doubles in Castles of burgundy

[mizzou95]

I've played a LOT of COB on this site and my doubles rate is ridiculous. When I asked AI what the chances of my doubles % of 17.22 over approximately 175000 rolls, it came back with this:

The chance of rolling a 17.22% double rate over 175,000 rolls is virtually zero. Getting a rate that high or higher has a 1 in 3.15 billion (3.17 × 10⁻¹⁰) probability.

I've brought this up several times but nothing has been done.

[lefalaf]

And this here folks is why you should not outsource your brain to generative AI/LLMs, aka autocomplete on steroids.

Did a quick normal web search and checked 3 probability sites to be sure, which all explained the simple math and gave the result. Took no time at all. The probability of doubles with two dice is 16.67%. 17.22% is very close to this so that is a perfectly reasonable outcome. There is nothing to be done.

You'll trust LLM hallucinations, but won't trust the random function in whatever language(s) BGA uses.

[Meamer]

In this case, the AI calculation isn't the problem. For a binomial distribution with a success rate of 1/6 and 175,000 trials, I get a probability of 3.05x10^-10 of getting at least 17.22% successes. Yes, 17.22% is very close to 1/6, but over 175,000 trials it should be *even closer*.

But where did that number, 175,000, come from? OP has played 3,495 games of CoB. In each game, you roll 25 times. That's 87,375 rolls, not 175,000. Plugging 87,375 trials into the binomial distribution calculation gives a probability of 6.32x10^-6. Still low, but not outrageously low.

That's *weak* evidence that there may be something fishy going on. But if so, I'd be more inclined to suspect the sometimes-dodgy BGA *statistics page* than the well-tested BGA random function.

[tbhp]

Remember that even the most advanced random functions only approximate randomness, they don't create true randomness, since their outputs are based on deterministic algorithms.

When you look at the graph of a random function, it shows you noise that looks random enough at a glance, but it still contains some non-random patterns. This might explain why it's unrealistic to expect the probability to fit the exact expected probability over a large number of rolls.

[Ehronde]

I've played a LOT of COB on this site and my doubles rate is ridiculous. When I asked AI what the chances of my doubles % of 17.22 over approximately 175000 rolls, it came back with this:

The chance of rolling a 17.22% double rate over 175,000 rolls is virtually zero. Getting a rate that high or higher has a 1 in 3.15 billion (3.17 × 10⁻¹⁰) probability.

I've brought this up several times but nothing has been done.

To judge if the rolls are really random, it's not enough to regard the rolls in the games you played. You have to regard ALL the games played on this platform. Even if 50% of your rolls were doubles, that's no evidence of a broken randomisation. It's unlikely, but not impossible. And if something is not impossible, it will happen occasionally.

[lefalaf]

I just pulled up the All Players' Average for doubles in Castles of Burgundy. 16.61%. That's pretty spot on for the 16.67% expected since it's not infinite rolls, although it is a rather high number (4.3 million games x 25 rolls a game as someone noted), and assuming stats were logged going back to the first game.

But regardless, it's rather close.

Also, the Winners' Average is 16.31%

Oh and mine is 21%. Gasp! (It's only 4 games.)

[yodamus]

Wow, with AI. The human brain will become worse than the cave man. It will cease thinking for many. Just ask AI. No need to think or calculate anything. Just ask AI. Brain rot. And as someone mentioned. Your stats per each and every game are usually a bit off. Due to playing a solo game, conceding a solo game. Or conceding any game I think. Many other little things affect those stats. They will be close but not entirely accurate.

[JimBut]

Remember that even the most advanced random functions only approximate randomness, they don't create true randomness, since their outputs are based on deterministic algorithms.

I see this a lot online - that computers can't produce random data. For almost all intents and purposes they can

BGA uses a cryptographically secure random function which is random enough to encrypt your banking details, it's perfectly random enough to roll some dice.

Rolling a dice is also a deterministic process but likewise is more than random enough.

When you look at the graph of a random function, it shows you noise that looks random enough at a glance, but it still contains some non-random patterns. This might explain why it's unrealistic to expect the probability to fit the exact expected probability over a large number of rolls.

If you suspect that PHPs random_int has non-random artifacts I'd urge you to contact their security team: https://www.php.net/contact.php

[Jellby]

Remember that even the most advanced random functions only approximate randomness

Remember that even the most sophisticate physical randomizations (rolling high-quality dice on certified casino tables, shuffling a deck several dozen times, measuring atmospheric "noise", etc.) only approximate randomness. Only a few physical processes are currently believed to be random (quantum collapse, radioactive decay), and that may be only because we don't understand them.

"Any sufficiently advanced technology is indistinguishable from magic", and any sufficiently advanced RNG is indistinguishable from true randomness.

[tbhp]

I see this a lot online - that computers can't produce random data. For almost all intents and purposes they can

BGA uses a cryptographically secure random function which is random enough to encrypt your banking details, it's perfectly random enough to roll some dice.

Rolling a dice is also a deterministic process but likewise is more than random enough.

Like Jellby pointed out, those are things that look random but since we live in a deterministic world, probably nothing is truly random. The question is less "does it perfectly fit the mathematical concept of randomness" and more 1) is it random enough to give players the experience of being random and 2) is it intentionally designed to favor certain players.