I can accept the fact that on a Roulette wheel (as long as there are no defects or imbalances in the wheel or ball) that the odds are the same each spin and previous spin outcomes have no influence over the current spin. However, if I see black come up 32 times in a row I am betting on red for the next spin.
Humans are bad at perceiving true probability, we naturally look for patterns as an evolutionary trait. We also have the cultural beliefs around luck which don’t actually have any basis in the real world—e.g. I’ve suffered some bad luck, but it’s surely about to turn around.
Gambling games are typically designed to exploit these two traps that most people will fall into without realising.
I heard someone say that luck is just chance with a personal attachment.
The important part is “internalizing” that one spin doesn’t influence the next. A red won’t be more likely after N blacks unless something specifically made it that way. Sequences like “long run of reds/blacks” don’t have any actual significance, but “seems like they should” because we’re heavily geared towards pattern matching.
That is why it is called a fallacy
You can always bet on odd/even in that case that way you have a chance no matter what colour it lands.
That’s why they added 0 and 00 (green) so it’s not quite 50/50 for odd/even or red/black.
There’s a story about a numbers runner from back in the day. Some people would bet a different number every day, but a lot would bet the same number every day, even if it never came up.
[The ‘numbers’ is a gambling game where you pick a three digit number; the runner would collect the bets and make the pay out. From the days before most places had a state run lottery]
Apparently all roulette wheels have some imperfections and the older the wheel the more pronounced the imperfections become. In other words, these imperfections tend to lead to the ball landing in the same places over and over again. I read an article about a group of gamblers that studied particular roulette wheels, analyzed their flaws, and then made a series of bets, winning big. But, this would tend to attract attention, so they never really played the same wheel more than once.
it’s to do with the priori
Tbh if I see black come up 32 times in a row I’m probably betting on black just because I’m gonna start getting suspicious this wheel has actually been biased towards black somehow and isn’t as random as it’s supposed to be. Is there such a thing as an inverse gamblers fallacy?
In a Bayesian sense this would be called updating your prior. You assume the wheel is truly random. After many observations that assumption seems not to hold so you adjust your prior probability that any given spin will land on black to be higher.
If you have good reason to believe it’s a fair wheel, that’s actually still just the gambler’s fallacy.
If you have no exceptional reason to believe it’s fair, it would be updating your priors, like the other commenter said.
Humans are bad at statistics and probability. We’re naturally wired to find patterns and connections and make decisions quickly without needing to perform calculations. It works for simple stuff but when things get a little complicated our “gut feeling” tends to be wrong.
My other favourite probability paradox is the Monty Hall Problem. You’re given the option to pick from 3 doors. Behind 2 of them are goats and behind 1 is a new car. You pick door #1. You’re asked if you’re sure or if you’d rather switch doors. Whether you stay or switch makes no difference. You have a 33% chance of winning either way. Then you’re told that behind door #2 there is a goat. Do you stay with door #1 or switch to door #3? Switching to door #3 improves your odds of winning to 66%. It’s a classic example of how additional information can be used to recalculate odds and it’s how things like card counting work.
@ImplyingImplications @alt_total_loser I think, probabilities are high, this includes those who confirm their proofs.
Often the problem descriptions suffer from equivocation and unclear process frame.
After you find out there’s a goat behind door #2, you have a 50% chance whether you stay on 1 or move to three. There are only two possible outcomes at that point (car or goat), so either way it’s a coin flip.
People will claim that you’re wrong, but you’re 100% correct. It’s always 50-50. You either win, or you don’t.
The important thing is that the host will always show you a goat, meaning the only way the other door has another goat is if you just so happened to pick the car the first time.
Take the situation to the extreme and imagine a hundred doors, and after you pick a door, the host opens 98 doors, all of them with goats behind them. Now which seems more likely, that you chose right the first time, or that the other door has the car?
My comment is clearly sarcastic…
You’re wrong, but you’re in good company. It’s a very counterintuitive effect. One technique that can be helpful for understanding probability problems is to take them to the extreme. Let’s increase the number of doors to 100. One has a car, 99 have goats. You choose a door, with a 1% chance of having picked the car. The host then opens 98 other doors, all of which have goats behind them. You now have a choice: the door you chose originally, with a 1% chance of a car… or the other door, with a 99% chance of a car.
Oh that’s so weird. I get it from a proof perspective but it feels very wrong.
My brain tells me it’s two separate scenarios where the first choice was 99:1 and after eliminating 98 there’s a new equation that makes it 50:50.
Now you have 2 choices: the door you chose, or the only other door left. One has a goat and one has a car. That’s fifty-fifty.
In your explanation, the door originally had a 1% chance, but after showing 98 goats, it has a 50% chance.
The important thing is that the host will always show you a goat, meaning the only way the other door has another goat is if you just so happened to pick the car the first time.
Take the situation to the extreme and imagine a hundred doors, and after you pick a door, the host opens 98 doors, all of them with goats behind them. Now which seems more likely, that you chose right the first time, or that the other door has the car?
The host’s intentions are irrelevant. Numerically, there are only two choices. That makes it fifty-fifty.
You think that even in the hundred-door case? Test it. Hell, even test it in the 3 door case. It is empirically not 50%.
If the host had an even chance to show you either door, you’d be right, but since the host always shows you a goat, the two events (picking a door and choosing whether to switch) are no longer independent, since if you pick a goat it forces the host to pick the other goat.
No. Taking it to the extreme with 100 doors, your first pick was a 1% chance to get the car. The host then shows you 98 other doors that all have goats.
What’s more likely? That you picked the right door when it was 100:1? Or that the other door is the one with the car?
There are 2 choices so they are equally likely
One of those choices is, itself, one of two choices. So it’s secretly three, but two of them look identical.
They’re really not.
The important thing is that the host will always show you a goat, meaning the only way the other door has another goat is if you just so happened to pick the car the first time.
Take the situation to the extreme and imagine a hundred doors, and after you pick a door, the host opens 98 doors, all of them with goats behind them. Now which seems more likely, that you chose right the first time, or that the other door has the car?
Your first paragraph made it click. Thanks!
You can test it empirically. It’s clearly not 50%.
There are only two options at that point. It MUST be 50-50.
Check out this book:
Here is an alternative Piped link(s):
The Gambler’s Fallacy is Really Odd
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never give up
You’re going to make it all back next time!
never surrender
By Grabthar’s hammer
Fallacy’s are Fallacys exactly because they prey on some human emotion or evolutionary brain quirk.
The amount of circular conversations I’ve had with people…
“So you’re telling me flipping heads 10 times in a row is likely? Then do it right now!”
“No, I’m just saying it’s not less likely than any other combination.”
“Oh I get it.” [Flips head] “Right so next ones got to be tails”
🤦Its not a fallacy. The problem is that in a perfect world, stuff is truly random. In the real world, things have biases.
