doubles in Castles of burgundy

[tbhp]

The whole premise of the OP is strange. Someone can correct me if I'm wrong, but isn't the benefit or detriment of doubles in this game highly situational?

But nothing about the OP indicates they're complaining about being disadvantaged. They just seem worried that it's not random.

I think this is a much more narrow usage of the word random than most people use, to the point of making the word useless, and I think you're just arguing semantics. For the purposes of a board game site computer functions are random enough

I don't think that's true. When people say that, for example, they want a slot machine to be random, what they mean is true randomness. They want the randomness to be perfect in a mathematical sense.

Of course, many of the people saying that are probably aware that perfect randomness may not be possible in the real world. But it doesn't change that it is what is meant when we use the word.

[tbhp]

But given that the overall frequency of doubles is slightly lower than expected, I was wondering whether the OP wanted BGA to do something about that and increase the overall frequency of doubles, or just to decrease the OP's frequency of doubles.

I guess both would be strange solutions to the problem. You don't fix randomness issues by rigging future games so that the overall probability becomes what you want. This is the same logic as the people who think they "should" be more lucky than normal in their future games to compensate for the bad luck they had in the past. That's not how randomness works.

[JimBut]

I don't think that's true. When people say that, for example, they want a slot machine to be random, what they mean is true randomness. They want the randomness to be perfect in a mathematical sense.

I think most people just want the outcome to be unpredictable and fair. If I have two sources of randomness - one being a magic box that uses some source of perfect randomness that produces dice rolls and one that uses a cryptographically secure function, like the one used in BGA you would not be able to differentiate the two.

I don't think most people would complain about one of these when they are unable to tell them apart

[tbhp]

I don't think that's true. When people say that, for example, they want a slot machine to be random, what they mean is true randomness. They want the randomness to be perfect in a mathematical sense.

I think most people just want the outcome to be unpredictable and fair. If I have two sources of randomness - one being a magic box that uses some source of perfect randomness that produces dice rolls and one that uses a cryptographically secure function, like the one used in BGA you would not be able to differentiate the two.

I don't think most people would complain about one of these when they are unable to tell them apart

You seem to think people only care about getting the illusion of randomness. If someone uses a slot machine, has a good time playing it, then later on they learn that the machine didn't fit the specifications, they would most likely complain or at least not find it normal.

[JimBut]

You seem to think people only care about getting the illusion of randomness. If someone uses a slot machine, has a good time playing it, then later on they learn that the machine didn't fit the specifications, they would most likely complain or at least not find it normal.

If the randomness is indistinguishable from true randomness I'm not sure it's an illusion, it's just random.

I'm not sure we'll ever agree as you seem to have a very black and white view of things

[tbhp]

You seem to think people only care about getting the illusion of randomness. If someone uses a slot machine, has a good time playing it, then later on they learn that the machine didn't fit the specifications, they would most likely complain or at least not find it normal.

If the randomness is indistinguishable from true randomness I'm not sure it's an illusion, it's just random.

I'm not sure we'll ever agree as you seem to have a very black and white view of things

And you seem to speak on behalf of other people despite having zero evidence for the strange perspective you imagine they have.

When people play a game and they use a dice, they don't just want to have the illusion that the dice is random. They want each side to have exactly a 1/6 chance of coming up.

Sure, probably most people realize that this is a unrealistic expectation (physically speaking, it's virtually impossible that the weight of the dice would be uniformly distributed), but it is the expectation they have regardless. It is how they want the dice to be, ideally. They just settle for the fact that it's less than perfect.

[JimBut]

When people play a game and they use a dice, they don't just want to have the illusion that the dice is random. They want each side to have exactly a 1/6 chance of coming up.

I agree people want a die to be perfectly fair and for each side to have the same probability. I am saying that a perfect source of randomness and a cryptographically secure computer RNG will both produce exactly a 1/6 chance of a side coming up. See my previous point:

If I have two sources of randomness - one being a magic box that uses some source of perfect randomness that produces dice rolls and one that uses a cryptographically secure function, like the one used in BGA you would not be able to differentiate the two.

[tbhp]

I am saying that a perfect source of randomness and a cryptographically secure computer RNG will both produce exactly a 1/6 chance of a side coming up.

Except we have zero evidence that it is exactly a 1/6 chance. That's what was discussed on the first page, that even the most advanced programs we have only approximate randomness. We can look at the outputs and observe that the distribution looks close enough to what a truly random program could have produced. But it is also possible that a not perfectly random program would create the same outputs. We have no way to "prove" whether the program we created is actually perfectly random. That's because in our current understanding of science, we have no idea how we would even go about creating true randomness in the first place. The best we can do is find workarounds that create results that look random enough.

[JimBut]

Except we have zero evidence that it is exactly a 1/6 chance

Again, If you have evidence that the PHP random_int function, or the randomness it is based on is producing output that is not fair I would urge you to contact the PHP Security team: https://www.php.net/contact.php as this would have an impact in wide areas of modern computer security.

If on the other hand you are unable to distinguish between "true" randomness and that of random_int then I'd say it's perfectly suited for rolling dice

[Jellby]

Except we have zero evidence that it is exactly a 1/6 chance.

Actually, with RNG algothims you can prove it's 1/6 (or whatever). You don't need evidence, you have mathematical proof (as long as you trust/assume the computer behaves according to the specifications). With a die, especially with a die you just got in your newly purchased game, there's indeed no evidence it will be 1/6, or even that the rolls are independent.

By the way, I'd leave "fairness" out of the equation. Ramdomness is not fair.