All possible moves one step from a given position sure.
But if you then take all possible resulting positions and calculate all moves from there, and then take all possible resulting positions after that second move and calculate all possible third moves from there, and so on, then the possibilities explode so much in number that you can’t calculate them anymore. That’s the exponential part I was refering to.
You can try and estimate them roughly, let’s say you’re somewhere in the middle of the game, there are 12 units of each side still alive. About half are pawns so we take 1.2 possible moves for them, for the others, well let’s say around 8, thats a bit much for horses and the king on average, but probably a bit low for other units. So 6 times 8 and 6 times 1.2, lets call it 55 possibilities. So the first move there are 55 possible positions, for the second you have to consider all of them and their new possibilitues so there are 55 times 55 or 3025, for the third thats 166375, then 9.15 million, 500 million, 27.6 billion, 1.5 trillion etc. That last one was only 7 moves in the future. Most games won’t be finished by then from a given position, so you either need a scoring function or you’re running out of time.
There are more possible chess moves (estimated at 10^120 for an average game) than there are atoms in the observable universe (estimated at 10^80). That is to say the number of possible chess moves has 40 more zeros on the end than the number of atoms in the observable universe.
Can you point to some souce showing how modern hardware can work these out easily?
All possible moves one step from a given position sure.
But if you then take all possible resulting positions and calculate all moves from there, and then take all possible resulting positions after that second move and calculate all possible third moves from there, and so on, then the possibilities explode so much in number that you can’t calculate them anymore. That’s the exponential part I was refering to.
You can try and estimate them roughly, let’s say you’re somewhere in the middle of the game, there are 12 units of each side still alive. About half are pawns so we take 1.2 possible moves for them, for the others, well let’s say around 8, thats a bit much for horses and the king on average, but probably a bit low for other units. So 6 times 8 and 6 times 1.2, lets call it 55 possibilities. So the first move there are 55 possible positions, for the second you have to consider all of them and their new possibilitues so there are 55 times 55 or 3025, for the third thats 166375, then 9.15 million, 500 million, 27.6 billion, 1.5 trillion etc. That last one was only 7 moves in the future. Most games won’t be finished by then from a given position, so you either need a scoring function or you’re running out of time.
Yep, those are the moves that can all be easily calculated very quickly on modern hardware
There are more possible chess moves (estimated at 10^120 for an average game) than there are atoms in the observable universe (estimated at 10^80). That is to say the number of possible chess moves has 40 more zeros on the end than the number of atoms in the observable universe.
Can you point to some souce showing how modern hardware can work these out easily?