-Jones and Brown will never shoot each other, as if they succeed, they're instantly killed after (by Smith).

-Knowing this, Smith also knows he will never have the first shot when it eventually comes to a 1v1, he can discard that. His choice now comes to who he wants to take out first (as a perfect killer he is) and who he wants to make that first 1v1 shot. Obviously optimal strategy for Smith is killing Brown as fast as he can and then Jones.

-If Brown realizes this, he will use his first and maybe only shot to try to kill Smith as otherwise he is dead for sure.

These leaves us with only 4 possible scenarios, regardless the chances of each one coming to happen:

A) Jones kills Smith, then Brown shoots Jones. Long term survival chances for Jones: less than 20%.

B) Jones kills Brown, then Smith shoots Jones. Long (and short) term survival chances for Jones: 0%.

C) Jones fails first shot, then Brown kills Smith, then Jones shoots Brown. Long term survival chances for Jones: Higher than 50%.

D) Jones fails first shot, Brown too, Smith kills Brown, and Jones has one chance to kill Smith. Long term survival chances for Jones: exactly 50%.

-As you can see, it's highly interesting for Jones to fail the first shot, so if he can do that intentionally, it would be highly recommended.

-While Smith is alive, Jones and Brown will never shoot each other, as if they succeed, they're instantly killed after.

-Knowing this, Smith also knows he will never have the first shot when it eventually comes to a 1v1, he can discard that. His choice now comes to who he wants to take out first (as a perfect killer he is) and who he wants to make that first 1v1 shot. Obviously optimal strategy for Smith is killing Brown as fast as he can and then Jones.

-If Brown realizes this, he will use his first and maybe only shot to try to kill Smith as otherwise he is dead for sure.

These leaves us with only 4 possible scenarios, regardless the chances of each one coming to happen:

A) Jones kills Smith, then Brown shoots Jones. Long term survival chances for Jones: less than 20%.

B) Jones kills Brown, then Smith shoots Jones. Long (and short) term survival chances for Jones: 0%.

C) Jones fails first shot, then Brown kills Smith, then Jones shoots Brown. Long term survival chances for Jones: Higher than 50%.

D) Jones fails first shot, Brown too, Smith kills Brown, and Jones has one chance to kill Smith. Long term survival chances for Jones: exactly 50%.

-As you can see, it's highly interesting for Jones to fail the first shot, so if he can do that intentionally, it would be highly recommended.

-Jones and Brown will never shoot each other, as if they succeed, they're instantly killed after (by Smith).

-Knowing this, Smith also knows he will never have the first shot when it eventually comes to a 1v1, he can discard that. His choice now comes to who he wants to take out first (as a perfect killer he is) and who he wants to make that first 1v1 shot. Obviously optimal strategy for Smith is killing Brown as fast as he can and then Jones.

-If Brown realizes this, he will use his first and maybe only shot to try to kill Smith as otherwise he is dead for sure.

These leaves us with only 4 possible scenarios, regardless the chances of each one coming to happen:

A) Jones kills Smith, then Brown shoots Jones. Long term survival chances for Jones: less than 20%.

B) Jones kills Brown, then Smith shoots Jones. Long (and short) term survival chances for Jones: 0%.

C) Jones fails first shot, then Brown kills Smith, then Jones shoots Brown. Long term survival chances for Jones: Higher than 50%.

C) Jones fails first shot, Brown too, Smith kills Brown, and Jones has one chance to kill Smith. Long term survival chances for Jones: exactly 50%.

-As you can see, it's highly interesting for Jones to fail the first shot, so if he can do that intentionally, it would be highly recommended.

-Jones and Brown will never shoot each other, as if they succeed, they're instantly killed after (by Smith).

-Knowing this, Smith also knows he will never have the first shot when it eventually comes to a 1v1, he can discard that. His choice now comes to who he wants to take out first (as a perfect killer he is) and who he wants to make that first 1v1 shot. Obviously optimal strategy for Smith is killing Brown as fast as he can and then Jones.

-If Brown realizes this, he will use his first and maybe only shot to try to kill Smith as otherwise he is dead for sure.

These leaves us with only 4 possible scenarios, regardless the chances of each one coming to happen:

A) Jones kills Smith, then Brown shoots Jones. Long term survival chances for Jones: less than 20%.

B) Jones kills Brown, then Smith shoots Jones. Long (and short) term survival chances for Jones: 0%.

C) Jones fails first shot, then Brown kills Smith, then Jones shoots Brown. Long term survival chances for Jones: Higher than 50%.

D) Jones fails first shot, Brown too, Smith kills Brown, and Jones has one chance to kill Smith. Long term survival chances for Jones: exactly 50%.

-As you can see, it's highly interesting for Jones to fail the first shot, so if he can do that intentionally, it would be highly recommended.