Let’s play dice
Another probability game.
You have a die and I have a die. You keep rolling your die until you get two 1s in a row. I keep rolling mine until I get a 1 and a 2 in row. The first one to reach the goal wins a dollar.
Would you play against me?
On average, I will reach my goal faster than you.
Imagine that on a move m we both get a 1. Obviously our chances to win on the next move are equal. But consider what happens when neither of us wins after rolling a 1. If you don’t roll a 1 on the move m+1 then you can’t win on the move m+2 too. But if I don’t roll a 2 on the move m+1, I can still win on the move m+2 if I get 1,2.