riddle answer: im thinking of a number

The answer is NO. You should not play.

The analytical people might say, “Hey, that’s just binary search!”

Which means you need at most $\log_2(100) = 7$ guesses.

It’s not a complicated strategy, for those who are unfamiliar, you just guess the middle number of the ranges each turn.

So first guess is always 50, then depending on if you are low or high, second guess is either 25 or 75, and so on. At most you will need 7 guesses.

So for our game, you would think, “hey that means I make 3 dollars each time in the worst case!”.

So let’s simulate a game:

I’m thinking of a number between 1 and 100.

Turn 1: 50

Low

Turn 2: 75

Low

Turn 3: 88

High

Turn 4: 82

High

Turn 5: 79

High

Turn 6: 77

High

Turn 7: Alright, 76!

Low

???

Wait what happened?

Well did I specify whole numbers…?

How many times would it take you to guess 76.11173?

Fork over that cash pal.