How many ways are there of playing a game of Chess?

This is a question that pops up from time to time. Someone gets curious and asks how many different ways are there of playing a game of chess.

The answer is astounding. In fact, there are more ways of playing a game of chess than there are stars in the known universe. Another way to fathom the number, is to imagine how many grains of sand it would take to fill up the Earth.

To give you a peek into just how great the number actually is, consider this:

For whites first ply (half-move)  of the game, he has 16 pawn moves to choose from and 4 knight moves. That makes a total of 20 options.

Now, for each and every one of those 20 options, black has 20 possible replies. So do the math:

20 x 20 = 400

So now we can see there there's actually 400 different ways of playing the very first move of the game.

Without venturing on the pain staking task of finding the exact number for the next calculation, we could just say that for each and every one of the 400 ways of playing the first move of the game, there lies another 400 ways to respond. Do that math....

400 x 400 = 160,000 (Pardon transpositions and the number is still gigantic)

That means there's roughly 160,000 ways of playing the first 2 moves of the game.

To keep things easy on the mind, lets just do a simple calculation to continue. 

Lets just pick a soft number like 40, and say there are 40 different ways to respond to each and every one of those 160,000 options.

160,000 x 40 = 6,400,000

So now, when we think of game consisting of a few dozen moves, it's easy to see why the number of possible games is greater than the number of starts in the galaxy. This is why openings like the Ruy Lopez, which have been played countless times, still enables players to find unfamiliar territory before the 20th move.

Dug a little deeper into this and found out that there are an incredible number of ways to play the first 10 moves. Here is the number:

169,518,829,100,544,000 x10¹²

I remember reading this in a Chess Life article if I remember correctly around 15 years ago. It's an interesting and astounding thought, even if it's not practical to know :D cheers

They always taught me there are 3 ways losing winning and drawing @_@ *mindblow*

I believe the correct answer is three. One way to play is to win, another is to lose, and the last way to play is to tie. That's only if someone is keeping score. A friend of mine says there are actually only two ways to play a game of chess. Sober, and not sober.

So Dark_Army , 1.7 x 10^27 ways after the first 10;  makes me wonder how many after the first 30 moves?  I don't have a calculator that big.   Way past a googol, we can say.  ?A centillion?  

Can't really wrap our minds around a number that large. It's like 1 with a quadrillion zeros after it. Something like that...