As Tyrrell points out, it's not as simple. When you're considering the strategy of what to do if you're on the giving side of the counterfactual ("Should P pay up if asked?"), the fact that you're in that situation already implies all you wanted to know about the digit of pi, so the strategy is not to play conditionally on the digit of pi, but just to either pay up or not, one bit as you said. But the value of the decision on that branch of the strategy follows from the logical implications of being on that branch, which is something new for UDT!