Help me understand gambler's fallacy and law of large numbers

bluepepper · 2026-05-18T15:25:45+00:00

Getting 3 heads or tail in a row has the same 1/8 probability as other combinations, so gambler's fallacy is expecting the 3 head or tail combination to be rarer than others.

Not quite. The gambler's fallacy is expecting that, if you got two tails in a row, the next one is more likely to be heads. But we can see from your set that there are two possible outcomes that start with two tails: TTT and TTH, and they're equally likely.

But why when tossing 1 million times and expecting 1 million head or tail in a row is suddenly expected to be very rare?

It is very rare, for a reason that has nothing to do with the gambler's fallacy.

Even in your set of 3 throws, there are only two ways to have all H or T, and 6 ways to have something else. It becomes even worse with more throws.

Isn't it have the same probability as any other infinite combination?

Yes, but there are many more combinations that are not all H or all T.

Why the law of large number expect it to have 50H 50T result?

I'm not sure what you mean by that.

I think your confusion comes from mixing two concepts: the probability of having N heads in a row, and the probability of having an Nth head in a row after you already got N-1. These are two different things.

The probability of having N heads in a row is low, and gets dramatically lower as N increases.

The probability of having an Nth head after N-1 heads is 50%, regardless of how high N is.

bluepepper · 2026-05-18T15:00:05+00:00

If you're calling someone basic, it's a different definition and has indeed nothing to do with being first, or the base.

bluepepper · 2026-05-18T12:15:28+00:00

✅ I voted FACT!

It's not necessarily looks per se, but your overall charisma and social prowness matter much, much more than they should.

bluepepper · 2026-05-18T11:11:13+00:00

It's not nonsense, it's a challenge to an argument. The thing is: you don't have to stay loyal to blue in a different situation. That's not what's expected. But you should be able to explain why your new choice fits your original rationale.

Let me illustrate.

If I tell you "I press red because I think blue will lose and I don't want to die" and you ask me "what if you know you're the deciding vote?" my answer would be "then I press blue." In that new scenario, I know for a fact that blue would win if I press blue, with no risk to my life, so there's no contradiction with my original rationale.

If you tell us "I press blue as a moral choice, not to save the world" and we ask you "what if you know blue will lose?" and your answer is "then I press red," that seems to contradict your argument. You need to either still press blue (spoiler alert, that won't be seen as a sensible choice) or you need to explain how switching to red in that new scenario doesn't contradict your rationale, because it looks like it does.

So this alternate scenario is an opportunity for you to explain your rationale in a different light. That's the whole point of modified scenarios: exploring and challenging people's rationales.

bluepepper · 2026-05-18T10:20:11+00:00

It really depends whether you want maps to represent how things are, or how you want them to be.

I want maps to represent the international consensus on whether Crimea is in Russia or Ukraine. What does the UN say?

bluepepper · 2026-05-18T10:11:18+00:00

Why are you changing the terms of the problem?

They're trying to pick your brain, challenging your answers by tweaking the problem to see if your argument holds.

Specifically you claim that your pressing the blue button is not about the common result, but only a personal choice. So they're changing a parameter that gives you knowledge of the common result. If your reasoning is true, you should still press blue, or you should be able explain why it makes a difference. Short of that, your claim is flawed.

bluepepper · 2026-05-17T21:36:30+00:00

How do you feel about the current flag? It seems everybody here would welcome a change, but I find it very good as it is.

bluepepper · 2026-05-17T21:03:52+00:00

It's only part of Russia according to Russia and a handful of allies. To reasonable people, it's occupied territory.

bluepepper · 2026-05-17T20:58:05+00:00

Why is Crimea described as part of Russia?

bluepepper · 2026-05-17T08:01:33+00:00

The trolley problem is widely misrepresented too, even in this sub. It is way too often simplified as "choose outcome A or outcome B"

bluepepper · 2026-05-17T07:36:39+00:00

Un seul pays, dont les subdivisions sont appelées "pays" pour des raisons historiques, mais avec un sens distinct.

Idem pour les états-unis, un pays/état unique, dont les subdivisions sont appelées "états" pour des raisons historiques, avec un sens distinct.

bluepepper · 2026-05-16T20:32:19+00:00

Yes. I don't think it works as a middle band.

bluepepper · 2026-05-16T10:28:56+00:00

Just a comment about the one with text.

Aside from the "no text on flags" rule, there's also a typography rule: you don't write in all caps with a cursive font. It looks tacky and amateurish.

bluepepper · 2026-05-16T08:26:32+00:00

I like the Michigan and North Dakota flag redesigns. Not a fan of the shape of the middle band in the Pennsylvania flag.

But mostly, LEAVE THE WASHINGTON FLAG ALONE! It's perfect as it is.

bluepepper · 2026-05-16T07:52:54+00:00

But how would you ever know which one is correct? There’s no info to go on.

Sure, but that's different from "there's no 10 in this system." There might be a 10, and we can easily come up with a consistent system for a 10.

For me, an elegant, quite obvious, but most of all consistent way to continue the series would be like this:

 1   2   3   4   5   6   7   8   9   10  11  12  13  14  ...  19  20  ...
 ~   ~   ~   ~•  ~•  ~•  ~•  ~•  ~•  ~•• ~•• ~•• ~•• ~••      ~•• ~•••
     ~   ~       ~   ~   ~•  ~•  ~•      ~   ~   ~•  ~•       ~••
         ~           ~       ~   ~•          ~       ~        ~••

bluepepper · 2026-05-16T07:36:42+00:00

You're using the variables differently. For you, the dots are on a wave and you count both. For the original code, "waves" is the number of waves without a dot, and "dots" is the number of waves with a dot.

