[math-fun] Erich Friedman's game

RCS:

But Erich's version has complications that make it more challenging.  First is the finiteness, and our goal is not to maximize our expected point total, but our chance of surmounting the three-point threshold.  Second is the chance for both players to alter their play based on the state of the game so far.

--indeed. It would be possible to solve the game by working backwards from the end state, using the result of the game-solve at the penultimate stage as the payoffs for the game 1 stage earlier, then solve that game, and so on. This is kind of in miniature the sort of problem faced by those building computerized poker players.