Warmup: Intro to HT

/ My son and I like to play a game called “Two Dots”. It’s pretty addictive. I believe there’re some neat statistics going on in the background (how many moves you’re allowed; the randomness of the occurrences of the various colors, etc.), but what I want to look at today is something simpler: the Two Dots “lottery” that happens each day.
Each day, the game offers you three doors, and behind one of the doors is the “grand prize”. It’s basically a shell game; once they show you where the prize is, the door closes, all the doors shuffle, and then you need to pick where you think the prize is.
And so, like a good street urchin, you try to watch the doors as they shuffle, but, since they all “stack up” right at the end, you essentially have to guess , anyway.
  1. (2 points) Max’s strategy was to always switch from day to day. Exaplain why (assuming that the prize was being randomly assigned to a one of the three doors) his strategy was no more advantageous than sticking with the same door every day. You can start up a Word Document and upload to BB when you’re done.
/

I, on the other hand, started always picking the center door. And, over the course of one month (n = 20 games; I only get to play every once in a while). In those 20 days, I have never once gotten the prize on the middle door. Assuming the prize is, indeed, randomly hidden behind one of the three doors,

  1. (1points) (w) What’s the chance that I would have never gotten the prize in 20 trials?
  1. (1 point) Copy and paste the following sentence with either “is” or “isn’t”, depending on how your results in #2 lead you to decide:

The prize, most likely, (is/is not)randomly hidden behind one of the three doors.

(keep reading!)

  1. (1 point) Explain the choice you made in #3!

In closing, I thought I’d just share with you the correspondence I recived back from the maker of Two Dots when I let him know about this discrepancy:

“Hi Sean,

Happy to hear your enthusiasm for the game. As for the Daily Prize, the doors are random and require more luck to get the big prize (took me a couple of months as well to get a big prize and then I was lucky enough to start getting it maybe once a month, maybe).

The doors are random and randomize base on patterns. If you pick a specific door each time, that creates a pattern and will make the doors randomize again.

Here's a tip I've been following to help me pick doors, if you notice there are Stars that pop up behind the doors. Choose the door where the Star pops up. Most times I get a single prize but there have been a few occasions where it's been random enough to help me get the big prize.”

So, we’ll test that next: