But if it is 100 heads in a row, Hamlet is having you killed.

Jimmy the Greek said that he could make money from gambling in Vegas because he never played the games; he would do things like “I bet that blackjack player will bust on the next round” and make bets on the outcomes of the games.

1. The chance that a cylinder of vast length would stand on either end approaches zero
2 The chance that the cylinder will remain on its third surface approaches one.
3. The two ends are plane surfaces
4. The third surface is circular
5. The lower dimensional similarity to Euclidean SRT….local flat space and GR with its marginally closed spheroid geometry.
6. The overall stability of the sytem
7. The possbility of motion and change as the cylinder rolls in a certain direction…..

Each time a coin flips, so long as great pains are taken to keep the flipping process random, the chance of heads vs tails is exactly the same. However I remind my students a coin has three sides, not two and the chance the coin will stand on end increases as the thickness of the coin increases. If a coin is thick enough and becomes a cylinder, landing on the ends becomes very improbable- and landing on its third side becomes almost certain.

Seen from its proper perspective….its complete perspective, the universe much more clsely approximates a cylinder of vast length than a coin….

You can take two views:

a. to let yourself be guided by empirical data: in this case, bet on heads.

b. to let yourself be guided by your theoretical understanding: I have no clear evidence to suggest that the coin is not fair, so equal probability. If I have, I will act according to a.

This hinges on what “no clear evidence is”. If you define it as no falsifying evidence, heads coud come up a millions time and you don’t change your stance, because it is not impossible for this to happen with a fair coin. But if a close analysis of the physical coin suggest a physical difference, this will falsify the hypothesis “the coin is not fair” and you act according to a.

In a Bayesian approach, you would look at the probability of the coin coming up head as a random variable, with is own prior distribution. The prior can be anything that describes your prior assumptions about the coin, before observing any flips. Some people may be very confident that the coin must be fair and they trust the coin flipper to be fair too – this would mean that their posterior belief, after observing 10 consecutive heads, would only shift by a little bit towards heads. Other priors are also possible.
However, one thing is clear: unless your prior distribution has a bias towards TAILS, you will always infer that a HEAD is more likely on the 11th flip.

In all kinds of thought experiments and logic puzzles (and in, like, every paper ever in moral philosophy), we’re told, “Assume you’re in situation X” and then asked to reason in some way from there. But the real world is never like that. Whatever information we have, we’re using not just to draw some conclusion conditional on being in situation X, but also to update our prior as to whether we really are in X.

What makes it trickier is that in social contexts we all have some very strong priors that we can’t articulate clearly, or that we’re not even conscious of.

I don’t think, though, that that misunderstanding implies that I’m “deeply confused about basic statistics.”

General Lesson: Any time we find that “math” disagrees with reality, the problem is never with “math”—it’s with us, for using the wrong math!

AKA

Black Swan vs Moore’s Law

http://nosingularity.blogspot.com/2011/09/black-swan-vs-moores-law.html