The Surprising Math of a Three Person Duel

Three gunslingers, A, B, and C are participating in a kindly three person pistol duel. They all have varying accuracies, and these accuracies are known to each other. It's our objective to use probability to determine A's best strategy for surviving this encounter. The solution, like in all duels, will require geometric series. #mathproblems #probability #mathpuzzle Check out the coolest math clothes in the world: https://mathshion.com/ Fifty Challenging Problems in Probability by Frederick Mosteller: https://amzn.to/3RWrcAl Join Wrath of Math to get exclusive videos, lecture notes, and more: https://www.youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join Outro music: https://youtube.com/shorts/tfifiSdTZRg Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● TikTok: https://www.tiktok.com/@wrathofmathedu ● X: https://x.com/wrathofmathedu 0:00 Intro 1:18 Pistol Duels 2:35 Solution 4:04 If A Hits B 8:19 If A Misses B 9:11 A's Strategy 10:50 Conclusion