/sci/ - Science & Math

>>15052127
Shifting probabilities would be very difficult. You would need something like a Galton-Watson Process.

But since this is static you can use the quadratic formula.

You can visualize this intuitively. Envision a 10 by 10 square with 50 squares shaded red that have E (Empty) in them and 30 squares shaded gold with G in them.

Then the perimeter of the 20 "Chest" squares in the bottom right has a darker boundary of its own 40x50 subsection of the grid. This subsection is bisected into two down the middle, which unfortunately for visualizing makes for fractional squares, but oh well.

Now shade 50% of the two smaller squares red and 30% gold. Then turn the other 20% into a new square and bisect it.

As you can see, each smaller square has identical shares of red and gold, but the size occupied by each gets smaller and smaller at each level. This is your sample space. It contains itself. This is exactly what the quadratic formula is for, to deal with copies within copies. With the golden mean, you can get infinite copies of the same rectangle with the same ratios. Neat stuff.