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TL;DR - pages and pages of word salad and pointless math which boils down to – the gambler's fallacy is a fallacy if the coin is unbiased, but maybe it isn't.
by paxys 3y ago
TL;DR - pages and pages of word salad and pointless math which boils down to – the gambler's fallacy is a fallacy if the coin is unbiased, but maybe it isn't.
- lupire 3y agoAnd it could be biased in either direction, so no one knows anything.
- hnfong 3y agoDoesn't this itself prove the article's point though? If you don't know anything, it seems rather presumptuous to say somebody has committed a fallacy.
- SamBam 3y agoI think it's slightly more interesting than that. It's not talking about bias (usually understood to mean that there's >50% chance that it lands on one specific side) but about independence. Many things aren't independent. The article mentions the odds that it will rain on day depends on whether it rained the previous day. Likewise, the odds of a bus arriving in a city with a well-organized strict bus schedule is less if a bus just recently arrived. How about blackjack? If I get an ace, are the odds still 1/52 that my next card will be an ace? Of course not. How about the lottery? Are the odds that a scratch-off ticket is a winner different if the previous ticket on the roll was a winner? I have no idea, but I wouldn't be surprised if the lottery runners introduced such shenanigans. I think that's the author's only point - that we shouldn't always assume independence. But it falls apart a little because it seems to be talking about coins (even if it's actually talking about koins), which is a domain that starts from the premise that events are independent.
- paxys 3y agoDependence on previous results is a form of bias. If a coin is more or less likely to show heads if the previous toss was heads, it is a biased coin.
- hnfong 3y ago> But it falls apart a little because it seems to be talking about coins (even if it's actually talking about koins), which is a domain that starts from the premise that events are independent. And that premise is empirically false as noted by the author. Now the question is whether it's meaningful to accuse people of committing fallacies in hypothetical scenarios where perfectly fair coins are real.
- friend_and_foe 3y agoThis word you used, "independent" has a term in these kind of probabilistic systems, its called "memory". A system is memoryless if the next outcome is not dependent on previous outcomes. A coin flip is such a memoryless system. The odds it will rain on a particular day is not independent of pervious outcomes; such a system is not memoryless. All the examples in your comment share this property and so the reasoning doesn't strictly apply to memoryless systems. The author is not making this point, and early on, he calls coin flips "Markovian" which is synonymous with "memoryless". Independence is assumed in this article.
- SamBam 3y agoHow on earth is a Markovian system memoryless? It specifically depends on what state you are currently in. That's memory. Independence is not assumed in the "sticky" or "switchy" states in the article. The probability of the next flip depends on the previous flip.
- friend_and_foe 3y agoSpecifically, Markovian means that the probabilities of potential future states are dependent on the current state only. This is memoryless (more specifically, it has what's called the Markovian property) because no past states have anything to do with the next state. You're right about the article.