…here's what I keep saying, "Nobody is rejecting the possibility of life forming in many star systems. However, if life is possible everywhere, why do we happen to be in a very unusual solar system?"
"Nobody is rejecting the possibility of winning a multi-billion dollar PowerBall in many states. However, if winning is possible everywhere, why do I happen to live in a very unusual state where there actually was a winner?”
Answer, fully vetted by multiple Vegas odd-setters:
…here's what I keep saying, "Nobody is rejecting the possibility of life forming in many star systems. However, if life is possible everywhere, why do we happen to be in a very unusual solar system?"
"Nobody is rejecting the possibility of winning a multi-billion dollar PowerBall in many states. However, if winning is possible everywhere, why do I happen to live in a very unusual state where there actually was a winner?”
Answer, fully vetted by multiple Vegas odd-setters:
“Just lucky, I guess.”
That really helps contextualize the conversation. Thanks!
…here's what I keep saying, "Nobody is rejecting the possibility of life forming in many star systems. However, if life is possible everywhere, why do we happen to be in a very unusual solar system?"
"Nobody is rejecting the possibility of winning a multi-billion dollar PowerBall in many states. However, if winning is possible everywhere, why do I happen to live in a very unusual state where there actually was a winner?”
Answer, fully vetted by multiple Vegas odd-setters:
“Just lucky, I guess.”
Great analogy. Even worse, it's like winning a powerball prize without knowing how many prizes were available, how many were given out, how many tickets were sold, or even what the rules are for winning.
he/him we all just have to live through it,
holding each other’s hands.
Nobody is rejecting the possibility of winning a multi-billion dollar PowerBall in many states. However, if winning is possible everywhere, why do I happen to live in a very unusual state where there actually was a winner?
Great analogy. Even worse, it's like winning a powerball prize without knowing how many prizes were available, how many were given out, how many tickets were sold, or even what the rules are for winning.
It only proves that you do not understand what I am saying .
Let me give you another analogy,
Just imagine there's a US state very different from all the other states. Now, imagine there's a winner in that unique US state and imagine we had no idea how many Powerball tickets were sold in the country. Imagine we had no idea what the odds of winning are. One would have to wonder why someone won the lottery there. Marcus's analogy completely misrepresents what I am saying.
Now, keep in mind that the odds of winning the Powerball are 1 in 292 million, not 1 in 10^100. We know there's likely to be a winner somewhere because enough tickets are sold, if the odds of winning the Powerball were 1 in 10^25, nobody would win it in a very long time.
Also, when there's a Powerball drawing, you don't expect multiple winners. Why should we expect alien life in the observable universe?
Last edited by doubtingthomas on Thu Jan 05, 2023 10:55 pm, edited 8 times in total.
"I have the type of (REAL) job where I can choose how to spend my time," says Marcus.
I'm not sure I can think of a quick and snappy way to make the full and exact calculation clear. It's a grind-it-out kind of thing, not really an idea that one can see in one view. But I can try to give a simple idea of when the simplified version is reliable, and why it fails when it fails.
Start with a background scenario. Suppose you and a friend have a regular bet in which you try to perform some tricky task, like throw a bullseye with a dart or something. Say your odds of succeeding are 1 in N, for some largish number N. If the bet has you pay your friend a dollar each time you try, and they pay you N dollars if you succeed, then it's a fair bet. On average you'll win N dollars back while paying N dollars to try N times.
Now the main question. Your friend offers to revise the bet as follows. You get to make some number T of tries for your dollar, and your friend will pay you if you succeed on any one of those T tries. To be concrete, you can imagine that T is 10. The payoff they offer now, though, is reduced from N dollars to N/T dollars. You have T times as many chances to win, now, so your odds have to be better, so a lower payoff is fair. Should you take this revised form of bet, or is your friend trying to screw you somehow?
The naïve guess says that if your chance of succeeding at one attempt was 1/N, then your chance of succeeding at least once in T attempts must be T times that, so T/N. So according to this naïve reasoning, the revised bet should be just as fair as the first bet and you might as well make your friend happy and take it.
