Game problem... clasic cups game with a twist, can you help?

Question

Ok, my question,, you have 3 cups, one with a bean under, you are blindfolded so you cant see of course, cups are mixed up, the game is can you chose an empty cup, (ie DONT find the bean). I want to know if you did this 23 times in a row,,, how many times would you have to play my game so that you "win" ie DONT find the bean? that make seance ?!? ie 1st go 2 in 3 chance of getting to 2nd round. Do that 24 times, whats the probility of never finding the bean? is

Answer 1

23 times would be 2/3 to the 23rd power or about .000891%.

A 24th time would be 2/3 of that or about .000594%.