My “Day I Left Pennsylvania” led me to some archived website posts (before blogs were invented) I had written many years ago. I’m re-posting them now. Bear in mind that most of the content in this series is over 5 years old. I have left the content more or less intact. I have removed some links and added some others — but that’s it. Enjoy!

After John W’s skepticism, I decided to put my code where my mouth is — please see:

http://amhill.net/projects/montyhall/

It has a simulator, demonstrating the superiority of switching, based on a sample size of 10,000 or less. Source code included.  Check it out!

For those of you who remember Let’s Make a Deal the idea of the three-door choice is very familiar. For those who aren’t familiar with Monty Hall and his extravaganza of game-showness, here’s the low-down:

The contestant is presented with a choice of three doors. Two of them have a goat, and one of them has a fabulous prize, like a new car, or a boat, or an evening with Brad Pitt, or whatever. (the contestants were mostly women, since at the time less women were in the workforce, therefore they were the target demographic). Anyways, here’s how it works. They pick one of the doors, then Monty reveals one of the two doors they did not choose; but the door revealed will always contain a goat. The contestant is then allowed to stick with their choice, or change it. The puzzle here is: Is it better odds, statistically speaking, to stick with your choice, or change it, after the goat is revealed? Most mathematicians have said yes in the past, but Marilyn Vos Savant disagreed. Here is a paraphrasing of her proof: Read the rest of this entry »

Popularity: 3% [?]

Tags: game theory, It's HISTORY, Puzzles, Unabashedly Nerdtastic

My “Day I Left Pennsylvania” led me to some archived website posts (before blogs were invented) I had written many years ago. I’m re-posting them now. Bear in mind that most of the content in this series is over 5 years old. I have left the content more or less intact. I have removed some links and added some others — but that’s it. Enjoy!

Yes it may be a magic card, but it inherently possesses a fundamental of game theory. For those of you who are not familiar with what that image to the right is, it is a card from the game Magic: the Gathering ,however it’s origin is unimportant, nor is whether or not you understand the nuances of the numbers and whatnot. The text in the lower-half of the card is what is important here. Allow me to elucidate in real-life terms….money!:

Let’s say that everyone (3 or more people) has 20 dollars. The game proceeds like this:

1. Each player hides a certain number of objects (poker chips, for example). The number must be greater than 1.
2. After everyone has their objects hidden, all players simultaneously reveal their objects to other players. The number of objects hidden is significant here, and should be recorded.
3. Everyone immediately loses the amount of money equal to the number of objects hidden, this goes into a “pot” in the middle. If a player has hidden more objects than he has money, all of his money is put into the pot instead.
4. Whoever had set aside the fewest objects loses half of their remaining money, rounded up.
5. Repeat steps 1 – 4 until only one player is left with any money. That player then wins it all.

Understand how to play? More importantly, do you understand how this illustrates game theory? All players must consider the actions of other players when making their own decisions. Read the rest of this entry »

Popularity: 1% [?]

Tags: game theory, It's HISTORY, Puzzles, Unabashedly Nerdtastic