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I saw a puzzle-type baseball game the other day. One player is the batter. Both of them show any amount of fingers on one hand at the same time. If they are different numbers, the batter is out. If the same - 1 is single, 2 is double, 3 is triple, 4 is home run and 5 is walk. This was a bit complicated to work out strategies so I wondered about the best strategy if: The aim of the batter is to get one man to home base. The aim of the non-batter is to get that one man out.
What is the best mixed strategy for both players, and how often can the batter win?
And then to get more complicated, you can try returning to the initial puzzle, more innings, etc.
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Steve_Farmer_Jr
 Senior Boarder
Posts: 75 
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If I were the non-batter, I would clear my mind and randomly throw 1s and 5s. Chances are the lead batter would get three outs before advancing 4 bases.
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Linda2
Senior Boarder
Posts: 64
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This is non-optimal; for example, with the bases loaded, it is obvious that the best stategy is to pick 1-5 evenly. Even with the bases empty, it seems clear that the pitcher should throw in an occasional four, although not very frequently.
One has to backtrack along the game tree to solve this problem, and I am not willing to put the time into it right now. (I am wasting too much time on those 8x8 ABC problems as it is.)
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