Suggestions for binary classification algorithm I am new to machine learning, so was hoping you might have some insights one what classification algorithm might be best suited for my data.

I have a data set of hundreds of predictions from each of ~100 forecasters. Each prediction is binary, and the outcome variable is binary.

So basically let's say I have data on 200 events. For each event, I have 1 prediction from each of 100 forecasters. Each of the 100 forecasters predicts each of the 200 events.

I am hoping for an output of some formula, for which I input the predictions of the forecasters for that particular outcome, and it renders an output for the probability of that outcome.

My main interest is in predictive accuracy.

Do you have any suggestions for what algorithms might suit this problem?
I would say support vector machine, support vector classifier. This will allow you to have as many predictors as you want. Also, you can improve your accuracy by tuning your model parameters. 

Here is another nice link for support vector classification

Since you did not mention any language, I would use python as there are so much online support and you resources available online. 

I would also check xgboost classifier. 

Let us know how did it go.