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What has a 1 in a million chance? (2010)

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Re: What has a 1 in a million chance? (2010)

#161

Post by cjohnson318 »

jampekka wrote: post #126
Scarblac wrote: post #19

> "Scientists have calculated that the chances of something so patently absurd actually existing are millions to one. But magicians have calculated that million-to-one chances crop up nine times out of ten." -- Terry Pratchett Making fun of the fact that if someone says "it's a million-to-one chance, but it might just work!" in fiction, you know it's going to work. In _Guards! Guards!_ this is taken to the point that…

TFA: "If you tossed the coins [20 tails in a row] then the first answer would be NO, unless I'm very confident you lack the ability to fool me … "

Yeah, what does this even mean? Isn't coin flipping a random process?

Re: What has a 1 in a million chance? (2010)

#162

Post by DeRock »

yboris wrote: post #158

My favorite mental visualization I came up with: imagine driving from New Jersey to Florida (substitute with a long drive you had). Mine was about 1,200 miles which at 60 miles per hour is 20 hours. That's 72,000 seconds of mind-numbing driving. Now if during the entire, exhausting, 20 hours of driving, you press a button, and it falls within the "danger zone" that lasts 15 seconds, you lose. The above example is bet…

15 seconds danger zone / 72,000 seconds of driving = 1 in 4,800

Any reason you chose those numbers? Trying to understand the significance of those odds.

Re: What has a 1 in a million chance? (2010)

#163

Post by ascorbic »

cjohnson318 wrote: post #161
jampekka wrote: post #126

Earlier quoted context omitted.

TFA: "If you tossed the coins [20 tails in a row] then the first answer would be NO, unless I'm very confident you lack the ability to fool me … "

Yeah, what does this even mean? Isn't coin flipping a random process?

I read it as meaning that there's a much better chance that you're able to perform a trick, so the chance is the probability of filpping them for real, plus the chance of you being able to perform a trick to make it seem that you have.

Re: What has a 1 in a million chance? (2010)

#164

Post by hughesjj »

teaearlgraycold wrote: post #155
erostrate wrote: post #133

The following are all ~ 1 in a million chance of death, or 1 micromort: Travelling 6 miles (9.7 km) by motorcycle Travelling 17 miles (27 km) by walking Travelling 20 miles (32 km) by bicycle Travelling 230 miles (370 km) by car Travelling 1,000 miles (1,600 km) by jet Travelling 6,000 miles (9,656 km) by train But switching from car to bicycle for short trips still increases life expectancy due to health effects. So…

As a cyclist that’s trying to not die, I also have to assume this heavily depends on where you’re cycling. Along a stroad? You’re dead. Country road with more bikes than cars? Much safer.

Also you can rack up miles on the interstate like no one's business on a road trip etc. imo it should be by unit time not unit distance but I could see the argument for distance

Same with planes. Like yeah if you wanted to make the same trip without a plane it's way more dangerous but what if you just wouldn't take the train from coast to coast in the first place?

IDK, imo time is the most important tradeoff for transport when doing per capital/etc measurements

Re: What has a 1 in a million chance? (2010)

#166

Post by Strilanc »

neilkk wrote: post #160
Strilanc wrote: post #89

Earlier quoted context omitted.

It's important to understand that when they said "bits" they didn't mean information in the Shannon entropy sense, but rather in the log-odds evidence sense. Gaining a Shannon entropy bit means learning the answer to a yes-no question that had 1:1 odds. Gaining a log-odds evidence bit means doubling your best-guess odds on a question you are uncertain about, from X:Y to (2X):Y. One Shannon bit is worth arbitrarily ma…

This isn't how the mathematics of odds works, as the GP correctly pointed out. An event which is 20:1 on is not 20 times more likely than certainty. Going from 1:4 to 1:2 means that the event has become twice as likely. But going from 2:1 to 4:1 does not: it means that the complementary event has become half as likely. Based on this, we can't do math with odds treating them identically to ratios. If you do the math c…

A log-odds of b bits means an odds of 2^b : 1 which means a probability of p = 2^b / (2^b + 1).

In the original comment, the evidence update was stated as going from 20:1 to 1:1000000 and it was claimed this was approximately 24 bits of evidence. The update is from 2^4.3:1 to 2^-19.9:1. Subtracting the exponents you get 4.3 - -19.9 = 24.2 which is approximately 24 as claimed. The "20" in 20:1 is correctly accounted for by the ~4 additional bits of evidence on top of updating from 1:1000000 to 1:1.

Clearly evidence bits behave very differently from entropy bits. Acquiring a single entropy bit is an update from 1:1 to 0:1 which is 2^0:1 to 2^-infinity:1. It's worth an unbounded number of evidence bits. It's important not to mix these two things up.

