Alice and Bob take turns alternatively on a $2020\times2020$ board with Alice starting the game. In every move each person colours a cell that have not been coloured yet and will be rewarded with as many points as the coloured cells in the same row and column. When the table is coloured completely, the points determine the winner. Who has the wining strategy and what is the maximum difference he/she can grantees?

[i]Proposed by Seyed Reza Hosseini[/i]
1. **Symmetry Argument for Bob's Strategy:**
   - Bob can use a symmetry strategy to ensure he always scores more points than Alice. Specifically, whenever Alice colors a cell \((i, j)\), Bob colors the cell \((i, 2020 - j + 1)\), which is symmetric to \((i, j)\) with respect to the vertical axis of symmetry of the \(2020 \times 2020\) board.
   - This ensures that Bob always colors a cell in the same row as Alice but in the opposite column, and vice versa.

2. **Point Calculation:**
   - When Alice colors a cell \((i, j)\), she earns points equal to the number of already colored cells in row \(i\) and column \(j\).
   - When Bob colors the symmetric cell \((i, 2020 - j + 1)\), he earns points equal to the number of already colored cells in row \(i\) and column \(2020 - j + 1\).
   - Since Bob colors the symmetric cell immediately after Alice, he will always earn exactly one more point than Alice did on her previous move.

3. **Total Points Calculation:**
   - The total number of cells on the board is \(2020 \times 2020 = 4080400\).
   - Since Bob always earns one more point than Alice on each move, the total difference in points between Bob and Alice after the board is completely colored is \(\frac{4080400}{2} = 2040200\).

4. **Maximum Difference:**
   - To show that this is the maximum difference Bob can guarantee, consider a greedy strategy for Alice. In this strategy, Alice colors a cell that maximizes her points on each turn.
   - Even with this strategy, Bob can always respond by coloring the symmetric cell, ensuring he earns at most one more point than Alice on each turn.
   - Therefore, the maximum difference Bob can guarantee is indeed \(2040200\).

In conclusion, Bob has the winning strategy and he can guarantee a win by \(\boxed{2040200}\).