I need a math genius to explain how many Chess positions there are.

I would disagree, as the game cannot go on indefinitely due to the 50 move rule. I think the longest recorded computer generated game was something like 6,000 moves or something like that.

Wow thanks

yes, if this rule would apply, but if you are not playing for a win or a draw, then there is no limit

this hurts my brain im going to say after the 1st move i cant count that high

The possibilities are countable infinity There are finite possibilities, but it will take almost forever to count every single one of them

Guinness Book Of World Records in the 1970s claimed that the number of possible chess games was larger than the number of atoms in the known universe. So clearly a somewhat complex game...

positions are not move sequences

Possible sequences of moves exceed the number of atoms in the visible universe. Possible positions do not.

Before you find your math genius, you need someone who understands words.

But irrespective of the large scale, it is not infinite neither countable to us

Just think of it like this. There are a lot of nonsense positions that are reachable, but have nothing to do with winning or losing. These positions can also be reached with opposite sides to move by triangulation (Kd1-Kd2-Ke1 for example). As long as the pieces can escape the pawns, then they can switch between each other or occupy almost any position on the board that can be reached within 50 moves without a pawn move or piece capture. The only real restriction to these sort of permutations is the king cannot be in check.
If you consider that.. and the number of different ways you can put together 50 moves + triangulating to get the same position with different sides to move, sometimes capturing enemy pieces as well.. the number of positions blows up very fast.

nah

https://wismuth.com/chess/statistics-positions.html

François Labelle has the math and computer backgrounds to get us close. I believe this link was put up when he was getting his Ph.D. at UC Berkeley.

To repeat the answer buried in previous pages:

My Chess Position Ranking project at https://github.com/tromp/ChessPositionRanking

obtained an accurate estimate on the number of legal chess positions of 4.8e44.

Hi, math genius here, i think qhat xoud have to do is sum up the possibilities for each number of pieces and take into account, which pieces there are, bishops for exaple can only go to half of the board and paens can only go to the quarters. What you do for each kind of piece is that you the nomber of squares left, s, and the number of those kinds of pieces, p, and then make the term s!/((s-p)!×p!). If one of you guys has time, you could put it into a calculator and then have the number of positions. Thaat number however could also contain postions like where both kings are in check.

Use multiplication rule

This rule does apply for all standard chess games, whether you are playing for a win/draw or not.

Get a super-strong computer and a computing genius would be better. The computer you need might already exist now (the strongest computer now is a 1100 bit quantum computer). I’m not that computing genius, so I can’t really be sure.