So sad.

Okay, so I didn't check what exactly the content of that mail was.. but I can imagine. It makes me sad how far love has been misunderstood.

Warum??

Eh, ben.

Pirate Game - revealed.

Completely overwhelmed by the response to my last post – I didn't take into account that a lot of you guys are as much geeks as I am :), – let me explain the solution strategy. It uses what is called 'backward induction':


If the oldest pirate (pirate 1) is the only survivor of the big massacre, he will keep all 100 pieces of gold.
Thus, whatever pirate 2 suggest, he is gonna be killed (even if he offers all the gold to the oldest, that one will still want to kill him).
Hence, pirate 2 will accept whatever offer pirate 3 makes, for the benefit of mere survival. So pirate 3 can keep all the gold to himself, and still get his own vote and that of pirate 2.
In order to survive, pirate 4 needs to get 3 votes: His own plus two of his fellows'. He knows that pirate 2 and 1 are easy to convince: He merely needs to offer them one single piece of gold. Then the remaining 98 pieces are all his. So: If pirate 5 dies, this is gonna be the outcome of the game: 98 pieces of gold for pirate 4, no gold for pirate 3, 1 piece of gold for pirates 2 and 1, no further deaths.

So what does the youngest pirate know?
- Pirate 4's vote is his if and only if he offers him 99 pieces of gold.
- Pirate 3's vote is his if and only if he offers him 1 piece of gold.
- Pirate 2's vote is his if and only if he offers him 2 pieces of gold.
- Pirate 1's vote is his if and only if he offers him 2 pieces of gold.
Since, in addition to his own, the youngest pirate needs two more votes, the highest amount of gold he can keep for himself is 97 pieces, give one to pirate 3 and two to either the oldest or the second oldest pirate.


However, in real life, most people don't think as far... so rest assured, with such bloodthirsty pirates, a few people will die because we fail to teach game theory to poor mortals around the world! :) :)

Pirate Game

Since the film 'A beautiful mind', everybody should have somewhat a notion of game theory. (Remember the bar scene with the blonde and her friends?)

So I'm taking this class this semester on the topic, (no worries, though, the FBI hasn't asked me to work for them yet). We analyze all sorts of games, and I'm just writing up the pirates game, modeling some business process (what did you expect? :)) :

There are 5 pirates, ranked from the oldest (1) to the youngest (5). After having looted 100 pieces of gold, they return to their island and decide to share the loot and retire. The way they propose to do it is the following:
The youngest pirate proposes first an allocation for the gold (assume that each piece of gold is not divisible). Everybody votes either in favor or against the proposal. If the proposal has strictly more than 50% of 'Yes' votes, then it is implemented and the game ends. If not, then the pirate is killed and eliminated from the game. Then the youngest alive makes a proposal. We do this until one of the proposals is accepted.

For completeness, assume each pirate prefers to be alive rather than getting killed. Also assume that between killing and not killing, a pirate always prefer to kill another pirate.

Always something happening in these maths classes. :)

More than mere kindness

I came across this quote by C.S. Lewis, and because I do have the best intentions to keep this website alive, I decided to start this revival by my reading highlight of the day.

There is kindness in Love: but Love and kindness are not coterminous, and when kindness [...] is separated from the other elements of Love, it involves a certain fundamental indifference to its object, and even something like contempt of it. Kindness consents very readily to the removal of its object – we have all met people whose kindness to animals is constantly leading them to kill animals lest they should suffer. Kindness, merely as such, cares not whether its object becomes good or bad, provided only that it escapes suffering. As Scripture points out, it is bastards who are spoiled: the legitimate sons, who are to carry on the family tradition, are punished (Hebrew 12:8). It is for people whom we care nothing about that we demand happiness on any terms: with our friends, our lovers, our children, we are exacting and would rather see them suffer much than be happy in contemptible and estranging modes. If God is Love, He is, by definition, something more than mere kindness. And it appears, from all the records, that though He has often rebuked us and condemned us, He has never regarded us with contempt. He has paid us the intolerable compliment of loving us, in the deepest, most tragic, most inexorable sense.

- C.S. Lewis, from 'The problem of pain'