Hi all. I have been working my way through the Probability course, specifically the section on Conditional Probability, when I fell upon this linked problem.
By solving the linked problem recursively, you find that you have a probability of winning the game.
I thought this would be a fun problem to program, so I wrote a program in Python 3 to solve this using Monte Carlo methods. The program and output of the program can be seen below.
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Assuming the program is correct, the probability of winning the game is approximately , as opposed to the original solution that states you have a chance of winning the game.
Can anyone explain what is going on here (it is very possible that my code has something wrong with it, or I am misunderstanding some fundamental concept. If you catch anything please point it out :)?