Coin Flipping Problem

Elo from LessWrong suggested this problem:

I write a sequence of n heads or tails on paper.

I then start flipping a sequence of n coins. If next coin does not match my sequence, I restart a new sequence of n coins.

What is the rule for the relationship between how many coins I need to flip to get the sequence I have pre-committed to and the length of the sequence of?

Discussion there:


Chances are

That one of these  days, weeks or months, an Ebola infected refugee will land on Lampedusa.

A crisis with such a humble begging could be quite severe. Oh, My Lord, couldn’t we rather get some financial crisis, even 10 times as big as anything we know? A possible prayer for many days which can follow such an event.

Evolution will select then. Humans and viruses who are going to survive. Countless viruses and perhaps many million of humans will die in the process.

Chances are, that it will simply not happen. That we are going to be lucky, once again.

EU parliament could and should discus this matter. So fellow Europeans, ask your elected representatives about this, now, while we are still fortunate!


Coulds, Musts and Rathers

First, there are no musts, only rathers with a very high probability. Still we will use must as an abbreviation for a highly probable rather (even 1.0 probable if there are any such), because everybody is used to. I’ll give you an example how this works.

Say, that I have just moved my chess king.

  1. it must be my at least second move in the game
  2. it is rather at least my third move in the game
  3. it is rather late in the game
  4. I rather have white pieces
  5. I am rather losing
  6. it is rather not a checkmate for my opponent
  7. it must not be a checkmate for myself
  8. I am rather not a Chinese
  9. I am rather an Armenian
  10. I am rather alive
  11. my opponent must not have a chance to en passant in his next move
  12. my opponent and me, are rather males

There are certainly thousands or even millions more such rathers nobody is aware of, in the above case, alone.

The number 8, what does it mean? I am rather not Chinese anyway, they are a minority in this world. But the fact, that I moved a chess piece decreases the probability of being Chinese from 1/5 to 1/10 or even less, since the game of chess isn’t very popular in China.

I am rather not an Armenian, it is 1/1400 that I was. But that was before I made this king move. Now it is at least 1/1000 that I am in fact an Armenian. Perhaps even 1/100, due to the popularity of chess there. The probability just went up, hence the rather qualificatior now.

What about 5? Apparently I am not attacking my opponent with a rook and at least one white queen on a nearly empty board, when there is little need for me to move my king. King is not very often an attacking piece when it moves it is rather under some pressure. Not always, only the probability for such a situation is bigger. Hence the rather qualificator.

In my comment to the msjr’s comment in the previous post, I gave an example, where it will rather be two, than an ace at the river at poker.

Whatever happens, at every corner, in any situation in this world, the vast cloud of rathers, updates itself with every new bit of information coming in. Actually it doesn’t update automatically, you have to do it yourself, just like a true detective or a true scientist. You have to calculate the rathers cloud on the premise of everything you know at any moment. This way, you will function just as a true scientist should. It is impossible, I know, but you have to try it sometimes.

There are always a lot of breathtaking rathers, in almost every possible situation. Some are quite useful.


Poker, a Few Facts

  1. at the standard game (before Texas Holdem), there is NO chance for a player to have the Flush Royal and for another to have 4 aces
  2. the probability of the same situation at the TH is so low, that those YouTube videos you can watch are most likely staged.
  3. any two “hands” at the showdown are NOT entirely independent events.
  4. the mere act of folding sends some information about the cards of other players to everybody else
  5. the next card to be shown is NOT independent of the bets (and folds) already made in the game
  6. not every set of five publicly seen cards is equally likely to occur. Aces are a bit rarer then twos.

Some did find those quite hard to understand, but they are all true. Some even apparently stranger facts might be out there, I wonder what they are.

mathematics, probability

A Doubt

My mother in law has been struck by lightning and bitten by a snake. She survived both.

Now, what are the probabilities of those events occurring? According to some Google search results, 1 in 10 thousand for each, perhaps 1 in 100 thousand. Which implies she is one in 100 million to one in 10 billion with both experiences!

