It seems to me EF's kind of scenario does arise in real life. Let me give some examples.
In an american football game, again, each "down" is like an individual game and total yardage is like EF's points so far.
i specifically use this example in class. students are given a simple game where the offense has to decide whether to run or pass, and the defense has to decide what to protect against. the offense has to try to get 10 yards in 4 tries to get a first down. baseball gives another example of a repeated game. each at-bat can be thought of a collection of pitches that are either balls or strikes, and the batter has to decide whether to swing or not. assuming some fixed probability of reaching base safely if the ball is hit into play, one can calculate theoretical odds of reaching base. i would be grateful for other real-life examples of these phenomena. erich