Let's return to the statistics question we considered in Part A: Can a person develop skill at playing a game of chance like Push Penny? Note 9
Let's say that a very determined person played 100 rounds of Push Penny with the following results (the number of hits out of four pushes per round):
Note: This is an ordered list (i.e., the first round was three hits out of four pushes, the second was two out of four, and so on).
Do these results suggest that our player has developed skill in playing the game? How might we analyze these data to answer this question? One approach would be to compare these 100 scores to the scores for a player who has no skill -- in other words, a player who is just making "random" pushes.
In order to do this, you must have a description of a random player -- specifically, you need to know the probability that a random push will hit a line.