Imagine you are playing a coin toss game. For each toss, you win $1 if it's Heads (H) and lose $1 if it's Tails (T). The game ends when you get two consecutive identical results (i.e., HH or TT). Assuming a fair coin and independent tosses, what is the expected value of your winnings from this game?

你正在玩一个投掷硬币的游戏。每次投掷，如果是正面（H），你赢1元；如果是反面（T），你输1元。游戏规则是：你一直投掷硬币，直到连续两次出现相同的结果（即HH或TT）时游戏结束。假设硬币是公平的，每次投掷结果独立。请问，你期望从这个游戏中赢得多少钱？