# Tag Info

### Why don't fair coin tosses "add up"? Or... is "gambler's fallacy" really valid?

Since you have asked for a non-formal answer, I shall try to oblige by not using any numbers or equations. Fundamentally, your question is, how does it come about that individual events can be ...

### Why don't fair coin tosses "add up"? Or... is "gambler's fallacy" really valid?

If the probability of heads = p , then the probability of tails = 1-p . If it's a fair coin, then p = 1-p and the probability of either heads or tails is p = 1/2. Now suppose the number of coin ...

### Isn't the notion that everything will occur in an infinite timeline an example of the gambler's fallacy?

It looks like you've hit upon the concept of almost surely in probability theory. Something occurs "almost surely" if it happens with probability 1, but there still exist situations where that thing ...

### Is the SETI project built on false premises?

Scientists use statistical significance measures all the time, discussed here: How improbable does an event have to be before we can say it didn't happen by chance? "Life occurring on earth ...

### Why don't fair coin tosses "add up"? Or... is "gambler's fallacy" really valid?

The convergence appears pretty quickly. This is your faulty assumption. It does apear pretty quickly. In most cases. But not at all every time. There are in some sense two layers of likelyhood: In ...

### Have I found a paradox, or is the universe digital? Or am I just plain wrong?

We run into essentially the same problem almost any time we try to combine the real numbers as described by mathematics with probability theory. When applying probability theory to something like a ...

### How does probability constitute as knowledge in justified belief theory?

There is no paradox here. What you knew for certain before the lottery was that there were 100,000 possible outcomes, in only one of which you would win. The result of the lottery does not change the ...

### Does Bayesianism give an out for pseudoscience that it shouldn’t deserve?

The first issue is that the presented hypothesis is actually two hypotheses. While the sentence "Adam can guess, using psychic powers, what the price of each stock in the world will be at the end ...
Accepted

### Does every possible event have non-zero probability?

The answer is no. Mathematically, if you have a continuous random variable, the probability of getting any one of its values is zero, but you can still get one, so zero probability does not ...

### Why don't fair coin tosses "add up"? Or... is "gambler's fallacy" really valid?

Yet we also know that the series will converge upon an equilibrium of heads:tails. I think this is your central problem. This is indeed the most probable result of a series of coin tosses, but ...

### What is unique about the quantum state of superposition?

I recently answered a similar question on physics.SE here. What is special about the probabilities of quantum mechanics is that the randomness cannot be explained by a theory of nature that is both ...

### Why don't fair coin tosses "add up"? Or... is "gambler's fallacy" really valid?

If you use a fair coin, the average of heads thrown will converge to 50%. However, the number of heads won't converge to half the coins thrown. While the percentage comes closer and closer to 50%, ...
Accepted

### Is all of probability fundamentally subjective and unneeded as a term outright?

In fact there is no way to define unique objective probabilities for anything that happens (or not) in the real world. Every definition of probability requires model assumptions that cannot be ...

### Isn’t everything absurdly improbable?

The probability of getting 100 straight heads is the same as any other sequence, yet the other sequences aren’t seen as improbable. Yes they are, if you put a piece of paper in a sealed envelope ...
Accepted

### Isn't the notion that everything will occur in an infinite timeline an example of the gambler's fallacy?

Here, I think, is a more succinct answer: Let's say we have a dice with 1 trillion sides. Then, the probability of a given outcome on the next roll of the dice is one-in-a-trillion. On the other ...

### Is there any rigorous definition of just one single random choice?

It's best to think of randomness as a model, not as a 'thing'. When we talk about a 'random event', we mean that at some time t0 we cannot predict with certainty the state of a system at time t1 (t1 &...

### Does every possible event have non-zero probability?

In Bayesian theory, the principle that every logically possible proposition has a probability that is never exactly zero, nor exactly one, is called the Cromwell Rule. The idea behind the principle is ...
Accepted

### Is it ever rational to stumble onto the conjunction fallacy in probability?

Well, the conjunction fallacy is a fallacy, so it's not rational to believe it. However... Suppose Dave tells you he was just robbed and that's why he's were late to meet with you. You are skeptical, ...

### Isn’t everything absurdly improbable?

Isn’t every event by definition improbable in the sense that each event precedes an infinite series of causes that could have (theoretically atleast) been different? Specific events don't have ...

### Have I found a paradox, or is the universe digital? Or am I just plain wrong?

Zeno's Paradox is not a paradox. It is an attack on loose thinking. By emphasising the infinite nature of one thing, and not mentioning the infinite nature of another, it confuses people into thinking ...

### Is getting 100 Heads in a row from a fair coin a miracle or not?

Yes, but only because every possible sequence of flips is a miracle. Consider. Suppose I flip a fair coin 10 times in a row. Say I get HTTHTTHTHT. Now that seems pretty normal, nothing remarkable ...

### Should X, if there’s no evidence for X, be given a non zero probability?

You mention Bayesians, so I'll reply in that context. The Bayesian framework is (roughly) a way to take a "prior probability" of a statement, multiply it by a factor accounting for new ...

### How does probability constitute as knowledge in justified belief theory?

In a lottery, the expectation that you will definitely lose is not justified. The expectation that you are very likely to lose with a tiny chance of a huge win is justified. Now the fact that you will ...

### How does probability constitute as knowledge in justified belief theory?

It is irrational to buy a lottery ticket, not simply because the chance of winning are low. The expected value of the money you gain is negative. In other words, if you had enough money to buy all ...

### Can a coincidence be evidence of a god?

Suppose for example that a person is standing on stage and says “God, if you exist, strike me with lightning right now” and a lightning strike occurs that barely misses him, is this evidence of God? ...

### Why don't fair coin tosses "add up"? Or... is "gambler's fallacy" really valid?

This is really math, not philosophy. Assume that you've tossed the coin so far m times and gotten n heads. The fraction of heads so far is n / m. Now you toss the coin one more time. There is a 50% ...

### Why don't fair coin tosses "add up"? Or... is "gambler's fallacy" really valid?

Because "converge to an equilibrium" doesn't mean an exactly equal number of heads and tails, it means the proportion of heads to tails approaches equality (with probability 1: the meaning of which ...