Game Show Winners Announced!
About a month ago, I held a contest which allowed users to choose between three different doors, Door #1, Door #2, and Door #3. Go here to read the full instructions for the contest for a little bit of context.
In the scenario, you, the contestant, initially chose Door #2. Then, once you picked Door #2, the host opened up the third door to reveal that behind Door #3 was a goat, instead of the Grand Prize...
At that time, you had to make a choice...
Do you keep Door #2? Or do you switch to Door #1?
If you're like me, you probably would have thought..."there's a 50/50 chance here, either door could be the answer." While it's true that either door could be the answer, one of the doors actually has a higher probability of being correct than the other.
Let's break it down...
When you first start, there is a 1/3 probability that the door you choose is the correct door with the grand prize, because only one door is a winner. Door #1 has a 1/3 probability, Door #2 has a 1/3 probability, and Door #3 has a 1/3 probability. Pretty basic so far.
Now, in this scenario, you initially chose Door #2, which has a 1/3 probability of being the correct door. The host opened up Door #3 to reveal a goat, eliminating one of the possible doors and removing one of the possible "losing" doors. Your initial choice of Door #2 still contains a 1/3 probability of being the correct door...but because the host eliminated one of the "losing" doors based on your choice, that means that Door #1 now has a 2/3 probability of being the correct door, while Door #2 still contains the original 1/3 probability.
It is NOT a 50/50 probability!
You should ALWAYS switch to the other door!
For an explanation, look up the Monty Hall Problem. You can play a game on this page that randomizes a winning door and demonstrates how switching results in a higher probability of success.
Did this confuse you or make you think twice? Don't feel bad, until I really thought it through, I would have thought it was a 50/50 probability between the two remaining doors as well. In fact, this puzzle has fooled many, many PhDs and statisticians.
The Winners!
A big thanks to all that played, the winners are those that chose to SWITCH to Door #1. There was a total of $3.36 ($2.27 + $1.09) in Author Payouts between the two posts I made about it, so I'm dividing up that amount to send to all the winners who participated. Please congratulate those who won:
Since there are 9 winners, the $3.36 will be divided into payments of $0.373 SBD for each of you. I'll also send a small token payment of $0.02 (get it?) to the 8 other people who participated but choose to keep Door #2.
Thanks for playing! For more news and games like this, be sure to follow me.