Throwing dice

This was an interesting question posted somewhere on the Internet. I rephrased it a bit as I understood it.

Suppose you're playing the following game: Each time you throw a dice you get the result payed out. If you throw 4 or more, you can throw again; otherwise, the game stops. How much are you willing to pay to play the game? 

The solution I came up with:

 If you write down a tree, you can see you're calculating the limit of: 


(1/6+...+6/6) + (3/6)( (1/6+...+6/6) + (3/6)( (1/6+...+6/6) + ... )) 


of which the fixed point is 


ϕ = (1/6+...+6/6) + (3/6)(ϕ) 


is ϕ = (7/2) + (1/2)(ϕ) 


is (1/2)(ϕ) = (7/2) 


is ϕ = 7


At most 7.


Corollary: if you take ϕ = (2/2) + (5/2) + (1/2)(ϕ) it is trivial to expand ϕ to (2/2) + (7/4) + (12/8) + (17/16) + ...

Bernanke is a genius?

I was looking at an English investor on the London School of Economics channel, and he called Bernanke an 'evil genius.' I don't know about the evil part, but it seems to me that he did everything right. So, this is what I think he did:

What do you do when your assets -mostly debt- in an economy deteriorate and everybody wants to sell them (actually everything) off, leading to possible deflation? You aggressively buy all bad assets at the central bank, supply lots of liquidity to the banks, wait a bit, and let them destroy the bad debt with the returning liquidity.

I am not even sure this leads to inflation since the bad debt is destroyed, but I will not claim to understand a lot of it...

Anyway, people complain about the enormous balance sheets of the Fed today, but at least the Fed now has an enormous capacity to fight inflation when they want to. Bernanke certainly cleaned up a lot of mess there.