Actually, though, you're getting at least slightly screwed, if you do this. The reason is that in every T attempts, which cost you 1 dollar, you will on average get T/N successes. Sometimes, though, you might get lucky and succeed more than once in those T tries. Under the sneaky terms of your friend's innocent-sounding revision to the bet, you don't get paid multiple times for winning multiple times in a set of tries. You just get paid the same N/T for winning any number of times in T tries. So some of the time, when you get lucky and succeed multiple times in T tries, you'll be wasting those lucky extra successes and not getting paid for them.
Suppose that over a year or something you play N sets of T tries, so on average you have T successes with which to win back the N dollars you paid to make all those N sets of tries. If you could spread out those T successes evenly, one each into T separate sets of tries, you'd get your N/T payoff T times, making back the N dollars you paid for N sets. But by good luck that actually turns out to be bad luck, some of your T successes are going to have been in the same set of tries. Those successes are wasted. You'll get less than T payoffs, so you'll make less than N dollars back from your friend.
That's why the odds of success do not actually just get multiplied by the number of chances, when you get more chances. Buying ten lottery tickets does not make you ten times more likely to win.
At least not quite. The problem in the naïve reasoning is that you might get extra lucky and win multiple times in the set of chances, but this would still only count as winning, because we're only talking about whether you win at all, not about how many times you win if you do. Once you understand this, you can use it to estimate just how badly your friend is trying to screw you.
How likely is it that you might succeed more than once in T tries? If it's not actually all that unlikely, then your friend is screwing you badly. If it's really unlikely, though, then the whole issue of wasting some successes by doubling them up is about an extremely rare scenario that you can afford to ignore.
So the rule of thumb is: first make the naïve estimate, by which if your chance on one try is 1/N then your chance in T tries is T/N. Then use the same kind of naïve reasoning to guess that since the chance of one success in T tries is T/N, the chance of two successes in T tries should be (T/N)^2. Ask yourself if (T/N)^2 is a small enough chance that you're prepared to ignore it, considering it essentially zero. If it is, then the only issues with your naïve logic are things that will essentially never happen, so you can stick with your naïve estimate. If (T/N)^2 is not that darn small, then you'd better reckon more carefully, if you don't want to get screwed.
So for example if a lottery ticket has winning odds of 1 in a million, then buying ten tickets instead of just one really does raise your odds of winning to very close to 10 in a million. The error in this naïve estimate would be something around (10 in a million) squared, which is 1 in ten billion. So your odds of winning with the ten tickets are really something like 9.9999 in a million. That's close enough to 10 in a million, I'd say.
Buying ten tickets in a kindergarten draw with prize odds of 1 in 10 does not raise your chance of winning to 1, though. 1^2 is still 1, which isn't a small chance at all. That's the tip-off that the naïve estimate isn't going to be good any more. The actual odds of winning at least once with ten shots at a 1 in ten chance are 1 - (1-1/10)^10, which is just over 65%. That's far enough short of the naïvely estimated 100% that you would get fired by an investing firm.
If T/N is still small, you can safely go with T/N. If it's not, you'd better do the full calculation.
Nobody is rejecting the possibility of winning a multi-billion dollar PowerBall in many states. However, if winning is possible everywhere, why do I happen to live in a very unusual state where there actually was a winner?
Great analogy. Even worse, it's like winning a powerball prize without knowing how many prizes were available, how many were given out, how many tickets were sold, or even what the rules are for winning.
It only proves that you do not understand what I am saying .
Let me give you another analogy,
Imagine you live in a state very different from all the other states. Image there's an unusually high level of corruption in that state and image the state has an unusually high average of Powerball winners. Marcus's analogy completely misrepresents what I am saying.
Now, keep in mind that the odds of winning the Powerball are 1 in 292 million, not 1 in 10^100. We know there's likely to be a winner somewhere because enough tickets are sold, if the odds of winning the Powerball were 1 in 10^25, nobody would win it in a very long time.
Also, when there's a Powerball drawing, you don't expect multiple winners. Why should we expect alien life in the observable universe?
