Bust at Ten

An arcade wheel has 8 8 equal sectors numbered 1 1 through 8 8 . You spin once and see the result f f . You may cash out f f dollars, or spin a second time. If the second spin shows s s , you collect f+s f + s dollars when f+s≤9 f + s \le 9 , but you bust and collect nothing when f+s≥10 f + s \ge 10 . For which first spins should you spin again, and what is the game worth played optimally?

Answer

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