Re: What has a 1 in a million chance? (2010)

#167

Post by drzaiusapelord »

erostrate wrote: post #133

The following are all ~ 1 in a million chance of death, or 1 micromort: Travelling 6 miles (9.7 km) by motorcycle Travelling 17 miles (27 km) by walking Travelling 20 miles (32 km) by bicycle Travelling 230 miles (370 km) by car Travelling 1,000 miles (1,600 km) by jet Travelling 6,000 miles (9,656 km) by train But switching from car to bicycle for short trips still increases life expectancy due to health effects. So…

Chicago to LA is about 2,000 miles.

So in the article about 200 miles driving (in California) is 1 in a million chance of dying. So lets use that number nationwide to be lazy.

Now we can move a decimal point over. So the death chances of a Chicago to LA drive is 100,000 in one. But you drive back, so then its that twice. Once in 50,000 people dying on a Chicago to LA and back roadtrip is extremely frightening. How many people from the midwest make this drive a year? Or from the east coast? How many don't make it back?

The USA, on average, has 100+ fatalities via auto transportation a day.

The above ignores serious injury, permanent disability, etc. Its just death. The chances of having to deal with a broken spine, losing a limb, blindness, 3rd degree burns all over your body, etc aren't even calculated, but those are real and far more common than death. Death being harder to achieve with modern medical treatments.

Cars are extremely dangerous. We downplay what it means to drive.

Re: What has a 1 in a million chance? (2010)

#168

Post by [deleted] »

hughesjj wrote: post #164
teaearlgraycold wrote: post #155

Earlier quoted context omitted.

As a cyclist that’s trying to not die, I also have to assume this heavily depends on where you’re cycling. Along a stroad? You’re dead. Country road with more bikes than cars? Much safer.

Also you can rack up miles on the interstate like no one's business on a road trip etc. imo it should be by unit time not unit distance but I could see the argument for distance Same with planes. Like yeah if you wanted to make the same trip without a plane it's way more dangerous but what if you just wouldn't take the train from coast to coast in the first place? IDK, imo time is the most important tradeoff for tran…

[deleted]

Re: What has a 1 in a million chance? (2010)

#169

Post by lcnPylGDnU4H9OF »

yboris wrote: post #158

My favorite mental visualization I came up with: imagine driving from New Jersey to Florida (substitute with a long drive you had). Mine was about 1,200 miles which at 60 miles per hour is 20 hours. That's 72,000 seconds of mind-numbing driving. Now if during the entire, exhausting, 20 hours of driving, you press a button, and it falls within the "danger zone" that lasts 15 seconds, you lose. The above example is bet…

> imagine having to throw a quarter out of the window, hoping for it to land within the proper 1 inch section of the road

This idea also helps to illustrate something which is intuitive to me but seemingly hard to explain. Sometimes when an event occurs people will exclaim, "Wow, what are the odds of that?!" and then if it turns out to be a seemingly unlikely event, then it becomes "wow, it's crazy that happened!".

But it's really not. Using the pull-quote as an example, it's the difference between 1) throwing the quarter out the window and drawing a circle around where it lands and 2) drawing a circle on the ground, hoping to land the quarter in it when it's thrown. Of course the exact result in the first case was unlikely but nobody predicted it so it's uninteresting.

Re: What has a 1 in a million chance? (2010)

#170

Post by neilkk »

Strilanc wrote: post #166
neilkk wrote: post #160

Earlier quoted context omitted.

This isn't how the mathematics of odds works, as the GP correctly pointed out. An event which is 20:1 on is not 20 times more likely than certainty. Going from 1:4 to 1:2 means that the event has become twice as likely. But going from 2:1 to 4:1 does not: it means that the complementary event has become half as likely. Based on this, we can't do math with odds treating them identically to ratios. If you do the math c…

A log-odds of b bits means an odds of 2^b : 1 which means a probability of p = 2^b / (2^b + 1). In the original comment, the evidence update was stated as going from 20:1 to 1:1000000 and it was claimed this was approximately 24 bits of evidence. The update is from 2^4.3:1 to 2^-19.9:1. Subtracting the exponents you get 4.3 - -19.9 = 24.2 which is approximately 24 as claimed. The "20" in 20:1 is correctly accounted f…

Yes, you are doing math with odds as though they are fractions or ratios, which is deeply incorrect. 20:1 is not the reciprocal of 1:20 but the complement. Odds ratios and similar calculations do not work like this. You can do this type of calculation using X:1 odds or 1:X odds but not both in the same calculation.

Or perhaps you can provide a reference to a justification of this type of calculation?

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