STATS 146 Discussion: Let's Play a Game

https://math.andyou.com/tools/montyhallsimulator/montysim.htm

Let's play a game! I'll show you three curtains. Behind one curtain is a new car but behind the other two curtains are goats. You want the car, not a goat! You choose a curtain, and then I'll open one of the other curtains to show you where one of the goats is. Then I'll give you an opportunity to change your choice to the remaining unopened curtain.

Summary:

(1) You pick a curtain. (2) I open one of the other curtains to show you a goat. (3) You either keep your first choice or change your choice to the remaining unopened curtain. (4) I open all the curtains and you either win the car or get stuck with a goat. (All the cars and goats are virtual!)

Your tasks:

1. Which strategy do you think is best in step (3) above - change your choice or keep your choiceor doesn't matter? Write a sentence or two about this BEFORE you move on to task 2.

2. Use the game simulator at https://math.andyou.com/tools/montyhallsimulator/montysim.htm to play the game twenty times. It's up to you to decide how to play - you can always change your choice, always keep your choice, or mix it up. Keep track of your results by filling in the table below.

Changed and Won	times
Changed and Lost	times
Kept Choice and Won	times
Kept Choice and Lost	times

3. Use your data from task 2 to re-evaluate the strategy you wrote about in task 1. Do you think your initial strategy was correct? If not, what do you now think is the best strategy? Write a paragraph explaining what the right strategy is and why. Support your argument with evidence from your data.

What to post:

1. Your initial sentence or two describing what you thought before you played.

2. The filled-in table showing the results of the 20 games you played.

3. The paragraph you wrote about what the right strategy is.

I have this discussion set so that you have to make your post before you can read any other posts. I think it will be fun to see if everyone comes up with the same revised strategy!