Imagine 10 basketball players lined up across from 10 hoops, with each player attempting a single shot into his own hoop at the same time. Assume each player is a 50% shooter and is not influenced by the other players. After all 10 players have taken their shot, tell each player:

- Put on a red shirt if the 3 players to the left of you each hit their shot

- Put on a blue shirt if the 3 players to the left of you each missed their shot

- Put on a grey shirt otherwise

If no one puts on a blue shirt, have everyone shoot again. Repeat until at least one player puts on a blue shirt.

Now choose a player with a blue shirt at random and ask him to step forward. What is the probability that his shot was successful? Round your answer to two decimal places.