Predict the next player's option for betting based on playing history?
this is a multi class classification problem.

There are many approaches you can use to solve this problem. 

You can first try Gradient Boosted Trees with libraries like xgboost or lightgbm. Both of those can be used in R or Python.

You can also use neural networks for multi class classification problems.

But there are many ways to solve a multi classification problem.

You can turn it into a multi binary classification problem. Since you have 300 options, you can train 300 binary classification algorithms on your data.

You can also try K nearest neighbours.