21–30 of 96 posts
For an honest roulette wheel (ignoring 0 and 00): What would you say about the logic of betting the next 100 spins will be 50% red and 50% black? Would you say something different about betting on black after 50 consecutive reds?
If 50 consecutive reds come up on a roulette wheel and you bet on black each time, then you might be a sucker. Someone was lying to you about that wheel being honest.
So the author presents the Monty Hall problem this way (very explicitly saying that the host knows where the prize is an will not reveal it): > You are given a choice of three doors, behind one is a prize. You can choose one door. The host of this game, who knows where the prize is, then opens one door without a prize (again – they know where the prize is and deliberately choose one of the unchosen doors without a pr…
"which to me makes intuitive sense" Your intuition is either very good or complete bollocks, or at least worryingly odd 8) Monty Hall is a really clever problem and worth studying in some depth. Whenever I've encountered it, the rules are always given without ambiguity. Even so, it is very hard to get to the bottom of the probabilities. You can reason your way through it and possibly get to the right answer, unaided.…
Imagine the problem this way: The host of a game show presents you with 100 doors, behind one of which is a prize. You pick one, and you know that your odds of having chosen the correct door are 1 in 100. The host, who knows where the prize is, then opens 98 other empty doors, leaving one. You know that the odds were 99 in 100 that the prize was behind one of those other doors, and the host just eliminated 98 of them.
...what am I missing here?
Earlier quoted context omitted.
Fun fact, the actual roulette wheel in casino has green zero. When betting on any color, you will always have less than 50/50 odds.
Funner fact, many even have a green double zero as well to tip it even further.
Even funner fact, even if there isn't a zero and you truly get 50/50 odds, you'll still hit ruin over the long run because the house has "unlimited money."
So the author presents the Monty Hall problem this way (very explicitly saying that the host knows where the prize is an will not reveal it): > You are given a choice of three doors, behind one is a prize. You can choose one door. The host of this game, who knows where the prize is, then opens one door without a prize (again – they know where the prize is and deliberately choose one of the unchosen doors without a pr…
Why would the host reveal the car when the contestant has a chance to switch doors?
So the author presents the Monty Hall problem this way (very explicitly saying that the host knows where the prize is an will not reveal it): > You are given a choice of three doors, behind one is a prize. You can choose one door. The host of this game, who knows where the prize is, then opens one door without a prize (again – they know where the prize is and deliberately choose one of the unchosen doors without a pr…
"which to me makes intuitive sense" Your intuition is either very good or complete bollocks, or at least worryingly odd 8) Monty Hall is a really clever problem and worth studying in some depth. Whenever I've encountered it, the rules are always given without ambiguity. Even so, it is very hard to get to the bottom of the probabilities. You can reason your way through it and possibly get to the right answer, unaided.…
So the author presents the Monty Hall problem this way (very explicitly saying that the host knows where the prize is an will not reveal it): > You are given a choice of three doors, behind one is a prize. You can choose one door. The host of this game, who knows where the prize is, then opens one door without a prize (again – they know where the prize is and deliberately choose one of the unchosen doors without a pr…
I don't really understand how you think the game could work if the host didn't know where the prize is? They'd keep accidentally revealing the prize, and then asking you whether you want to switch to the other remaining door, at which point... what's the point? The game is over. I've not usually seen it explicitly stated like this that the host knows, but it's always seemed obvious to me that they must.
And a third version where the host only asks you to switch if you initially picked the car, and otherwise always ends the game early.
The best part is that during the game you can't actually tell which rule set you are playing with!
Earlier quoted context omitted.
"which to me makes intuitive sense" Your intuition is either very good or complete bollocks, or at least worryingly odd 8) Monty Hall is a really clever problem and worth studying in some depth. Whenever I've encountered it, the rules are always given without ambiguity. Even so, it is very hard to get to the bottom of the probabilities. You can reason your way through it and possibly get to the right answer, unaided.…
Maybe I'm just misunderstanding something then? I'm not trying to be dismissive or act like I think I have some special intuition here. It really does just seem straightforward. Imagine the problem this way: The host of a game show presents you with 100 doors, behind one of which is a prize. You pick one, and you know that your odds of having chosen the correct door are 1 in 100. The host, who knows where the prize i…
Earlier quoted context omitted.
"which to me makes intuitive sense" Your intuition is either very good or complete bollocks, or at least worryingly odd 8) Monty Hall is a really clever problem and worth studying in some depth. Whenever I've encountered it, the rules are always given without ambiguity. Even so, it is very hard to get to the bottom of the probabilities. You can reason your way through it and possibly get to the right answer, unaided.…
Maybe I'm just misunderstanding something then? I'm not trying to be dismissive or act like I think I have some special intuition here. It really does just seem straightforward. Imagine the problem this way: The host of a game show presents you with 100 doors, behind one of which is a prize. You pick one, and you know that your odds of having chosen the correct door are 1 in 100. The host, who knows where the prize i…
To get the subtlety here, you probably need to model it which is what I did. That's why I'm an IT bod these days, with a Civil Engineering degree and not a mathematician or statistician.
So the author presents the Monty Hall problem this way (very explicitly saying that the host knows where the prize is an will not reveal it): > You are given a choice of three doors, behind one is a prize. You can choose one door. The host of this game, who knows where the prize is, then opens one door without a prize (again – they know where the prize is and deliberately choose one of the unchosen doors without a pr…
Here's some explanation: https://betterexplained.com/articles/understanding-the-monty...
I find TFA's argument about the gambler fallacy not being associated with regression to the mean quite hand wavy.
"Regression to the mean is not a power in the universe that ensures that statistics work out in the end, it is purely a probability."
Who said the opposite?
The gambler making the gambler's fallacy basically says that after successive black streaks it's more likely to see a red. They aren't saying that there's some "power in the universe" ensuring it. They're saying it's just more probable.
And in a way it is: assuming a non-biased roulette, each successive repeat N-same-streak should be increasingly less likely.
Taking all the groups of N rolls and showing that any N-same-streak going is just one of the possible permutations same as any other (and thus any N+1, N+2, N+3, etc. would be too) doesn't really cut it.
If you happen to actually see a 1000th black roll streak in a casino, you'd better suspect the roulette is rigged/biased, than naively think that "well, even with random independent events, there are bound to be large streaks".