Ask The Wizard #411

No, I disagree.

Money management is overrated. It doesn't matter how player's play a game of luck like roulette, the house edge cannot be dented in either direction.

As to the argument that the casino can simply outlast the player until he goes bust, it is possible the casino will go bust first. Consider a player with a $10,000 bankroll against any MGM-Mirage casino. The market cap of MGM-Mirage, at the time of this writing, is $11,168,000,000. Further assume, for the sake of argument, the company owned 100% of its stock. If the player played until either side went bust, he would have a 1 in 1,116,801 chance of winning the entire company. Given the large player volume, eventually some player would be successful.

The short answer is each state starts with at least one. Then, each additional seat is awarded one at a time to the state that would realize the "greatest benefit" from that seat.

It gets more complicated in how the "greatest benefit" is calculated. Here are the details:

1. Calculate the "multiplier" as the geometric mean of (1) the percentage increase in total seats with the extra seat and (2) the percentage increase in total seats if the state had one more seat than it actually does. To put it in a formula, if n is the current number of seats, then the multiplier is 1/sqrt(n*(n+1)).
2. Calculate the "priority value" as the product of the multiplier and population of the state.

Do this calculation for every state. The state with the greatest priority value gets the next seat.

Let's look at Nevada, for example. The 2020 population was 3,104,614 and it already has 4 seats. The multiplier is 1/sqrt(4*5) = 1/sqrt(20) = 0.223607. The priority value is 3,104,614 * 0.223607 = 694,213.

Not that you asked, but if the congress added a 436th seat, it would go to New York. The following table shows priority value for all 50 states in order.

As to your second question, yes, that is possible. I had to fidget for a while to find a situation where this happened. First consider a hypothetical country with the following six states. With 15 total seats, the allocation would be as follows:

Next assume there was a census and the populations changed significantly, but the total remained the same at 3,900 and Anxiety increased in population from 400 to 401. It would get only one seat with 15 states.

I wish to emphasize I had to tinker with the numbers for quite a while to find a situation where this happened. Overall, I find the method quite fair.

Here is my solution (PDF).

This question is asked and discussed in my forum at Wizard of Vegas.