# Maximizing payoff when a 'dont care' state is present

Consider the following:

1. We have a training dataset ($$y_i$$, $$\mathbf{x}_i$$) $$i \in [1,n]$$ where $$y_i \in \{-1, 1\}$$.
2. We can build any model (logistic / SVM / anything else) to predict $$y_i$$ given $$\mathbf{x}_i$$ using this training data.
3. We are then given a new set of predictors $$\mathbf{x}'_j$$ where $$j \in [1, m]$$ and we need to predict the corresponding $$y'_j$$ for each $$\mathbf{x}'_j$$ using our model.
4. Each $$y'_j \in \{-1, 1, 0\}$$.
5. For each $$y'_j \in \{-1, 1\}$$, if correct we are rewarded with $$1$$ dollar and if wrong we are penalized $$1$$ dollar.
6. For each $$y'_j = 0$$, there is no reward or penalty (this is a 'don't care' state).
7. We want to maximize our payoff.

What's the best approach here? I think building a logistic regression model where we set $$y'_j = 0$$ if the probability is close to $$0.5$$ is the best way to go but I haven't been able to flesh this out yet.