While his name wasn't really spoken well enough during the episode, we find out the serial killer of the first episode of Sherlock is an overlooked Taxi Cab driver. He offers Sherlock a ride to doom after he realizes that the detective is on to him.
And he knows Sherlock well, as he knew Sherlock would get into the cab on his own free will to figure out how the taxi cabbie was able to commit murders that seemed to be suicides.
Which is explained with two bottles. One has a good "medicine" and one has a bad one. The victim allegedly picked one and the taxi cabbie would take the other at the same time. Sherlock asked what if he refused his offer and had a gun pointed at him.
Which Sherlock knew was really a lighter. But Jeff Hope decides to taunt Sherlock to "play the game" anyway.
John Watson manages to find them but he's in the wrong building.
So John manages to mortally wound Jeff Hope before Sherlock did something. I loved this episode and scene, but it is oddly one of the few Sherlock mysteries that remained a mystery. Did Sherlock pick the right one? Or was it a bigger trick? Maybe both choices were bad? I could imagine the cabbie had an antidote already in his system that neutralized the affects of the poison. I kind of think the whole 50/50 chance idea was smoke and mirrors.