Implementing simulation with monads

Monads are expected to pass through a kind of pipeline: a monad will be passed as an argument to a function and a similar monad will be returned as the value of the function. The functions must be designed to accept and return similar structures.

We'll look at a simple pipeline that can be used for simulation of a process. This kind of simulation may be a formal part of a Monte Carlo simulation. We'll take the phrase Monte Carlo simulation literally and simulate a casino dice game, Craps. This involves some stateful rules for a fairly complex simulation.

There is some strange gambling terminology involved, for which we apologize. Craps involves someone rolling the dice (a shooter) and additional bettors. The game has two phases of play:

• The first roll of the dice is called a come out roll. There are three conditions:
  • If the dice total is 7 or 11, the shooter wins. Anyone betting on the pass line will be paid off as a winner, and all other bets lose. The game...