massive complexity improvement for fictitious play

[louisabraham]

Currently, fictitious play stores count vectors and recomputes each time the payoff of each move by matrix multiplication before selecting the best move.

• move = payoff.argmax() costs $\mathcal{O}(n)$
• count[move] += 1 costs $\mathcal{O}(1)$
• payoff = matrix @ count costs $\mathcal{O}(n * m)$

Instead, one could just update the payoff vector with payoff += matrix[:, move] in $\mathcal{O}(n)$.

Even better, the matrix can be stored transposed to be able to write matrix[move] which is more cache efficient.

[drvinceknight]

This sounds like a great improvement. Would you like to work on a PR for this?

[louisabraham]

sure, it's like 10 sloc
will do after lunch