Consider a (fair) coin-flipping game with two (2) players where

each player has a 50% chance of winning with each flip of the coin. That is, you and your

opponent bet on a Head or Tail at each flip - If you both bet on the same outcome (whether right or wrong, the game continues). After each flip of the coin the loser transfers one penny to the winner (unless tied). The game ends when one player has all the pennies.

Suppose each of you have two (2) pennies

(a) Flip 1: You bet Heads. What is your chance of winning a penny?

(b) Flip 2: Suppose you won Flip 1. Should you switch your bet to Tails ? Explain

(c) Will this game eventually end ? [ Google ] Explain

I've been stuck with this question all day, thank you so much