Improbability Principle

I too had never heard of this. Nor am I known for my mathematical or statistical acumen but a couple of minutes reading the Wiki page on the problem clarified it immediately. To be more specific, the little diagram showing the one-third and two-thirds relationship before and after the opening of the third door made it obvious. 

Now, perhaps someone could explain to me the gambler's fallacy and whether there is a relationship to this Monty Hall problem? As a naive young man, I visited a casino and figured that if I waited for the roulette wheel to deliver three blacks in a row then I had a much better chance of winning on red. Not only that but if I didn't win on that bet, I would double the stake on the next spin. And so on. As it happened, I won a fair amount so, believing that I had stumbled upon a foolproof system, I went back the next night and lost all of my winnings (and more). The great lesson for me was to stay away from gambling. I only discovered later that this was a well known fallacy.

As long as you have a big enough bankroll, that approach is fairly fool-proof! With a medium sized bankroll, however, it takes too long to squeak out any winnings, since you have to start with such a small bet so it doesn't grow too quickly, and you always run the risk of getting bankrupted if you happen to lose 10-12 times in row (which I have seen more than once at a casino). But if you have unlimited funds, it's a way to make money (though I think they would toss you if they realized what you were doing. They aren't big fans of idiot-proof ways to extract the money from the casino, shockingly).

Well, I notice lots of people, proponent and non-proponent alike, who don't get it.

Do you think this misunderstanding contributes to whether or not someone is a proponent?

Linda

I have no idea how much disprobabilia might be involved in various beliefs.

~~ Paul

Fascinating, never heard of it before.

Acting intuitively, I also fell straight into into the trap and gave the last two doors 50:50.

But, found it much more difficult to fall into the trap when there were more doors, and didn't fall into the trap at all when it was presented as the pea under one of three cups.

Despite spending an hour reading about it, returning back to the initial problem again, I could still feel I was intuitively attracted to giving the last two doors 50:50.

I like this explanation the best, because it involves no probability:

What if Monty offered you both of the other doors?

~~ Paul

Now, perhaps someone could explain to me the gambler's fallacy and whether there is a relationship to this Monty Hall problem? As a naive young man, I visited a casino and figured that if I waited for the roulette wheel to deliver three blacks in a row then I had a much better chance of winning on red. Not only that but if I didn't win on that bet, I would double the stake on the next spin. And so on. As it happened, I won a fair amount so, believing that I had stumbled upon a foolproof system, I went back the next night and lost all of my winnings (and more). The great lesson for me was to stay away from gambling. I only discovered later that this was a well known fallacy.

I wrote a simulation of the St. Petersburg Paradox, which is related to the Gambler's Fallacy. It involves flipping coins. The longest sequence of tails I saw was 31. And that was with only about an hour's simulation.

~~ Paul

I wrote a simulation of the St. Petersburg Paradox, which is related to the Gambler's Fallacy. It involves flipping coins. The longest sequence of tails I saw was 31. And that was with only about an hour's simulation.

~~ Paul

And that tells me I was right to abandon my sure-thing, get rich quick scheme

I wrote a simulation of the St. Petersburg Paradox, which is related to the Gambler's Fallacy. It involves flipping coins. The longest sequence of tails I saw was 31. And that was with only about an hour's simulation.

~~ Paul

So after 31 blacks, put the house on red?

As long as you have a big enough bankroll, that approach is fairly fool-proof! With a medium sized bankroll, however, it takes too long to squeak out any winnings, since you have to start with such a small bet so it doesn't grow too quickly, and you always run the risk of getting bankrupted if you happen to lose 10-12 times in row (which I have seen more than once at a casino). But if you have unlimited funds, it's a way to make money (though I think they would toss you if they realized what you were doing. They aren't big fans of idiot-proof ways to extract the money from the casino, shockingly).

Berkeley this is terrible advice!  With a big enough bank roll playing longer and longer you will pretty much assure yourself of losing it all using this - or any other - legal method. You’re forgetting about the the non red or black squares (0s), that make the odds less than 50-50 to land on either red or black. 

The gamblers fallacy depends on not realizing that each spin is completely independent of the previous one. Each spin has exactly the same chance of landing on red or black or green independent of th last spin of the last million spins. 

The only way to be up in roulette long term is to stop once you are ahead.

The only way to be up in roulette long term is to stop once you are ahead.

My father's technique was to watch the wheels for an hour or so before beginning play. He said that he almost always found one that was slightly out of calibration. Of course, he only played at a few casinos and never won too much, so they didn't throw him out on the street.

~~ Paul

My father's technique was to watch the wheels for an hour or so before beginning play. He said that he almost always found one that was slightly out of calibration. Of course, he only played at a few casinos and never won too much, so they didn't throw him out on the street.

~~ Paul

This topic reminds me of a Dunninger mentalism card game i used to play with a friend long ago. I'd usually win. Not sure how I did, but I suspect I was simply weighing the odds, maybe a form of card counting for what the next card would be.

The gamblers fallacy depends on not realizing that each spin is completely independent of the previous one. Each spin has exactly the same chance of landing on red or black or green independent of th last spin of the last million spins. 

Excluding PK effects, of course.