Generalized Monty Hall Problem Simulation

Generalized 'Monty Hall' problem simulation with graphing and theortical value calculator for the switch strategy win percent

Theoretical Monty Hall Problem

The General formula for the problability of getting a car after switching is given by the formula :

• Number of Doors(D)
• Number of Cars(C)
• Number of Doors to be opened by the host(O) \

Additional Reading: Higher Variations of the Monty Hall Problem

Installing requirements.txt:

pip install -r requirements.txt

Program Description:

The user defines the parameters for the problem:

• Number of Doors(D)
• Number of Cars(C)
• Number of Doors to be opened by the host(O)
• Number of Trials (N)

The classic parameters for the problem are (3 doors, one car and one door to be revealed).
The simulation then runs for (n) number of times, and each time picks a door then the host reveals a number of doors that don’t contain the prize. Then, the simulation tries out 3 strategies and records the results
• Stay at the chosen door
• Switch to an unopened door
• Random: make a random choice between all unopened doors

The win percentage for each strategy vs number of trials is plotted in real time

Sample Run:

Times to play ? 10000
Choose total number of doors : 3
Total number of cars : 1
Number of Doors to be opened : 1

Output

The simulation results in 10000 trials:

Strategy	Win percentage
Stay	34.04
Switch	65.96
Random	49.78

Theoritcal Switch win percentage	Simluation Switch win percentage
66.66666666666666	65.96

License

MIT