get a roll 10 times out of 10. But people etc etc. You know where I'm going with this.

I'd like to think that if a person consistently throws random dice in a random pattern and gets a negative outcome, then luck is real.

[Xantalos]

Or his throw is shit.

[MrWiggles]

Yea, but you can't really tell if the RNG of a computer game is acting weird either because how its RNG'ing those numbers is hidden. It also probably isn't behaving as the definition for random you want.   Most RNG's tend to be weighted.

And humans are also pretty terrible at being able to recognize what is random. Random doens't look like how we intuitively want random to look like.

Anyway...
For OP question.

There are plenty of dice rolling engine out there that can show ya. Though you can do it be hand, in a very tedious fashion.

So the number of combination that any group of dice can make, is 6 to the power of number dice rolled.
So for two d6 (6^2), the the total number of combination is 36. There are 36 different combinations that two d6s can make, with a range of 2-12 for their total.

And then you can work out the 2d6 bell graph yourself pretty easily. Get a piece of paper, and then we're gonna make a bar graph. List the bottom the values between 2 through 12. And then record how many dice combination make those values.

So for 2, there is only one combination of the 2d6 that make 2. Snake Eyes. Then for 3, there is two combination of dice that make 3. One pip and Two Pip, and Two Pip, and One Pip. And for 4 there are three different combination that total 4. One Pip, Three Pip. Three Pip , One Pip. Two Pip, Two Pip.

So on and so forth.

And this bar graph will illustrate the bell curve of the probability of 2d6. Just draw a snakey line over the top of the bars. It'll make a rough bell shape.

[lawastooshort]

Thanks for the replies.

Sounds like they just want to know how you check if (/to what extent) a RNG is biased or not. Which computer RNGs often are, just as dice can be loaded or whatev'.

So it’s not so much is the RNG biased overall or long term, but is the selection of results one person got biased, or rather, “unlucky”

Far as I can tell, OP, your answer depends on the RNG that's being used. 25d6 or 100d6 might not be a big enough sample size to be able to tell if the RNG the game's using has gone wonky or not.

That’s kind of one of the questions – I wonder what sample size I’d need to be able to say that being 1 lower than the average of 3.5 is as it were statistically significant and therefore definitely “unlucky”


So can someone say, “oh, the dice were against me” and to be 95% sure, or did actually they not roll enough dice to be able to be sure?

I fear I may now spend my lunch and beyond trying to make a graph of x = dice rolled and y = variation from the mean at which point it can be shown to be 95% definitely unlucky.

[Tack]

Just like that, we've charted the luck stat.
Those hatchling sexers better take a step back.

[Reelya]

Well in stats, the confidence interval is actually the probability that the average falls in a certain error range. So the result is defined by these three numbers - the average, the confidence rating and the confidence interval (error margin).

If you want to apply stats theory to luck in dice, you take all the existing dice rolls and apply regular statistics to estimate a 95% confidence interval on your existing dice rolls. If the error range doesn't contain the correct mean of 3.5 then you can say you are 95% sure that this set of dice rolls were lucky or unlucky. But I think that won't actually prove anything about whether this streak of rolls will continue.

[lawastooshort]

Excellent, thank you!

I think you’ve made clear what I was getting confused about – so I can at least now work out that given the dice rolls and their number, they were (or most probably weren’t) statistically significantly bad, and therefore you can’t complain.


Now I might be able to work out how to turn this into a useful/less graph.

Of course, I know it doesn’t really prove anything, but it was gnawing at me.

[MrWiggles]

Penn Jillette, of the magician dou Penn and Teller, I think said it best. "Luck is statics taken personally."