Gambler’s Fallacy and the Regression to the Mean
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Re: Gambler’s Fallacy and the Regression to the Mean
#2It is very annoying in business. Arguing that two outcomes are equally likely when one has happened many more times than the other is an exercise in frustration. It takes a certain level of courage, charisma and stubbornness to argue that there is no evidence that 2nd best is just as good as best when there is a measurable difference between two options.
This is a big contributor to why markets perform so well in my humble opinion. People who see past the gambler's fallacy to the actual odds of things working get rewarded, and the people who assume the current leader must be doing something different and better than the competition get punished.
> When your variable disease is expressing its worst symptoms, you are likely to feel better in the future
This is the influence of time & the healing process, not a regression to the mean. Symptoms in a given sickness' progression aren't random variables in a practical sense. It goes no symptoms -> bad symptoms -> lingering symptoms -> better (or permanent symptoms, bad luck :[ ).
Re: Gambler’s Fallacy and the Regression to the Mean
#3It is very annoying in business. Arguing that two outcomes are equally likely when one has happened many more times than the other is an exercise in frustration. It takes a certain level of courage, charisma and stubbornness to argue that there is no evidence that 2nd best is just as good as best when there is a measurable difference between two options. This is a big contributor to why markets perform so well in my…
> Arguing that two outcomes are equally likely when one has happened many more times than the other is an exercise in frustration
Are they actually equally likely though? Perhaps there comes a point where one must consider if observed outcomes match with assumed probabilities.
Or are you just having arguments about whether the unfavored outcome is 'overdue.'
Re: Gambler’s Fallacy and the Regression to the Mean
#4It is very annoying in business. Arguing that two outcomes are equally likely when one has happened many more times than the other is an exercise in frustration. It takes a certain level of courage, charisma and stubbornness to argue that there is no evidence that 2nd best is just as good as best when there is a measurable difference between two options. This is a big contributor to why markets perform so well in my…
> Arguing that two outcomes are equally likely when one has happened many more times than the other is an exercise in frustration Are they actually equally likely though? Perhaps there comes a point where one must consider if observed outcomes match with assumed probabilities. Or are you just having arguments about whether the unfavored outcome is 'overdue.'
Funnily enough, I might have been thinking of the exact opposite of the Gambler's fallacy. My mistake, sorry. But it still seems related to me and I'll explain what I was thinking anyway:
For reference: https://www.omnicalculator.com/statistics/coin-flip-probabil...
There is a 20% chance that in 7 coin flips there will be >5 heads. By symmetry, 40% chance that there are >=5 heads or >=5 tails.
If you look at a series of events (say, annual results) and one has exceeded the other in 5/7 years, that doesn't tell us that one is consistently better than the other. But people aren't good at accepting that.
Re: Gambler’s Fallacy and the Regression to the Mean
#5> “I know that the fact that the roulette wheel has come up red 10 times in a row tells me NOTHING about spin #11. On the other hand, I know that over time, there will be just as many black spins as red spins, so at least intuitively, a black spin seems at least a little more likely to come up next in order to push that ratio back towards 50/50. Are these two principles actually in tension with each other? If not, how do we resolve the apparent tension? If yes, isn’t it the case that there must be “some” validity to the gambler’s ‘fallacy’?”
To this my answer would be: if you are doing millions and millions of spins then you should see roughly 50/50 but that just means over a few million spins it will balance out -- and even then it's not usable for predictions because it's not exact. Also, in a similar long sequence you would expect that in 2046 spins you see 10 of a single color in a row. That's not such an outrageously big number...
Re: Gambler’s Fallacy and the Regression to the Mean
#6So 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 prize), and then ask if you want to change your choice to the other unopened door. If you change your choice your odds of winning go up from 1/3 to 2/3.
which to me makes intuitive sense. Every other time I've encountered this it's usually presented in a very ambiguous way, where it isn't clear if the host has any information about what's behind the doors. If the host is choosing a door randomly and it doesn't happen to contain the prize, your odds don't improve if you switch your answer.
...I guess I just want to say that I think the Monty Hall problem is dumb. It's not some mind blowing truth of probabilities that human brains can't grasp; it's just a poorly worded problem that causes you to make incorrect assumptions.
You could argue that if you don't know whether or not the host has any knowledge about where the prize is you might as well switch, because if they do you've improved your odds and if they don't you haven't made things worse. But still, the "problem" itself doesn't seem that interesting.
Re: Gambler’s Fallacy and the Regression to the Mean
#7> “I know that the fact that the roulette wheel has come up red 10 times in a row tells me NOTHING about spin #11. On the other hand, I know that over time, there will be just as many black spins as red spins, so at least intuitively, a black spin seems at least a little more likely to come up next in order to push that ratio back towards 50/50. Are these two principles actually in tension with each other? If not, ho…
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.
Re: Gambler’s Fallacy and the Regression to the Mean
#8> “I know that the fact that the roulette wheel has come up red 10 times in a row tells me NOTHING about spin #11. On the other hand, I know that over time, there will be just as many black spins as red spins, so at least intuitively, a black spin seems at least a little more likely to come up next in order to push that ratio back towards 50/50. Are these two principles actually in tension with each other? If not, ho…
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.
Re: Gambler’s Fallacy and the Regression to the Mean
#9So 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…
In the Monty Hall problem the host always knows where the prize is. It’s a mind blowing problem because usually a person’s intuition is wrong. For almost everyone they need to carefully analyze the problem in order to understand why their intuition is wrong. There are lots of such examples in math.
Re: Gambler’s Fallacy and the Regression to the Mean
#10So 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.