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PM_ur_Rump t1_ja8ad7h wrote

Reply to comment by someone76543 in ELI5: why does/doesn’t probability increase when done multiple times? by Reason-Local

Or it could go down as everyone involved is now being more cautious.

I forget the exact scenario that inspired the conversation, but the person I was arguing with was definitely talking about the "odds" in the context of simple odds in the manner of "if a one in a million chance thing just happened, it's now probably closer to one in two million it happens again."

Odds only change when directly linked.

So if you are gambling on a dice roll and you bet that it will land on six, it's a one in six chance. If it does, and you bet on six again, the odds are still just one in six.

To change the odds, you would need to bet that it lands on six twice, because now you have linked the two rolls before they happen.

In the case of the plane crash, the odds of two planes crashing for independent reasons on the same day, involving the same airport, are much higher than a single plane crashing. Unfortunately for our hypothetical travellers, one plane already crashed, bringing the odds back down to the standard single-event odds.

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generous_cat_wyvern t1_ja8jk1c wrote

The issue when it applies to the real world is that you rarely get truly independent events. And also probability is based on assumed knowledge (or lack thereof), so gaining information changes probabilities.

An example is you have a shuffled deck of cards, and you're betting on the odds of the top card being an Ace of Hearts. The probability at this point is 1/52. If you happened to notice a flash of red as the dealer was shuffling, nothing about the deck changed, but now your odds are 1/26 because of additional knowledge.

If the first place crash revealed some information that wasn't available before, that can change the probability calculation, even if nothing else changed about the situation.

Also in a theoretical situation you accept the circumstances presented as fact. In the real world, those assumptions could be wrong, or someone could be flat out lying to you. Like if someone flipped a could 25 times and it landed on heads every time, mathematically you'd say you still have 50/50 for the next toss. But you are assuming that it is indeed a fair coin and not a weighted or double-headed coin. If you want into someone on the street taking bets, you have to factor in not just the odds at face value, but also the odds that they're cheating.

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nicktam2010 t1_jaa4hup wrote

Which is why they investigate aircraft crashes so thoroughly? So that a slight change in design, processes, procedures etc will further the body of knowledge about aircraft and the odds will decrease

It's the basis of all safety, I suppose.

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PM_ur_Rump t1_ja8sbsp wrote

Again, this was a discussion about theoretical simple odds. The real world isn't a coin flip, and like you pointed out the odds may be weighted in ways you don't know. But yeah, this was about him thinking that a die landing on six made it less likely to land on six again.

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generous_cat_wyvern t1_ja9n5ab wrote

Right, the OP was talking simple odds, but the thread shifted to talking about plane crashes I think we exit the realm where simple odds apply. It makes sense when we're talking about dice.

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PM_ur_Rump t1_ja9oemf wrote

I only brought it up because the guy I'm talking about was specifically talking about it in terms of simple odds, not arguing the fact that air travel is a very complex thing.

It was very much an application of the gambler's fallacy to a real world event, one that has extremely hard to quantify odds with countless variables to begin with.

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