# Negative counterfactual regret

I am reading the paper Regret Minimization in Games with Incomplete Information on CFR algorithm.

On page 4, the paper defines $$R^{T,+}_{i,\text{imm}}=\max\{R^{T}_{i,\text{imm}}, 0\}$$ after equation (5). I am confused why it is necessary? It seems to me that since in the definition of $$R^{T}_{i,\text{imm}}$$ the regret is computed with respect to the optimal action.

• As everything is in expectation, is mixed-action going to make any difference?

Isn't $$R^{T}_{i,\text{imm}}$$ always nonzero already?