Two people are playing an interesting form of a number guessing game, with the following rules:
- One person is the guesser, and one person is the thinker.
- The thinker thinks of a number from 1 to 2925 inclusive, and can't change it mid-game.
- The guesser has 25 guesses to guess the number. If they take more than 25 guesses to guess the number, they lose. The guesser can't guess anything other than a number, or they lose.
- Every time the guesser guesses, the thinker must (honestly) give one of three responses: your guess is too big, your guess is too small, or your guess is the correct number. If the number is correct, the guesser wins.
- There's a catch. Every time the answer is "too big", the guesser loses a life. The guesser has three lives at the start of the game. If they have no lives left, they lose.
Is there a way for the guesser to always win this game? If not, how can they maximize their winning chances?