[1/6] can only mean that out of 6 times rolling the dice, the 6 will occur one time, right? — spirit-salamander
The question that arises is what this 1/6 means philosophically or, if you like, mathematically. — spirit-salamander
How many times the gambler has rolled that night has no bearing on whether the next roll will be a double six." (Philip Goff - Our Improbable Existence Is No Evidence for a Multiverse) — spirit-salamander
A probability is not a surety of what will happen. A probability of 1/6 of the occurrence of the six doesn't ensure that the six will occur within 6 rolls. — TonesInDeepFreeze
The idea that the outcomes of a coin-toss will "balance" out i.e. you'll get an equal number of heads and tails is based on infinity. — TheMadFool
In other words, yes the gambler is correct in expecting a tails after a streak of heads but what he can't know is when his streak will end. — TheMadFool
If a probability of 1/6 for the occurrence of the six does not ensure that the six occurs within 6 rolls, then the 6 could never occur. — spirit-salamander
It would not be ensured that the six occurs in 60 throws, not in 600, not in 6000, and so on. — spirit-salamander
But what is the point of using probability if it is not reliable? — spirit-salamander
(Your understanding of probability is way off though. — SophistiCat
Let's assume 600 rolls. What would be the most probable result of an ideally rolled ideal dice? An absolutely even distribution? So 100 times the 1, 100 times the 2, 100 times the 3 and so on to 100 times the 6? Or 0 times the 1, 200 times the 2, 50 times the 3, 150 times the 4 and so on until the sum is 600?
I would say that the ideal dice must give an absolutely even distribution. If it were a little less ideal, you might have 99 times the 1, 101 times the 2.... . In other words, small unevenness. For example, the completely anti-ideal die would give 600 times 5, and all the others 0. The absolutely anti-ideal dice would have an infallible tendency to exclusively one number.
This means that probability is not based on complete chance, but on strict laws of probability. That is, if I have already rolled the 3 100 times in a row, the 3 should not occur again according to the ideal rolled ideal die. The probability in this case would be 0. The chance would consist in the fact that one cannot know which of the other numbers occur, but the probability law forbids that the 3 occurs again. — spirit-salamander
one would have to conclude that there was manipulation involved. — spirit-salamander
I find the concept of infinity problematic with the idea of probability. The idea is that at infinity all the numbers on a die have fallen equally. But the infinity knows no completion. It goes on and on. Therefore it would generate a bogus argument. — spirit-salamander
Gambler's fallacy?? — TheMadFool
If the payout is proportionate to the odds — TonesInDeepFreeze
Is this way off? — spirit-salamander
You can try it yourself at home. Roll the dice 600 times and write down the results. There will be an approximately even distribution. Now my argument was about a dice as a thought thing, the perfect dice rolled perfectly. The distribution should be perfectly even. If this were not the case, one would have to conclude that there was manipulation involved. — spirit-salamander
But what is the point of using probability if it is not reliable? — spirit-salamander
This probability = W = (1/6)^5 * 5/6 — TheMadFool
There is no upper limit on how long a streak can be. — TonesInDeepFreeze
Purely mathematical probability is not taken necessarily to be matched every time by real world outcomes. — TonesInDeepFreeze
Take the simplest example of a coin toss. The chance of heads is 1/2. But that does not entail that heads comes up exactly 50% in every experiment. — TonesInDeepFreeze
one must always add an imaginary closed overall context — spirit-salamander
possible worlds — spirit-salamander
we could set the machine so that it always alternates the conditions. First like this, then like that, and so on. Surely here we could say that there is a 50% probability? — spirit-salamander
But if you start off assuming that the probability of each possible outcome in a single trial is 1/6 and then end up concluding that the probability of a particular outcome in the next trial is more than 1/6, then you have contradicted yourself. — SophistiCat
So real coin flips are nowhere close to what you think perfect coin flips ought to be. In fact, perfect coin flips would have to be manipulated to produce an alternating sequence: heads, tails, heads, tails, etc. Anything else would violate your criteria of perfection. — SophistiCat
Probability is a measure of uncertainty. Where you can make a perfectly reliable prediction, you have no need of probability. — SophistiCat
if I rolled 6 on the first roll, the probability of a 6 appearing again on the second roll would be minimally lower. Lower in the sense of something like 0.0000000000000000000001. This is not meant to be mathematically correct. — spirit-salamander
What is the 1 here, what is the 6 and what / and how do they relate to the real world? — spirit-salamander
our probability formula is empty and meaningless [?] — spirit-salamander
It's not mathematically correct and there's no reason to think it's empirically correct. In an empirical situation, if you suspect that one side of the coin has an advantage, then after a side comes up, one would expect that the probability of it coming up next is higher not lower. — TonesInDeepFreeze
That is an expectation but it is not ensured. — TonesInDeepFreeze
If you thought probability is meaningless, wouldn't you be just as happy if the doctor told you that the chance of surgery survival is 1% as if he told you it was 90%? — TonesInDeepFreeze
But how would it like with Laplace's Demon? — spirit-salamander
In the case of the dice, one would say that it is quite evenly shaped, without one side having more weight than another. — spirit-salamander
The 1/6 seem to be the mathematical expression for it (laws of nature and the absence of the manipulation). — spirit-salamander
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