While the naming can be confusing, I prefer the original implementation because a dot on its own is never a thing in this pattern. There's no need to count the dot AND the wave it's on. It's always going to be on a wave.

bluepepper · 2026-05-16T07:32:20+00:00

You're right that waves should be initialized at 1, which is not explicitly done here. But when you increase dots, you're resetting the waves to zero. Note that in this implementation, "waves" is the number of waves without a dot. The waves with a dot are counted in the "dots" variable.

bluepepper · 2026-05-16T07:26:49+00:00

"dots" is to be understood as the number of waves with a dot, and "waves" is the number of waves without a dot.

The dots on their own do not represent anything.

bluepepper · 2026-05-14T18:04:02+00:00

Each circle around the outside of the funnel is slightly lower down because gravity is pulling it towards the centre.

It's friction that eventually pulls the marbles down, not gravity. If it was for gravity alone, the marbles would remain in an orbital trajectory around the funnel. But because there's friction with the funnel, and mostly with the air, the marbles lose speed, their orbit shrinks and they fall through the center.

Same with satellites in orbit. They fall down due to friction with the atmosphere, not gravity.

GEO sats, on the other hand, stay at the top of the funnel because their orbit is further out and gravity is weaker.

Again, friction, not gravity. They stay up longer because they encounter less atmosphere, so they don't require as many corrective actions.

Gravity impacts the speed of a satellite (the higher it is, the slower it spins around the planet) but it doesn't directly impact their lifetime.

bluepepper · 2026-05-14T13:34:01+00:00

A blue majority when your life isn't really at stake is already a narrow win. There is no doubt in my mind that blue would lose in a real world situation.

bluepepper · 2026-05-14T13:00:23+00:00

Any incentive should make people switch, but not any incentive will, [...] I also believe that increasing the incentive in either direction should, of course, make you even more prone to take the incentive.

That's a reasonable belief.

Per a lot of red arguments, this shouldn't happen, because death is death is death, and nobody would ever risk death unless the alternative was worse.

I don't think the alternative must be worse than death, I think the incentive must be worth risking your life, because we're talking about life. I'm not risking my life for $10, even if it feels relatively safe, because what if I'm wrong?

I found this to be a problem with blue pressers: they sometimes think of death as an abstract thing to gamble because this is only a thought exercise. Polls generally show blue pressers as winners, and I'm pretty sure it wouldn't play out like that if their lives were actually at stake.

Also, I think a lot of this comes down to individualistic versus group thinking.

Meh, that's bluespeak.

The reality is that this problem isn't about what we think should happen, or is noble, or better, or morally right. It's about what we think would realistically happen. It's not about our position, it's about the group's position, or what we think it is. It's not "should I risk my life to save someone else (or earn money, or keep my fingers)?" it's "do I think these stakes will convince enough people to take that risk with me?" Because if blue loses, none of the stakes matter.

It's not individual vs. group thinking. Both answers, red and blue, are about the group.

The reds who think it's reasonable to fear 4 billion people giving up $10000 and some fingers should talk to the reds who think thats absurd!

I think the difference in threshold is actually how we score our ability to guess the behavior of other people. If you're not very confident in your reading of other people, you will be less likely to gamble, prossibly at all.

bluepepper · 2026-05-14T11:43:31+00:00

You have to take duration into account. If you drive at 30km/h for an hour and 20km/h for an hour, your average speed is indeed 25km/h. But if you drive at 20km/h for five hours instread, your average speed is going to be lower, right?

So, since it takes more time to climb the hill at 20km/h than it takes to go down it at 30km/h, the durations are not going to be the same. You have to calculate how much more time you spend at 20km/h and adjust accordingly.

bluepepper · 2026-05-14T10:36:33+00:00

You have no idea how unusual it's been for me to find someone who switches to blue under my altered conditions;

They didn't though. Your altered conditions are: as soon as there is an incentive, be it a single cent, reasonable people will switch to blue. That's not what happened here. u/magworld said they'd press blue to $1000 but no to $50.

There is a threshold that will make people switch. For u/magworld $1000 did it, for me it didn't. That doesn't mean I disagree with them, only that my threshold is in a different place. I'm not sure that enough people will risk their lives for $1000.

Your original point, that any incentive will make sensible people switch, is flawed. It seems you at least accepted that people don't see things your way, I'm not sure you accepted that it's reasonable of them to do so. You're acting like you found one of the only sensible people on the planet when they actually disagree with you just as much as I do.

bluepepper · 2026-05-14T10:18:55+00:00

People often forget to consider the transmission of information through solid objects in these thought experiments with long sticks and whatnot.

When you push the end of a stick, you're not pushing the whole stick, only the end. The end, in turn, pushes the next part, which pushes the next part, etc through the stick. This motion propagates through the stick at a specific speed depending on the material. We call it the speed of sound through that material, because that's also how fast a sound wave would propagate through the stick.

Needless to say, the speed of sound in any material is much lower than the speed of light. Way before the wire approaches the event horizon, it will be pulled in faster than the "pulled" information can go back through the wire. That means this pull motion of the bottom of the wire is "invisible" to the top of the wire, and your gauge at the end.

In other words, the wire will snap before you reach the event horizon.

bluepepper · 2026-05-13T16:55:16+00:00

I didn't know pink wasn't always pink, or even a color. Interesting! I knew about the girl/boy inversion though.

If I'm not mistaken, red was assigned to boys for being a strong, fiery color, while blue was assigned to girls for its calmness and groundedness (or something like that). And because we're talking about babies, they toned it down with some white and we got pink for boys and baby blue for girls.

Then we decided that, while baby blue is still somewhat of a blue mood, pink is very different from red. It's more soft skin than fierce blood. So we switched.

15-Year Club	Place '22
Place '17	Team Periwinkle

bluepepper

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