Checkmate

You will play three chess games in a row against opponents in this order: Tolga, Douwe, Tolga. Your chance of beating Tolga in a game is 10% and of beating Douwe is 90%, with the results of the games independent. You win a prize if you win two games in a row (i.e. games 1 and 2, or games 2 and 3).

What is the probability that you win the prize? Give the answer as a decimal.