Two guesses to beat opponent's one guess on a 1–299 number game

[derekderek123]

You are playing a number guessing game. A random integer will be chosen from 1 to 299. You get two guesses at the number and your opponent only gets one. Whoever gets closest to the random number when it is chosen is the winner. If you have to make both of your choices before your opponent picks his number, then what choices should you make to maximize your chance of winning the game? Assume that your opponent is good at this game.

I got (75,225) (76,225) (75,224). What you guys think?

 

[mfb]

I moved the thread to our homework section as it's homework-like.

Yes, what you found is the optimal strategy (+-1 depending on how ties are treated). Your opponent has three reasonable options, and you want to make all equally bad: Guess 1 below your lower guess (they win if the number is below your lower guess), guess in between your guesses (50% chance to win if the number is between your guesses), or guess 1 above your highest guess. That means you should guess at 1/4 and 3/4 into the possible range.