The Gambler

As a followup to the previous lecture, we reexamine the gambler model. We begin by providing a model solution for the gambler function, as described in the previous notes. However, we would like to take this a few steps further.

• To produce graphs such as those given in the previous lecture notes, comparing the chance of success and average number of bets to the starting bankroll. Here is an example showing the statistics for last classes challenge of goal=100, p=0.49.
  
• To produce graphs that plot the success percentage and average number of bets relative to the probability.
  
• Although we already track the average number of steps for a given trial, we wish to update our code in order to compile statistics, for each possible bankroll value, of how many steps begin with that bankroll.
• To animate a single trial showing the current bankroll along the way, as well as a summary of what percentage of time was spent with each intermediate bankroll.

As a step in this direction, here is an updated version of the gambler.m file that provide an animation of the process when trials==1, and which can track the number of steps spent at each individual bankroll.