Mixed strategies can be useful for several reasons. First, they can help you avoid being exploited by your counterpart, who might anticipate your actions and respond accordingly. For example, if you always offer $20,000 for the car, your counterpart might always reject it and counteroffer with a higher price, knowing that you will not budge. By using a mixed strategy, you introduce some randomness and unpredictability into your behavior, making it harder for your counterpart to exploit you. Second, they can help you achieve a better outcome in situations where there is no dominant or optimal pure strategy. For example, if you are playing rock-paper-scissors with your counterpart, there is no pure strategy that guarantees you a win or a tie. However, if you use a mixed strategy where you play each option with equal probability, you can expect to win, lose, or tie with equal frequency, which is the best you can do in this game. Third, they can help you create value and expand the pie in negotiations, by allowing you to explore different options and trade-offs. For example, if you are negotiating the terms of a contract, a mixed strategy could involve offering different combinations of price, quality, delivery, warranty, and so on, with different probabilities, and seeing how your counterpart reacts. This way, you can discover their preferences and priorities, and find potential areas of agreement or mutual benefit.