How do we determine the saddle point in game theory?

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I am a little confused of why this works.

If a$_i$$_j$ is positive, row player pays the column, and vice versa.

\begin{bmatrix} 3 & -5 & 6\\ -2 & 1 & 8 \\ 3 & -6 & 7\\ \end{bmatrix} Row player will pick 6, 8, and 7 for i=1,2,3

Col player will pick -2, -6, and 6 for j=1,2,3

Saddle = 6 at (1,3)

Why would row player pick the max value if thats what hes paying to column player? Shouldn't it be the other way around?