Binomials and entropy

If my binomials, two, both have p=q then 

Log2 (k N), N being the number of coin tosses is entropy.  But if I have two binomials sharing coin tosses, the N becomes a fraction, n1  n2, The total coins tosses drops out on a comparison. Since they share the arriving coin tosses, they are relatively prime in the number of coin tosses.

Each binomial is a sample size, and needs be  sampled as -iLog(i).  That is the idea of optimum portfolio, Apportion coin tosses to make this as true as possible. This is maximum entropy estimation rather than least squares.

The states and districts are not balanced at maximum entropy, we are stuck with coins tosses of about five to one. Think of the traveling salesman going from capital to capital, trying to keep the ratio. The imbalance means the p does not equal q, the two binomials will be skewed. There is an interest cost that balances them yet again if we know the number tosses.   That interest cost is the is really the ratio of the net share between states and districts. If the deal is lousy, the third binomial, Pauli and his exclusions, will lower the amount paid. The Pauli exclusion says you have to make a deal now, one deal and only one deal.