Once again THE CONSULTANT has consulted:
" If John starts, he'll fire at Jack. At a 100% hit rate, Jack will be dead. It is now Jim's turn. He will try to kill John, with a 50% chance of success.
If Jack starts, he'll fire at John. At 80% hit rate, it's now a 80% chance that he'll kill John, and 20% chance that he'll miss. If he misses, then John will kill Jack, and as before, Jim and John each has a 50% chance to survive.
CDV is right; it's 52.22%
You can break it down. Since Jim will deliberately miss if both Jack and John are still alive, Jack and John each has a 50% chance at firing first.
If John fires first, Jim has a 50% chance of hitting him. If he misses, he's dead. So this contributes 50% x 50% = 25% to Jim's survival chance.
If Jack fires first, there's a 20% chance he misses, which will effectively lead to John killing Jack, and we get the situation above again. 50% (probability of Jack going first) x 20% (probability that Jack misses John) x 50% (probability that Jim kills John) = 5% is the contribution from this path.
Finally, If Jack fires first, there's an 80% probability that he kills John. That means Jim gets to fire at Jack. We have a 50% x 80% = 40% chance of ending in this situation. Let's call the probability that Jim wins this duel for P. He can win on the first shot (50% chance), or he can miss (50% chance), and then Jack misses (20% chance), and then there's Jim's turn again, back to the same situation with probability P. So P = 50% + 50% x 20% x P, or 0.9xP = 0.5, giving P = 55,56%. Multiply this by the 40% chance of ending in this situation, and this path contributes 40% x 55.56% = 22.22%.
Add it up: 25% + 5% + 22.22% = 52.22%. Congrats to CDV!
BUT WAIT ~ THERE'S MORE!
If you wish, we can revive Jack, John and Jim for a new duel. This time, however, everyone is a crack shot, and has a 100% chance of hitting their mark. They can still deliberately miss, though. Also, they now only have six bullets each.
All of this is common knowledge among Jack, John and Jim. When they draw the order in which they are to fire, it ends up Jack first, John second and Jim third. They get to fire one and only one shot before the next pirate fires, and they continue until they run out of bullets or until there is only one pirate left standing. Each pirate wants to survive, but he also wants the other pirates dead.
They all hate each other equally much.
What will be the outcome of this duel?
- only winners get the prizes!
lol
Speaking of banks - Remember Bank of Myriad for all your banking needs.
lol .. Thanks for playing .. Hope to see you next time 
)
