A Simulation of the Monty Hall problem.
https://en.wikipedia.org/wiki/Monty_Hall_problem
To validate the results here is a state table showing the possible sequences of goats and car. It's showing that Sticking should give a 33.3% win rate vs 66.6% win rate.
| Stick | Switch | ||||
|---|---|---|---|---|---|
| Sequence | car | goat | goat | ||
| Stick | guess | reveal | 1 | ||
| Switch | guess | reveal | Switch | 0 | |
| Sequence | goat | car | goat | ||
| Stick | guess | reveal | 0 | ||
| Switch | guess | Switch | reveal | 1 | |
| Sequence | goat | goat | car | ||
| Stick | guess | reveal | 0 | ||
| Switch | guess | reveal | switch | 1 | |
| Sequence | car | goat | goat | ||
| Stick | guess | reveal | 0 | ||
| Switch | switch | guess | reveal | 1 | |
| Sequence | goat | car | goat | ||
| Stick | reveal | guess | 1 | ||
| Switch | reveal | guess | switch | 0 | |
| Sequence | goat | goat | car | ||
| Stick | reveal | guess | 0 | ||
| Switch | reveal | guess | switch | 1 | |
| Sequence | car | goat | goat | ||
| Stick | reveal | guess | 0 | ||
| Switch | switch | reveal | guess | 1 | |
| Sequence | goat | car | goat | ||
| Stick | reveal | guess | 0 | ||
| Switch | reveal | switch | guess | 1 | |
| Sequence | goat | goat | car | ||
| Stick | reveal | guess | 1 | ||
| Switch | reveal | switch | guess | 0 | |
| ------- | ------- | ------- | ------- | ------- | ------- |
| Total | 3 | 6 | |||
| Percentage win rate | 33.33333333 | 66.66666667 |
Here is the output from running the code:
How many games? 100000000
The result for stick is a 33.322797% win rate, the result for switch is a 66.663946% win rate out of 100000000 games.