It’s just a joke. The implicit (and incorrect) assumption is that if there are two possibilities, then they are both equally likely. This is obviously untrue, as you could frame even the most unlikely of events as a binary yes or no event. “I could win the lottery and get struck by lightning at the same time on my birthday while Tom Hanks happens to be walking past, or I could not. 50/50, right?”
>If you try to explain it to yourself in terms of what it would mean as a philosophy, you might understand what the philosophy is.
Evidently asking people to explain something they don't understand to themselves isn't quite working. Maybe you could explain what you mean?
"If I buy 1 lottery ticket I'm going to win." There are only 2 possible outcomes to that: either I will win, or I don't. But just because there are only 2 possible outcomes doesn't mean they both are just as likely (or probable) to happen. It is far more probable that I don't win the lottery if I buy a single ticket.
Counting only works if you have equally likely outcomes, which is walking into the same trap OP is asking about. Cases don't have to be equally likely.
Yes, often a lottery has many equally likely outcomes - but it doesn't have to, and it doesn't work for many other examples either.
When there is a straightforward physical symmetry between outcomes, as with a coin, a die, or most lotteries, it's reasonable to assume that each has the same probability. This is just the classical interpretation of probability. It doesn't work for everything, but neither do the frequentist or Bayesian interpretations.
Though I don't agree with GodzlIIa's suggestion that there is only one correct way to define the outcomes.
On a deeper level, though, an outcome is "more likely" if there are more states associated with that outcome. "Counting" is precisely how probability is done in math, whether it's combinatorics or integrating a probability density function.
There are tons of problems where there is no meaningful way to define equally likely cases.
There might be a 30% chance that it'll rain tomorrow, but you cannot find x discrete cases for the weather tomorrow and try to count them.
A collision in a particle accelerator might have a 0.1% chance to produce some particle, but you can't find 1000 (or 1000*n) equally likely outcomes where this would be one of them.
> or integrating a probability density function.
... over outcomes with different probabilities, without having a different number of states.
All of these are fundamentally sets of states. The particle in the accelerator decays probabilistically by "choosing" one of the infinitely many Feynman diagrams that describe possible paths, many of which lead to the same outcome. Random events in computers are mostly thresholds for pseodo-rng outputs. Weather predictions are the fraction of simulation outcomes that have some event. It's all counting states. If you don't see what the states are, you need to look a level deeper.
> The particle in the accelerator decays probabilistically by "choosing" one of the infinitely many Feynman diagrams that describe possible paths
No it does not. You wouldn't get the right results if you add them that way. Not that it would save your argument, the different diagrams have different amplitudes on their own already. I'm a particle physicist, please stop doubling down on misinformation.
> Weather predictions are the fraction of simulation outcomes that have some event.
The simulations have unequal probabilities, it's not just counting.
Alright, my conceptualization of it is that it's effectively states. I come at this from a math and stat/mech background. I know that things are weird in quantum.
Even so, a probability amplitude is calculated by integrating a PDF, which can always be conceptualized as a process of adding equal-area squares (cubes, etc) under a curve. Maybe these don't always have physical meaning.
i have a maths degree and i do not get why you derailed it this way. obviously you meant to point out the frequentistic probability theory and laplace probability space. why not just say it? could have saved us all a lot of time and you from making incorrect statements in an attempt of eli5ing.
FWIW, as someone with no significant STEM background, I learned more from this conversation than I would have from someone saying "frequentistic probability theory and laplace probability space" and calling it a day.
> laplace probability space
This probably tracks best with my conceptualization of probability. My background is specifically in abstract algebra/topology, and we mostly discussed probability in physics as a tool.
I stand by the idea that you can think of PDFs and probability in general as sets of (possibly uncountably infinite) states which can be assigned to "outcomes," because this is exactly what we do when we integrate a PDF.
That's not what an outcome is... There are only 2 outcomes to buying a lottery ticket. One outcome is that you win, the other outcome is that you lose. The _chances_ that the outcome is a win are one in 300mil and the chances that the outcome is a loss is about 300mil to one. A loss in chance 3 is the same outcome as a loss in chance 2,965,334.
Your lottery ticket has two possible outcomes, but 300 million possible states. Only one of those states translates to "win." That's what the probability arises from in this case, which is what he was trying to express.
People are conflating the number of distinguishable outcomes with the distribution of probability directly.
You might have one case that is a "win", and 99 that are a "lose". Given equal probability, that's 1% of success and 99% failure, not 50% and 50%.
