Using a two-player coin game paradox in the classroom

This classroom paradox is an effective tool to motivate students to accept as fact only those things that are backed by reasonable evidence. A two-player game consists of repeated tosses of a loaded coin, until one of the player's three outcome sequences.for example, Tails, Heads, Tails (THT).occurs. Player 2 chooses his or her sequence after hearing Player 1's choice. The question is, if we know that the probability of Heads is 70%, does Player 1 or Player 2 have the advantage? To their detriment, nearly all students will want to go first and select HHH, which is not even the best choice for the universally disadvantaged Player 1. This example can be presented at several different levels, tuned to the background of the class.