I know there are a few college students here.

[denthor]

I have noticed when I toss a single d20 dice it normally comes up with say a 5.

When I toss two dice the number changes more often to something different.

So the question is does throwing more dice really change the probability of different numbers coming up?

Would this be an example of chaos theory?

[Yora]

Every dice is rolled independently from all the others. It does not make any difference whether you roll them one after the other or all at once.

Any differences you see are coincidental, and probably almost entirely observation bias. You don't notice when a result is unremarkable and only take notice when the result seems significant.

[Keltest]

There are a lot of different reasons for why one number would be showing up on a die more often than others. It could be that the die is simply balanced improperly, for example.

It could also just be confirmation bias. You expect the single die to roll a 5 more often, so you take notice more often when it does, and less often when you roll it with another die.

[Segev]

There can also be a major de-randomizing effect based on HOW you roll your dice. Some people naturally kind-of toss them in a way that slides them so they stay mostly same-side-up, and shake them in their hand in a way that doesn't really fully tumble them. If you add a second die, you create more impacts which can further the tumbling and also alter how it's thrown so it's more likely to roll.

To test this, you could try getting a cup to roll your single die in, instead of rolling it in your hand. Shake it well, covering the opening, making sure to let it really clatter around in there. Then dump it out without letting it settle in the cup. This should achieve a similar result to adding a second die, if this is really the effect you're seeing.

I have often done the "add a second die" trick when I notice dice behaving...badly. I like to pretend it's because I'm tricking the dice by not telling them which one I'm going to use (though I do call it out ahead of time to not actually cheat), but the above is my best hypothesis on why this DOES tend to finally result in streaks being broken.

In the end, though, whether you're observing a bias confirmation effect or a real phenomenon is less relevant than whether your solution, superstitious or not, is satisfying to you. At least when it comes to playing games. I do applaud an inquisitive mind looking into the reality underlying it, though.

[MoiMagnus]

Would this be an example of chaos theory?

No.

One simple way of thinking about it is to consider that you never roll two dice at the same time (one of them is going to stop first), so when you roll two dice, it is like rolling one and then rolling the other one.

If you roll a die and obtain 5, and then roll a second die, you have:
1/20 chances of obtaining a second 5.
1/20 chances of obtaining a 15
18/20 chances of obtaining something other then 5 or 15.

If you roll a die and obtain 15, and then roll a second die, you have:
1/20 chances of obtaining a 5.
1/20 chances of obtaining a second 15
18/20 chances of obtaining something other then 5 or 15.

As you see, the result of the second die is not changed at all by the result of the first die.

But you might says "but rolling a pair is very rare with two d20?"
And you are wrong, rolling a pair is probability 1/20, which is the same as rolling a 20 with one d20.
The reason why you are wrong is because you think "rolling a double 5 is very rare, hence rolling a pair is rare too", but a pair can be a pair of 1, or a pair of 2, or a pair of 3, ... Which is already far more frequent than just rolling specifically a pair of 5.
The good way to think about it is "rolling a pair is equivalent to 'the second die has the same result as the first die', and since there are 20 results possible, the second die has 1/20 probability of rolling the same as the first die".

[JAL_1138]

Other than changing your rolling technique, there’s no way rolling a second die can change the probability of any given result on the first die.

You may be rolling them differently or the dice physically bouncing against each other may offset the bias of an unbalanced die, but the explanation would be physical; the mathematical probability doesn’t care if you roll one die or ten thousand dice.

[KillianHawkeye]

What does this question have to do with college students??

[denthor]

What does this question have to do with college students??

I was originally going to ask for math majors. Decided it was to narrow of a focus. So I widen it to college students.

Since many if them can answer a question like this.

[John Campbell]

If you have bad rolling technique or badly unbalanced dice, adding a second die can change things up. But more likely it's just a combination of small sample size and confirmation bias.

[Kardwill]

There can also be a major de-randomizing effect based on HOW you roll your dice. Some people naturally kind-of toss them in a way that slides them so they stay mostly same-side-up, and shake them in their hand in a way that doesn't really fully tumble them. If you add a second die, you create more impacts which can further the tumbling and also alter how it's thrown so it's more likely to roll.

It would only matters if you start from a set position, though (like if you're deliberately cheating by taking the dice in your hand so that one particular face is up, then sliding it).
If you simply grab a dice (which will often end up with some random face up in your hand), tumbling or sliding shouldn't really matter much.

(Yeah, I don't like tumbling tools like cups or dice towers. Too noisy ^^)

[Lorsa]

I was originally going to ask for math majors. Decided it was to narrow of a focus. So I widen it to college students.

Since many if them can answer a question like this.

What if you have graduated from college? Do you suddenly fail to be able to answer this question?

