I am designing a treasure hunt game where users start of at a fixed number of steps (x) away from the treasure. The user responses are either a or b. A correct answer places the user one step closer to the treasure, a wrong answer takes the user one step away from the treasure. (maximum steps away from the treasure is x.). The two options have a 50% chance of being right on each question. The Game ends when player is 0 steps from the treasure.
Is it correct that the user will always get to the treasure in 2x moves? Or is it 2^x (2 power x)?
Is there anything a player can do to increase their chances of winning? Is there a way I can make the game harder. (Apart from increasing x)?
Please keep the answer simple.