PhilipTai

Right. Local storage is much more performant and cost effective than network storage. I tried to run some iops sensitive workload on cloud. It turns out I need to pay several thousands dollar per month for the performance I can get on a $100 nvme ssd.

Seems like an accurate emulation of the real capitalism, as intended by the game creator.

No. There is really no difference whether CEO is paid in cash or in stock, regarding the negative impact of the pay.

Scenario 1: CEO get paid $50 million in stock. Scenario 2: CEO get paid $50 million in cash. And then the company raise $50 million from stock market, so that it will have the same amount of cash as scenario 1.

They are the same.

For Fibonacci sequence,

             x = 1x^1
      x * g(x) =        1x^2 + 1x^3 + 2x^4 + 3x^5 + 5x^6 + ...
  + x^2 * g(x) =               1x^3 + 1x^4 + 2x^5 + 3x^6 + ...
  ------------------------------------------------------------
  =       g(x) = 1x^1 + 1x^2 + 2x^3 + 3x^4 + 5x^5 + 8x^6 + ...

Hence,

     x = (1 - x - x^2) * g(x)
  g(x) = x / (1 - x - x^2)

The techniques of constructing such sequences have been studied formally in combinatorics under the name "generating function".

http://en.wikipedia.org/wiki/Generating_function

In this case, the sequence 1, 2, 4, ..., 2^n has the generating function,

  g(z) = sum[i = 0 to inf] (2^i * z^i) 
       = 1 + 2z + 4z^2 + ... 
       = 1 / (1 - 2z)

Substituting a small number 10^-k, such as z = 0.0001 gives 10000/9998, and then right shifting by dividing 10000 leads to 1/9998.

What more interesting is that some other useful sequences can often be obtained from the function, by operations like differentiation and integration, or adding / multiplying with other functions.

For example:

  2z + (4*2)z^2 + (8*3)z^3 + (16*4)z^4 ...
  = d/dz(g(z))
  = d/dz(z * 1 / (1 - 2z))
  = 2 / (1 - 2z)^2

Put z = 1/10000 = 0.0001, this yields 50000000/24990001 = 2. 0008 0024 0064 0160 0384 ...