Originally posted by demonseed
This is an old one so excuse me if you have encountered it before.
A truel is similar to a duel only there are three participants instead of two: in this case there are Mssrs Black, Grey and White. Mr Black is the worst shot hitting the target 1/3, Mr Grey is slightly better hitting the target 2/3 and Mr White never misses. To make the truel fairer Mr B urns, until one is left standing.
The question is: where should Mr Black aim his first shot?
Mr. Black should aim his shot ANYWHERE but at one of the other treulers.
If he did fire at one and hit, it leaves the other with a shot at him at at least 66% chance of hitting. Therefore Mr. Black's only has a 0 - 33% chance of surviving the first round and then a 33% chance of shooting his opponent in the second round. Not exactly great odds.
If he fired and missed, it leaves Mr. Grey a one shot chance to take out his biggest threat (Mr. White). Either way, Mr. Grey will make his 66% chance of hitting Mr. White or he will miss and Mr. White will shoot him as he's Mr. White's biggest threat. Then which ever one of the 2 is left standing one has to duel with Mr. Black. Which is the best possible outcome for Mr. Black as he avoids the 0 - 33% survival chance from the other option and skips straight to dueling with the remaining man.
Therefore, Mr. Black should force the miss on his first shot by not aiming at anyone in order to get down to the one-on-one duel situation with him shooting first.