# I Is throwing dice a stochastic or a deterministic process?

#### Aidyan

As far as I understand it a stochastic process is a mathematically defined concept as a collection of random variables which describe outcomes of repeated events while a deterministic process is something which can be described by a set of deterministic laws. Is then playing (classical, not quantum) dices a stochastic or deterministic process? It needs random variables to be described, but it is also inherently governed by classical deterministic laws. Or can we say that throwing dice is a deterministic process which becomes a stochastic process once we use random variables to predict their outcome? It seems to me only a descriptive switch, not an ontological one. Can someone tell me how to discriminate better between the two notions?

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#### StoneTemplePython

Gold Member
It depends on how you want to model it. It is frequently profitable to try to model it both ways -- sometimes you'll get the same result but different insights (e.g. with the heat equation) depending on how you look at it.

Sometimes one way will be a dead-end -- e.g. for monitoring games of craps, to my knowledge casinos use very little physical modelling and a lot of probability.
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I have concerns that the motivation for this thread is on the border of philosophy

#### jedishrfu

Mentor
Games of chance are often best modeled stocastically even though we know given enough information and computing power we can predict the outcome.

For casinos this results in being ever vigilant against those players who might buck the odds using inside knowledge of the game mechanics and playing to certain weaknesses found.

Roulette play is probably a better example where once the ball is set in motion then classical physics and initial conditions can predict outcome.

Heres how some folks tipped a stochastic game to be a more predictable:

#### StoneTemplePython

Gold Member
Roulette play is probably a better example where once the ball is set in motion then classical physics and initial conditions can predict outcome.
also of interest, Claude Shannon's roulette exploits with the first wearable computer:

#### Aidyan

So, as I understand it, saying that throwing dice or playing roulette or tossing coins is not a stochastic process but a deterministic one, makes no sense. It depends on how one tries to describe it. (?)

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#### fresh_42

Mentor
2018 Award
So, as I understand it, saying that throwing dices or playing roulette or tossing coins is not a stochastic process but a deterministic one, makes no sense. It depends on how one tries to describe it. (?)
It is a deterministic one but you won't get even near the chance to know all parameters. E.g. how would you model the thermodynamic behavior of air? And this for every molecule!

Thus the result will be a probabilistic process, simply because your ingredients are already probabilistically modelled. But even without, we have made some serious progress since Laplace, and it's not quantum mechanics alone. See e.g. chaos theory. The French mathematicians Henri Poincaré and Jacques Hadamard discovered as early as the end of the 19th century that even simple dynamic systems such as the three-attracting body lead to very complicated trajectories. And even in elementary physical processes such as the movement of a mass point along geodesics, small deviations of the initial angle lead to any large changes in the result.

#### Mark44

Mentor
Mentor note: "Dices" is a word in English, but is unrelated to the small cubes with spots. You can have one die or two or more dice. I have edited several posts in the thread to fix this minor problem.
So, as I understand it, saying that throwing dice or playing roulette or tossing coins is not a stochastic process but a deterministic one, makes no sense. It depends on how one tries to describe it. (?)

"Is throwing dice a stochastic or a deterministic process?"

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