Keep in mind here is what YOU said was YOUR point:
…here's what I keep saying, "Nobody is rejecting the possibility of life forming in many star systems. However, if life is possible everywhere, why do we happen to be in a very unusual solar system?"
And now you'd like to add this:
dt wrote:
It only proves that you do not understand what I am saying .
Let me give you another analogy,
Imagine you live in a state very different from all the other states. Image there's an unusually high level of corruption in that state and image the state has an unusually high average of Powerball winners. Marcus's analogy completely misrepresents what I am saying.
No, it doesn't. All you are doing in the above is stating what it is you think makes your solar system Powerball state "highly unusual."
Which makes my analogy of your argument still exactly correct:
"Nobody is rejecting the possibility of winning a multi-billion dollar PowerBall in many states.
However, if winning is possible everywhere, why do I happen to live in a very unusual [by virtue of being corrupt] state where there actually was a winner?”
Answer, fully vetted by multiple Vegas odd-setters:
No, it doesn't. All you are doing in the above is stating what it is you think makes your solar system Powerball state "highly unusual."
Let me repeat the problems with your bad analogy
1. We know how many tickets are sold. We don't know how many "just right" conditions for life exists in the observable Universe.
2. Just imagine there's a US state very different from all the other states. Now, imagine there's a winner in that unique US state and imagine we had no idea how many Powerball tickets were sold. One would have to wonder why someone won the lottery there.
3. We don't expect multiple winners after a Powerball drawing, why should we expect alien life in the observable Universe?
4. If there's a really big multiverse, then alien life is likely to exists in other universes.
"I have the type of (REAL) job where I can choose how to spend my time," says Marcus.
No, it doesn't. All you are doing in the above is stating what it is you think makes your solar system Powerball state "highly unusual."
Let me repeat the problems with your bad analogy
1. We know how many tickets are sold. We don't know how many just right conditions for life exists in the observable Universe.
2. Just imagine there's a US state very different from the a states. Now, imagine there's a winner in that unique US state and imagine we had no idea how many Powerball tickets were sold.
3. We don't expect multiple winners after a Powerball drawing, why should we expect alien life in the observable Universe?
4. If there's a really big multiverse, then alien life is likely to exists in other universes.
1.
" how many tickets are sold"
IS NOT AT ALL ANALOGOUS, under any interpretation of your analogy, TO:
"how many just right conditions for life exists in the observable Universe. "
2.
"Just imagine there's a US state very different from the a states. Now, imagine there's a winner in that unique US state and imagine we had no idea how many Powerball tickets were sold."
and?
3.
"We don't expect multiple winners after a Powerball drawing, why should we expect alien life in the observable Universe?"
Seriously? You are using the rules of a man-made game to try to justify your non-expectations of "alien life in the observable Universe?"
4
" If there's a really big multiverse, then alien life is likely to exists in other universes."
Your If--then statement is based on absolutely nothing at all. You haven't even made a compelling theoretical argument. You are simply stating nonsense.
" how many tickets are sold"
IS NOT AT ALL ANALOGOUS, under any interpretation of your analogy, TO:
"how many just right conditions for life exists in the observable Universe. "
"Just imagine there's a US state very different from the a states. Now, imagine there's a winner in that unique US state and imagine we had no idea how many Powerball tickets were sold."
and?
And imagine we had no idea what the odds of winning the Powerball are. Wouldn't you suspect that something fishy happened in that state? Remember, that state is unique and has high levels of corruption.
Your If--then statement is based on absolutely nothing at all. You haven't even made a compelling theoretical argument. You are simply stating nonsense.
No, you are just cherry picking the things I said.
You ignored this for example: It's very hard to prove what matters for the formation of life. It's much easier to prove that our solar system is unique. If the solar system is "a cosmic oddity", then that would be a strong hint that life is extremely rare in the universe.
Last edited by doubtingthomas on Thu Jan 05, 2023 11:19 pm, edited 4 times in total.
"I have the type of (REAL) job where I can choose how to spend my time," says Marcus.