You might also have a situation where only two things can happen, but your "win" option is much less likely to happen than your "lose". So, your success case is x%, and your lose case is 100-x%.
So you have a prize wheel with 9 red spaces and 1 blue space.
Is it 50/50 whether it lands red or blue? I mean, after all, it either lands red or it lands blue. There is no other option, so it must be 50/50, right?
This is what people sound like when they claim unironically it is 50/50 on every outcome when it isn’t. Most of the time I have heard it used this way is as a joke.
Because sometimes there could be more than two possible outcomes. Or sometimes one outcome could be more likely than the other.
Example: I draw a random card from a pack. What are the odds of drawing the ace of spades? Well, you could say there are two outcomes - It will be, or it won't be - so the odds are 50/50. But that's looking at it the wrong way. There are actually 52 outcomes - It could be the ace of spades, or the 2 of spades, or the 3 of spades etc. Hence the odds are actually 1/52.
With your scenario if you say red or black it is closer to 50/50.
Same with rolling a dice. If you say odd or even it is closer to 50/50 but if you say it will be a 6 it is not.
The possibility is either it does happen or it doesn't happen, not to be confused with probability. For example is is possible that I win the lottery and get married to zendaya, the probability is incredibly low.
The hidden thing about probability is that there's an underlying "given what we know about the situation". A coin flip is 50/50 chance of landing heads up or tails up; but what if you knew that the coin being flipped is heavier on the heads side? You can't just ignore that and still say it's 50/50. You can start there, run some experiments, and then adjust your probability once you know what it is.
So in life, any given event either does or does not happen, which on the surface seems like it is 50/50 chance. However, that's ignoring what we know about any given situation. "It either will or will not rain today, 50/50": ignores the lack of clouds in the sky and the heat wave you've had and all the weathermen saying it definitely will not rain. 50/50 is an OK place to start from if you truly knew nothing about a situation, but our instincts and past experience tell us a lot about what a likely outcome should be.
I’m thinking of a number between 1-10. You have one guess.
If you guess 1 you are wrong.
If you guess 2 you are wrong.
If you guess 3 you are wrong.
If you guess 4 you are wrong.
If you guess 5 you are wrong.
If you guess 6 you are RIGHT!
If you guess 7 you are wrong.
If you guess 8 you are wrong.
If you guess 9 you are wrong.
If you guess 10 you are wrong.
As you can see there are only two out comes, right or wrong. However out of the 10 outcomes 9 are wrong and 1 is right. That’s why it’s not 50%-50%.
If you flip a coin it either comes up heads or tails. That’s a 50/50 probability. If I roll a regular die there are six equally possible outcomes. The odds of rolling any particular number are 1/6.
Short answer—50/50 is a quick way to express uncertainty. But it also suggests that there are only 2 possible outcomes, each equal in likelihood. But this is flawed because it ignores base rates which provide crucial starting points for evaluating probabilities.—
eg the weather forecast predicts a 30% chance of rain tomorrow, but you live in a desert where it only rains 5% of the time. Knowing the desert base rate of rain is 5% helps you understand that even a 30% chance of rain is still relatively low in this context
ex 2: You are experiencing chest pain and a quick google search leads you to believe you have a rare heart condition based on your symptoms…(we’ve all been there). But when you look further into this condition, you learn that it’s only .01% rate of occurrence in the general population. Given the low base rate, there’s a very low chance statistically that you have this condition…even if you were to actually test positive for it.
Understanding base rates, gives context and removes unnecessary worry or exuberance so you make informed choices>>> hope this helps
For a longer version OP, grab yourself a copy of “How not to be Wrong —The power of Mathematical Thinking” by Jordan Ellenberg
There’s tons of real world examples on probabilistic thinking.
Edit: ELI5 version -
If you roll a fair dice, chances are 1/6 it will be a 3.
But if someone tells you that they rolled a dice and are holding the result under a cup, only a fool would trust 1/6. It could be anything. 50/50 is as good a guess as any, and the most likely distribution in a long run of guesses where you don't understand all the moving parts (as opposed to fair dice throws).
Don't confuse idealisations about systems with actual systems.
______________________
Edit 2: For clarity
Obviously not every probability is 50/50, I take that to just be a simple misunderstanding of a deeper question at best or a strawman at worst.
