Here is the standard causal graph for Newcomb's problem (note that this is a graph of the agent's actual situation, not a graph of related historical data):

Given that graph, my CDT solution is to return the action A with highest sum_payoff { U(payoff) P(payoff | do(A), observations) }. Given that graph (you don't need a causal graph of course), my EDT solution is to return the action A with highest sum_payoff { U(payoff) P(payoff | A, observations) }.

That's the easy part. Are you asking me for an algorithm to turn a description of Newcomb's problem in words into that graph? You probably know better than me how to do that.