- Gets 7 points with probability 1/2, 3 points with probability 1/2.
- Gets 4 points with probability 1.
- Gets 10 points with probability 2/5, 0 points with probability 3/5.
What is the right strategy? Initially play action 1 and towards the end possibly switch to action 2 if you are ahead and action 3 if you are behind.
Many sports have these kinds of actions to keep the game exciting even if one player has a lead. Action 2 corresponds to using a closing pitcher, or a prevent defense. Action 3 is using a pinch hitter, pulling the goalie or the "Hail Mary" pass.
Quidditch doesn't have these options rather having a final move that usually dominates the rest of the scoring. The scoring rules of Quidditch is J.K. Rowling's biggest blunder in the Harry Potter universe.
Sometimes you do see action 2 moves earlier in a game. For example in football, after a touchdown a team can either kick for an extra point or run a short play to try for two. Kicks are are rarely missed and the plays are successful slightly more than half the time. Yet most coaches just kick unless there is a significant advantage to go for two.
The choices above apply to many more arenas than just sports. Obama and Clinton have been following actions 2 and 3 respectively over the last few weeks. Which approach will work? We'll find out tomorrow.