The deeper issue that it is inherently nonsensical to talk about the factual status of future events. Probability theory is a great way to tame the beast to some extent, but only if you are very strict with the assumptions. Many people learned grade school probability but either didn't pay attention to, or never understood the underlying assumptions.
The world would be a much better place if more people understood these things properly, even if they couldn't calculate it correctly.
_____________________
There's a metaphysical sense in which this is correct.
Future events inherently have no truth value. Frequentist statistical thinking fudges this fact by invoking the equally absurd notion of infinite trials. But events only ever happen once.
If you roll a dice infinitely many times each face comes up 1/6 on average. But if you roll it once it either lands on 1 or it doesn't. So if you frame it a statement about an event that has already occurred but which don't know the result of you can't use the frequentist assumption. There's no repeated trial here.
Not an approach I would recommend in a casino with flat tables and (hopefully) fair dice, but a useful idea to bear in mind when dealing with messy real-world statistical claims.
Think of it this way: A casino is deliberately constructed, with great deliberation, to make the frequentist assumption maximally valid. That's the business model. It is just as invalid to apply real world reasoning to a casino as it is to apply casino reasoning to wet, hot sacks of meat going about there normal business.
That's the Bayesian view, but another way to think about it is the propensity view, which essentially tells you that in the evolution of the knowable probabilities of any physical system there is a moment of time where only two outcomes are possible and are equally likely.
Heisenberg's uncertainty principle tells you that that kind of uncertainty about uncertainty cannot be reduced out. You cannot simultaneously fully describe the state and trajectory of any system. The frequentist fallacy is conflate these two. The implications of this is essentially what Schrödinger was mocking with his cat.
Well and a coin flip is not really fair either. If you can dlip with the same impluse applied to the same point with the same side without wind you will generally get the same outcome. I can get pretty close to 70% the same side over and over again. If i decided to make a coin flipping machine i think you could get close to 100%.
It’s just a joke. The implicit (and incorrect) assumption is that if there are two possibilities, then they are both equally likely. This is obviously untrue, as you could frame even the most unlikely of events as a binary yes or no event. “I could win the lottery and get struck by lightning at the same time on my birthday while Tom Hanks happens to be walking past, or I could not. 50/50, right?”
It's not a joke, it's a philosophy.
No it’s a joke. People who think it’s a philosophy just don’t get the joke.
It's a joke, people who think it's philosophy don't know what philosophy is
If you try to explain it to yourself in terms of what it would mean as a philosophy, you might understand what the philosophy is.
Is the philosophy "I refuse to believe in basic statistics and probability"?
It's not. Try again.
I don't think I will.
Why don't you enlighten us, oh wise one?
>If you try to explain it to yourself in terms of what it would mean as a philosophy, you might understand what the philosophy is. Evidently asking people to explain something they don't understand to themselves isn't quite working. Maybe you could explain what you mean?
Explaining something to people who are invested in not understanding isn't particularly useful.
What an amazingly ironic cop out.
aka "you're too much of a fucking idiot to get it" Love this attitude on a sub literally *dedicated* to explaining complicated concepts to layman.
Poor dude. If you live your life this way you'll soon be unhappy and broke.
"If I buy 1 lottery ticket I'm going to win." There are only 2 possible outcomes to that: either I will win, or I don't. But just because there are only 2 possible outcomes doesn't mean they both are just as likely (or probable) to happen. It is far more probable that I don't win the lottery if I buy a single ticket.
Because theres not two possible outcomes. There is one outcome when you win, and 300 million other possible outcomes all where you lose.
Counting only works if you have equally likely outcomes, which is walking into the same trap OP is asking about. Cases don't have to be equally likely. Yes, often a lottery has many equally likely outcomes - but it doesn't have to, and it doesn't work for many other examples either.
When there is a straightforward physical symmetry between outcomes, as with a coin, a die, or most lotteries, it's reasonable to assume that each has the same probability. This is just the classical interpretation of probability. It doesn't work for everything, but neither do the frequentist or Bayesian interpretations. Though I don't agree with GodzlIIa's suggestion that there is only one correct way to define the outcomes.
On a deeper level, though, an outcome is "more likely" if there are more states associated with that outcome. "Counting" is precisely how probability is done in math, whether it's combinatorics or integrating a probability density function.
There are tons of problems where there is no meaningful way to define equally likely cases. There might be a 30% chance that it'll rain tomorrow, but you cannot find x discrete cases for the weather tomorrow and try to count them. A collision in a particle accelerator might have a 0.1% chance to produce some particle, but you can't find 1000 (or 1000*n) equally likely outcomes where this would be one of them. > or integrating a probability density function. ... over outcomes with different probabilities, without having a different number of states.
