Saturday, January 10, 2009

Shannon is a Big Ole Girl

Everyone loves big girls, I know I do! However Shannon is so gargantuan she really deserves a special place in the hearts of the lovers of the large. I thought seriously about peppering this article with a litany of "Shannon is so big" jokes but no, I'm going to keep it classy.

Ok maybe a few.
Shannon is so big, when she dances the band skips.
Shannon is so big, when she puts on Guess jeans, the answer pops out.
Shannon is so big, the last time Shannon saw 90210 was on a scale.
Shannon is so big, when she went to the movies she sat next to everyone.
Shannon is so big, whenever she goes to the beach she's the only one that gets a tan.

I am, of course, referring to the Shannon Number which is the (theoretical) number of possible positions that could occur in a game of chess. Now, this insanely obese number encompasses even silly chess positions that would never occur over the board such as:
1. d4 Nf6 2. c4 Ng8? 3. b4 Nf6 4. a4 Nf8?

In other words, the Shannon Number does not prune any "unlikely" positions. It includes everything. So what is the exact number we are talking about here?
The number is 10^120 (Ten to the one hundred twentieth power). Which means a game of chess has approximately... 1,000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000 different positions give or take a couple hundred billion. After having studied it for a bit, I'm almost positive half of these positions come from the first 10 moves of the Sicilian Defense.

Putting it in Perspective

The human mind has almost no way of measuring how ridiculously massive this number is, but hopefully I can help. While you are reading these numbers keep in mind how fast they increase each time you raise a power. It's staggering, the numbers increase almost exponentially.

Large Numbers

10^2 Years – Less than 1% of humans reach this age.
10^3 Miles – Driving Distance from Miami, FL to Washington DC
10^4 Maniacs – Pop Band From the 80's, also unofficial name for Al-Qaeda.
10^5 Dollars – Less than 20% of American households earn this figure in one year
10^6 People - The number of people who attended Obama's inauguration
10^7 Subscribers – Number of people who play World of Warcraft
10^8 Seconds - 3.1 Years
4.55 * 10^9 Years - (less than half of 10^10) Approximate Age of the Solar System
10^10 People - Almost twice the number of people alive today
10^11 People - The approximate number of people who ever ever existed.
10^15 Seconds - 31 Million Years
5*10^20 Positions - (Exactly Half of 10^21) Total number of positions in a game of Checkers
10^25 Stars - Approximate number of stars in the entire Universe
10^78 Atoms - Estimated number of atoms in existence, everywhere, period.
10^120 Positions - Shannon Number
10^121 Calories - Number of Calories in a Big Mac Value Meal

Checkers is Solved

Checkers has been solved... eh... sort of. Since Checkers is basically Chess for idiots, there are some similarities. One of the most important similarities is endgame tablebases. Checkers has an endgame tablebase with every possible position with 10 pieces or less. For those counting that's 39 Trillion positions. Dr. Jonathan Schaefer, the purveyor of Checkers cracking, found a narrow opening sequence that forced play into this vast ocean of endgame play with a winning line. Therefore by a sort of sandwich method (solving the back end and then solving the front end) they came to a line of play that is best. The good news for the black side is that Checkers is a forced draw with best play.

However, make no mistake, the brains behind solving checkers did not brute force calculate all 500 Billion Billion positions. According to Dr. Schaefer, if the human foot contained 50,000 checkers positions, that foot would have to walk every square inch of Earth in order to find every possible checkers positions. Amazing!

Checkers is the most complex game to date that has been solved. Other casualties include tic-tac-toe, connect 4, hex and next on the radar is Othello. If these games can be solved can chess be solved too? Could we wake up tomorrow and read world headline news that chess is no longer a mystery? Well yes! And no. Can chess be solved? Absolutely. Do we have the capability to do it? Not a chance. Not anytime soon anyway.

Let's Solve Chess!

I propose we write a book. When I was a kid I always wondered why someone doesn't just make a book with all the possible first moves and the best responses to all of those moves, so on and so forth. Even as a kid I figured this book would be "pretty" thick. I just had no idea how monumental it would be to author this book. In order to create this book we need to solve every chess position so let's do it. Let's say we were able to put together 1 billion computers (which is a little more than half the total number of computers on Earth). Each computer was able to solve 1 billion positions per second. It would only take 3.17 * 10^94 years for all 1 billion computers to solve chess. So the editor is going to have to wait for a little bit for our book to come out.

Now if we were actually going to print this book, we need to consider paper and thickness let's take a look at that. So we can reasonably assume it's going to be difficult to put this book into one volume. So let's break it up over a mere 100 Million volumes. So we will have 100 million books that is all inclusive of every position in a chess game. We will use small print and put 100,000 positions on each page. That means each volume will contain 10^102 number of pages, approximately 3 times the size of "War & Peace". If we were able to find paper that was 1/1000th of an inch thick, then each volume will be 1.5 x 10^94 miles thick. Also for what it's worth, one volume would weigh approximately 17,846,306,832,821 tons. Can you imagine the shipping cost from

I don't know about you but I think our beloved chess is quite safe from being cracked anytime within the next 10^3 years.

1 comment:

  1. hahaha you're very talented, I enjoyed this alot !