This is a very uncomfortable for my worldview.  It shouldn’t have happened. Unless of course, if for example the snake wasn’t real. She didn’t see the snake, only a small painful wound which the doctor interpreted as a snake bite.

There is another explanation. She is a very outgoing person, and for this kind the statistics may be very different, perhaps even more so in this part of the world. Additionally we are not talking about two independent events here. Among lightning struck people a snake bite may be quite common. Think about Bear Grylls for example; some people keep pushing their luck against all the natural elements.

Unfortunately, all such apparent mysteries are not as easy to explain. Niel Armstrong had a problem, I am not sure he was aware of. He should of asked himself – what’s more probable: that I am to be the first man on the Moon, for which the odds are at least one in 100 billion, or that I am just a lunatic with a delusional memory? The odds for the latter are about one in a million.

Here Andrei Kolmogorov and his complexity comes to the rescue. Armstrong had photos and movies, not merely memories. Other people would have to have conspired with him, when he was telling his space stories. Therefore, the complexity of a possible illusion/conspiracy would be much greater than 47 bits. Much, much more. So, Armstrong, as a rational man, ought to believe he was indeed the first man on the Moon.

The alternative was much less probable.

This is also why you don’t need to believe that you are a materialized Boltzmann brains. A picture like the one you are looking at with your eyes just now, would come with only a tiny minority of all Boltzmann brains.

Always go with the shortest possible bitstring when you are in doubt. The shortest complete explanation is always the most probable.

Almost always.








I Can’t Believe It, But I Try To

Years ago, we met at the pub, like many times before and since.

Him: A meteorite was found in the Hills.

Me: Was it actually found or just seen falling?

Him: Found, by somebody I know, and you also met him before, at least once.

Me, pondering silently: It’s been more than a century, since the only bolide in the whole country was picked up. The area of 20,000 square kilometers has yielded 1 meteorite per 100 years. Now he is telling me the local area of less than 1000 square kilometers has brought us the second in the last year? It’s 1 in 2000.

Me: Maybe.

Reality proved him right, it really happened, despite my disbelief.

mathematics, physics, probability

Grey Hole

We all know what black holes are. The places where matter goes, but from whence it can hardly return. To the extent that it does come back, it does so due to Hawking radiation. Very, very, very slowly.

Because of this, black holes are actually grey holes – a very dark shade of grey.

What about some other examples of grey holes in different contexts? There are plenty of them, in various contexts. Western Germany was once a grey hole for Eastern Germans. Once across the border, they hardly ever came back to the East, not vice versa. Until the whole country was swallowed, in a span of 45 years from 1945 to 1989, this was a clear case of a figurative grey hole, swallowing not only the Eastern Germans, but also the Turks and the people from the Balkans, as well as many others.

The USA is another, even bigger example of a demographic grey hole. For centuries it has attracted and kept many of those who travelled there. Some Americans escape to Sweden or to the UK, but not that many, by far.

A bathroom sink-hole is a grey hole for your hair. They tend to go there, but they hardly ever come back. There are lots of gruesome grey holes everywhere we live. We must exhort special effort to make those clean again.

Whenever the probability of an object O, travelling from A to B is greater than the probability of the same object travelling from B back to A — B is a grey hole for O kind of objects.

Then, we have a build-up of such a grey hole, until the directional probabilities change. The water molecule in the kitchen air has a small chance of colliding with the ice already built up in your freezer. There is a much lower chance of it ever coming back spontaneously. Therefore ice is growing in all older models of deep freezers. There is no energy for those molecules to come back once they land on ice.

Antarctica is the same kind of a grey hole. When a water molecule from the Pacific lands there, it simply lacks the energy to return to the sea – at least when the temperature is, on average, 40 degrees bellow zero. Which it is now, and has been thus for a long time already.

Understanding this rather trivial fact, prevents you from being baffled, like certain scientists allegedly are as to why the Antarctic ice is growing.

A lake in the European Alps, is a grey hole for water molecules from the glacier above. The probability of them travelling to the lake and then to the sea is greater than vice versa. At least until it becomes much colder than it has been for centuries now.

There is no science more powerful than simple maths. If the simple maths/physics doesn’t agree, then no fancy science is even feasible.