Monty Hall — Consider Only Strategy Dec 2022

There’s an excellent post by randerson112358 that presents a comparison of strategies for the fiendish Monty Hall problem. For me, comparing strategies offers an irrefutable argument in favor of switching doors.

https://medium.com/swlh/simulate-the-monty-hall-problem-using-python-7b76b943640e

Thanks for the great post !

I offer a tight excerpt summary; read the post by <strong><em>randerson112358</em></strong> for the enlightening details

look at the STRATEGY of NEVER switching

Never switching choices:

Probability of Winning = 1/3

Probability of Losing = 2/3

look at the STRATEGY of ALWAYS switching

The prize is behind #2

Scenario #1: You choose door #1 — Host opens #3 — You switch to #2 — WIN !

Scenario #2: You choose door #2 — Host opens #3 or #1 — You switch to #1 or #3 — LOSE

Scenario #3: You choose door #3 — Host opens #1 — You switch to #2 — WIN !

Switching choices:

Probability of Winning = 2/3

Probability of Losing = 1/3

Much better chances

look at a fictional scenario where there are 100 doors

… you choose one of the doors randomly. Your chance of choosing the door with the prize is 1 / 100 which is 1%. The host then reveals to you 98 other doors that contain a goat leaving just your first choice and one other unopened door, so we know one of them contains the prize and the other contains the goat.

Do you still think, given this scenario that you have only a 50% chance of winning by switching or not switching since there are two unrevealed doors left ?

Two other websites

There’s a website that presents a Monty Hall simulation; it keeps score for staying and switching. It has a manual and an automatic mode. In the manual mode, you can mix strategies while you play; the score is kept for each strategy.

They say experience is the best teacher.

https://www.mathwarehouse.com/monty-hall-simulation-online/

And how about the tree approach ?

I find it substantial, convincing, and artistic.