Switch Craft: Is the Switch Strategy Still Optimal When the Monte Hall Game Is Expanded to More Than Three Doors?

Overview

Objectives/Goals It is well established that a "switch strategy" gives you a better chance of winning a prize in the traditional 3-door Monte Hall Problem. The objective of this study was to see if the "switch strategy" would still be preferred if you played the game with more than three doors. Additionally the goal was to see how the statistical chances of winning would change and could be predicted. Methods/Materials Cups, toy goats, toy car, computer, Microsoft Excel. Wrote a code to simulate playing the game on a computer automatically. Use this to show the results from playing the game 10 times, 100 times, 1000 times etc. up to 1,000,000 times. Results The "switch strategy" gave you a better chance of winning the prize, even when the game was played with more than three doors. Conclusions/Discussion I predicted a formula for the chances of winning if you played with "n" doors and always switched. That formula is (n-1)/n.

Competition history

• CSEF 2017 Mathematical Sciences · Entry J1503

Resources

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