I would like to add that, for something truly random, it doesn't matter if you take the random number one at a time or two at the same time. If the outcome is determined randomly, it will follow the same distribution.

However, dice are NOT truly random, as some have hinted at. They do, in fact, follow Newtonian mechanics. However, small changes in the initial state will have drastic changes on the final state (which is how it ties to chaos theory). This is why rolling dice will, in practice, be best described by a random distribution.

The only truly random things in our physical universe (that we know of) can be found within the realms of quantum mechanics.

The conclusion is that if you do an experiment with rolling 100 different d20's about 1000 times and find that the number 5 comes up in what would be statistically significant "too much", then you have a way of rolling the dice that makes this number more likely. For example, maybe you always have 20 facing up, hold your hand at the same height and tilt it in the same way.

Before we can conclude that however, you have to do the experiment, and not just say "I think 5 comes up too often". How many rolls have you made? How many dice have you tried? How often does it come up? How often do other numbers come up? Give us the data!

[Segev]

It would only matters if you start from a set position, though (like if you're deliberately cheating by taking the dice in your hand so that one particular face is up, then sliding it).
If you simply grab a dice (which will often end up with some random face up in your hand), tumbling or sliding shouldn't really matter much.

(Yeah, I don't like tumbling tools like cups or dice towers. Too noisy ^^)

You can certainly deliberately attempt to alter the side that is facing up "differnetly" each time you grab it, but if you just pick it up the same way each time, you may well be putting it in roughly the same position and through the same motions each time.

Trust me: when I start using the "two dice" trick, it's not because I was cheating. I'm not above biasing things in my favor in the following fashion: If I'm on a streak of good luck, I want it to continue, and won't necessarily change anything deliberately; if I'm on a streak of bad luck, I want it to stop, so after a few times, I'll start deliberately trying to change things to see if I can at least gain an illusion of control over the RNG.

Yes, I know it's mostly superstition, but it makes me feel better, and the point of gaming is to have fun. :P

[Man_Over_Game]

No.

One simple way of thinking about it is to consider that you never roll two dice at the same time (one of them is going to stop first), so when you roll two dice, it is like rolling one and then rolling the other one.

If you roll a die and obtain 5, and then roll a second die, you have:
1/20 chances of obtaining a second 5.
1/20 chances of obtaining a 15
18/20 chances of obtaining something other then 5 or 15.

If you roll a die and obtain 15, and then roll a second die, you have:
1/20 chances of obtaining a 5.
1/20 chances of obtaining a second 15
18/20 chances of obtaining something other then 5 or 15.

As you see, the result of the second die is not changed at all by the result of the first die.

But you might says "but rolling a pair is very rare with two d20?"
And you are wrong, rolling a pair is probability 1/20, which is the same as rolling a 20 with one d20.
The reason why you are wrong is because you think "rolling a double 5 is very rare, hence rolling a pair is rare too", but a pair can be a pair of 1, or a pair of 2, or a pair of 3, ... Which is already far more frequent than just rolling specifically a pair of 5.
The good way to think about it is "rolling a pair is equivalent to 'the second die has the same result as the first die', and since there are 20 results possible, the second die has 1/20 probability of rolling the same as the first die".

Spot on here.

If you are expecting to roll a 5, you're going to have twice the chance of rolling a 5 when rolling two dice than you would with rolling one. Only one of the two dice have to roll what you're expecting, so it's effectively confirming a bias that's locked into your head. You aren't always paying attention to what you're NOT getting.

Gambling is similar; you don't always pay attention to how much you lose, only how much you win. We expect our expectations to be met, and we often ignore facts to confirm what we believe is true.


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Math experiment for you. Make 5 rolls of 2d20, and write down each die's roll. Then record the sum of each set, which should be near 21. After you're done with all 5 sets, find the average (add them all the set sums, divide by 5), and you should get something very near to 21.

Now take a look at the first column of your pair of dice rolls, so you're just looking at 1 of the 2 dice from each set, and see if there's a major pattern there.

Multiple dice are less random than a single dice, but this only matters when determining their values as a set. When recording values individually, they're all equally random.

[Cliff Sedge]

(College professor here - okay, not really, but I teach college level math and physics at a high school):

So the question is does throwing more dice really change the probability of different numbers coming up?

No.

Would this be an example of chaos theory?

No - or at least, not-quite.

However, rolling multiple dice simultaneously creates more opportunities for the dice to change their orientation during the roll because of more collisions with nearby objects.

If you are rolling the single die properly (i.e. not trying to influence it with cheater's hand techniques) then it shouldn't make a difference. Either way, the die or dice should bounce and roll around enough times before settling on one of their faces that the result can't be predicted by a normal human.