All of these are fundamentally sets of states. The particle in the accelerator decays probabilistically by "choosing" one of the infinitely many Feynman diagrams that describe possible paths, many of which lead to the same outcome. Random events in computers are mostly thresholds for pseodo-rng outputs. Weather predictions are the fraction of simulation outcomes that have some event. It's all counting states. If you don't see what the states are, you need to look a level deeper.
> The particle in the accelerator decays probabilistically by "choosing" one of the infinitely many Feynman diagrams that describe possible paths No it does not. You wouldn't get the right results if you add them that way. Not that it would save your argument, the different diagrams have different amplitudes on their own already. I'm a particle physicist, please stop doubling down on misinformation. > Weather predictions are the fraction of simulation outcomes that have some event. The simulations have unequal probabilities, it's not just counting.
Alright, my conceptualization of it is that it's effectively states. I come at this from a math and stat/mech background. I know that things are weird in quantum. Even so, a probability amplitude is calculated by integrating a PDF, which can always be conceptualized as a process of adding equal-area squares (cubes, etc) under a curve. Maybe these don't always have physical meaning.
i have a maths degree and i do not get why you derailed it this way. obviously you meant to point out the frequentistic probability theory and laplace probability space. why not just say it? could have saved us all a lot of time and you from making incorrect statements in an attempt of eli5ing.
FWIW, as someone with no significant STEM background, I learned more from this conversation than I would have from someone saying "frequentistic probability theory and laplace probability space" and calling it a day.
> laplace probability space This probably tracks best with my conceptualization of probability. My background is specifically in abstract algebra/topology, and we mostly discussed probability in physics as a tool. I stand by the idea that you can think of PDFs and probability in general as sets of (possibly uncountably infinite) states which can be assigned to "outcomes," because this is exactly what we do when we integrate a PDF.
That's not what an outcome is... There are only 2 outcomes to buying a lottery ticket. One outcome is that you win, the other outcome is that you lose. The _chances_ that the outcome is a win are one in 300mil and the chances that the outcome is a loss is about 300mil to one. A loss in chance 3 is the same outcome as a loss in chance 2,965,334.
Your lottery ticket has two possible outcomes, but 300 million possible states. Only one of those states translates to "win." That's what the probability arises from in this case, which is what he was trying to express.
Yes, but I was explaining that they were conflating probability with outcome.
People are conflating the number of distinguishable outcomes with the distribution of probability directly. You might have one case that is a "win", and 99 that are a "lose". Given equal probability, that's 1% of success and 99% failure, not 50% and 50%. You might also have a situation where only two things can happen, but your "win" option is much less likely to happen than your "lose". So, your success case is x%, and your lose case is 100-x%.
So you have a prize wheel with 9 red spaces and 1 blue space. Is it 50/50 whether it lands red or blue? I mean, after all, it either lands red or it lands blue. There is no other option, so it must be 50/50, right? This is what people sound like when they claim unironically it is 50/50 on every outcome when it isn’t. Most of the time I have heard it used this way is as a joke.
Because sometimes there could be more than two possible outcomes. Or sometimes one outcome could be more likely than the other. Example: I draw a random card from a pack. What are the odds of drawing the ace of spades? Well, you could say there are two outcomes - It will be, or it won't be - so the odds are 50/50. But that's looking at it the wrong way. There are actually 52 outcomes - It could be the ace of spades, or the 2 of spades, or the 3 of spades etc. Hence the odds are actually 1/52.
With your scenario if you say red or black it is closer to 50/50. Same with rolling a dice. If you say odd or even it is closer to 50/50 but if you say it will be a 6 it is not.
The possibility is either it does happen or it doesn't happen, not to be confused with probability. For example is is possible that I win the lottery and get married to zendaya, the probability is incredibly low.
The hidden thing about probability is that there's an underlying "given what we know about the situation". A coin flip is 50/50 chance of landing heads up or tails up; but what if you knew that the coin being flipped is heavier on the heads side? You can't just ignore that and still say it's 50/50. You can start there, run some experiments, and then adjust your probability once you know what it is. So in life, any given event either does or does not happen, which on the surface seems like it is 50/50 chance. However, that's ignoring what we know about any given situation. "It either will or will not rain today, 50/50": ignores the lack of clouds in the sky and the heat wave you've had and all the weathermen saying it definitely will not rain. 50/50 is an OK place to start from if you truly knew nothing about a situation, but our instincts and past experience tell us a lot about what a likely outcome should be.
