“Only a step away from victory!" your crew murmurs as they gasp for air, having been utterly defeated by the guardian of the treasure. Some lament the absence of Jana, but with the show of skill you beheld, even Jana's brute strength would not scathe him. That menacing aura could be none other than the infamous Don Vito Corleone, who was said to have escaped death and scrounged the world for his lost position. He silently moves towards your stunted frame, and makes an offer that you can't refuse.

Michael comes forward, prepared to take you on. Both of you will partake in a blindfold shooting competition. There is a board set up; in each round, the person whose bullet hits the board first gets 1 point. The first person to gain a 2 point lead over their opponent wins the game; and their life!

Vito is generous; he looks at your skills and gauges the probability of you winning a round to be close to zero, i.e. exactly $0.1729$. Now, Vito is a man of his word: he keeps his answers close, but questions, closer. He believes that if you prove to be worthy of the treasure by calculating your chances of winning, he will spare your group and let you spend some time with your family. With your pride as captain, and the lives of your crew at stake, can you stand up to the guardian boldly and give the correct answer? If you can, then do it!

What is your probability of winning the game? Round your answer to 4 decimal places. For example, if you think that the answer is $0.12345$, then you should answer $0.1235$ (note the $4$ rounded up to $5$).