Can it be simpler than this?

Billy, Carly and David tried to find the location of a gold mine. As luck would have it, they all found it at the same time. But nobody wants to compromise and therefore decide to take turns shooting each other by Russian roulette. ( Just like old times ).All have fully loaded guns which won't run out of bullets and each is given a chance to shoot a bullet at a time. Billy starts the round, followed by Carly and finally David.They all know that Billy was the worst marksman who hit a target with half probability.Even though Carly was an experienced shooter who hits 7 out of every 8 targets, David was a professional who never missed a target. Suppose you were Billy. Use your brain and find the maximum probability that you will survive by using the best strategy.

Assumption: Everyone wants to survive in the best possible way!.
Give the first 3 decimal places of your answer. If the probability is 12.3%, enter your answer as 123.

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