Transposing mathematical content into gaming

Our proposal draws inspiration from the work of Martin Gardner. In Gardner (1974) a coin toss game is presented: “If [a penny] is flipped three times, there are eight equally probable outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH and TTT. One player selects one of these triplets and the other player selects a different one. The penny is then flipped repeatedly until one of the chosen triplets appears as a run and wins the game.” We implemented a web-based version of the game: students are challenged to choose a triplet of coin toss outcomes (e.g. “head, head, tales”, or HHT). Afterwards the computer chooses another triplet (e.g. HTH), and the coin is tossed until one of the chosen triplets appears; the player whose triplet appears first wins. At the GAME conference, we demonstrated the online implementation of the game and showed that the computer indeed always has a better chance of winning. We also provided explanations of the underlying mathematics.