#its chess

Sherlock : It's not a game, it's chance

Jeff Hope : It's not chance, it's chess

Okay so what is one of the greatest questions in all of Sherlock. Aside from the obvious, how did Sherlock fake his death, the question is, which pill was poison in the first episode. 

So we are learning about game theory in my stat class and it got me thinking. 

So the game is really, there are two pills, one is poison, one isn't. The victim  chooses which to take and the cabbie takes the other. One dies and the other lives. This would seem like a fifty fifty situation except for the fact that the cabbie has never lost. He keeps repeating to Sherlock, “Its not chance its chess”.

So what is the cabbie’s play? Well, lets look outside of Sherlock. Where else have we seen a situation like this? The Princess Bride. Yeah thats right. This same situation happens in the Princess Bride where Weasley and Vinzzini play with poisoned wine for the princess. Well, how does that scene end? Weasley actually put poison in both cups. 

Sherlock was counting on Moriarty to play fair. That was his mistake. By choosing either pill, Sherlock already lost. The cabbie and Moriarty must have rigged the game because why would they risk killing themselves? The cabbie was immune to whatever poison was in the pills so which ever pill the victim chooses they will die. The cabbie knew he won the second Sherlock began to choose his pill. There is no other possible explanation as to how the cabbie knew he would survive every time.