Why all problems are not in P complexity?
Chess is a fixed, finite problem. Because there's no input, you can solve it in a constant amount of time.

Computational complexity considers problems with inputs and looks at how the cost of the computation increases as the input gets longer. For example, you could generalize chess from an $8\times 8$ board to an arbitrary $n\times n$ board and ask how the time taken to compute which side can force checkmate varies as a function of&nbsp;$n$.  Certain versions of this problem (it depends on exactly what rules you take) have been proven to require an amount of time that is exponential in&nbsp;$n$, which implies that they can't be solved in only a polynomial amount of time.