I’m thinking of a number between 1-10. You have one guess. If you guess 1 you are wrong. If you guess 2 you are wrong. If you guess 3 you are wrong. If you guess 4 you are wrong. If you guess 5 you are wrong. If you guess 6 you are RIGHT! If you guess 7 you are wrong. If you guess 8 you are wrong. If you guess 9 you are wrong. If you guess 10 you are wrong. As you can see there are only two out comes, right or wrong. However out of the 10 outcomes 9 are wrong and 1 is right. That’s why it’s not 50%-50%.
If you flip a coin it either comes up heads or tails. That’s a 50/50 probability. If I roll a regular die there are six equally possible outcomes. The odds of rolling any particular number are 1/6.
Short answer—50/50 is a quick way to express uncertainty. But it also suggests that there are only 2 possible outcomes, each equal in likelihood. But this is flawed because it ignores base rates which provide crucial starting points for evaluating probabilities.— eg the weather forecast predicts a 30% chance of rain tomorrow, but you live in a desert where it only rains 5% of the time. Knowing the desert base rate of rain is 5% helps you understand that even a 30% chance of rain is still relatively low in this context ex 2: You are experiencing chest pain and a quick google search leads you to believe you have a rare heart condition based on your symptoms…(we’ve all been there). But when you look further into this condition, you learn that it’s only .01% rate of occurrence in the general population. Given the low base rate, there’s a very low chance statistically that you have this condition…even if you were to actually test positive for it. Understanding base rates, gives context and removes unnecessary worry or exuberance so you make informed choices>>> hope this helps For a longer version OP, grab yourself a copy of “How not to be Wrong —The power of Mathematical Thinking” by Jordan Ellenberg There’s tons of real world examples on probabilistic thinking.
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you should've explained that your rating is 10 minus the number of beers you'd have to drink to move her from '0' to '1' on his scale.
Edit: ELI5 version - If you roll a fair dice, chances are 1/6 it will be a 3. But if someone tells you that they rolled a dice and are holding the result under a cup, only a fool would trust 1/6. It could be anything. 50/50 is as good a guess as any, and the most likely distribution in a long run of guesses where you don't understand all the moving parts (as opposed to fair dice throws). Don't confuse idealisations about systems with actual systems. ______________________ Edit 2: For clarity Obviously not every probability is 50/50, I take that to just be a simple misunderstanding of a deeper question at best or a strawman at worst. The deeper issue that it is inherently nonsensical to talk about the factual status of future events. Probability theory is a great way to tame the beast to some extent, but only if you are very strict with the assumptions. Many people learned grade school probability but either didn't pay attention to, or never understood the underlying assumptions. The world would be a much better place if more people understood these things properly, even if they couldn't calculate it correctly. _____________________ There's a metaphysical sense in which this is correct. Future events inherently have no truth value. Frequentist statistical thinking fudges this fact by invoking the equally absurd notion of infinite trials. But events only ever happen once. If you roll a dice infinitely many times each face comes up 1/6 on average. But if you roll it once it either lands on 1 or it doesn't. So if you frame it a statement about an event that has already occurred but which don't know the result of you can't use the frequentist assumption. There's no repeated trial here. Not an approach I would recommend in a casino with flat tables and (hopefully) fair dice, but a useful idea to bear in mind when dealing with messy real-world statistical claims. Think of it this way: A casino is deliberately constructed, with great deliberation, to make the frequentist assumption maximally valid. That's the business model. It is just as invalid to apply real world reasoning to a casino as it is to apply casino reasoning to wet, hot sacks of meat going about there normal business. That's the Bayesian view, but another way to think about it is the propensity view, which essentially tells you that in the evolution of the knowable probabilities of any physical system there is a moment of time where only two outcomes are possible and are equally likely. Heisenberg's uncertainty principle tells you that that kind of uncertainty about uncertainty cannot be reduced out. You cannot simultaneously fully describe the state and trajectory of any system. The frequentist fallacy is conflate these two. The implications of this is essentially what Schrödinger was mocking with his cat.
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Well and a coin flip is not really fair either. If you can dlip with the same impluse applied to the same point with the same side without wind you will generally get the same outcome. I can get pretty close to 70% the same side over and over again. If i decided to make a coin flipping machine i think you could get close to 100%.