9 days to kill his older brother, or else his younger brother will be executed? Did Stanley have marbles loose to assume Charlie would kill one brother to save another? Clear odds were that he would end up with 1 out of 3 instead of 2 out of 3.
Mountain Man
You got it right. That's one of the reasons I love this movie!
This is how I interpreted it:
Stanley had the two brothers, Mikey & Charlie, right at the beginning of the movie, but he didn't have Arthur. The town wanted Stanley to punish/kill Mikey & Charlie, but Stanley knew that Arthur would kill him for harming his brothers. Stanley had only one option in this respect: Hold one brother as ransom, so the other brother has no choice but to kill Arthur.
I think this added more depth & drama to the scene where Mikey is being whipped & Stanley is pleading for them not to. I think Stanley even tells his wife at some point, "If they do this, we are dead". He had no choice but to trust the brother that could plausibly carry out this proposition, Charlie.
As you pointed out with the odds, Stanley was screwed either way. He couldn't win over the towns people, and keep Arthur from wanting revenge no matter what he decided. That's what makes this movie so awesome for me. I could see the movie going in 3 different directions towards the end & the direction Cave chose was perfect in hindsight.