Did Sherlock have the good pill or the bad pill?
Okay, I’m going to dismiss the idea that there are two bad pills. We know that the cabbie always took the other pill with his past victims. It’s not in the nature of a serial killer to change their methods. He’s also motivated to stay alive and kill more. For every person he kills, more money goes to his children. He’s not about to give up and commit a definite suicide just because Sherlock Holmes comes around. Love is a much more vicious motivator.
The cabbie also knows which pill is good and which is bad. It’s chess. Otherwise he would be on a very lucky run of Russian Roulette.
"I know how people think. I know how people think I think."
Okay so initially he gives you a bottle. Your first instinct will probably tell you he’s a threat, so he gave you the bad bottle. But what if it’s a bluff and it’s actually good? What if he anticipated this and it’s a double bluff? A Triple bluff?
People would drive themselves mad trying to figure out what he’s thinking. They are too eager to make the game clever, they’re over-complicating it. "That’s your weakness, you always want everything to be clever".
Sherlock took the bottle that wasn’t handed to him. He trusted the first logical instinct.
Also, the cabbie obviously knows how to bluff. But when Sherlock chooses his bottle, the cabbie takes the other pill out of the bottle and stares at it. Why would he stare at it so intently if he has done this four times before? Because this is something new? His right hand also remained steady throughout the game, but when he holds up the pill it’s shaking. He’s under stress.
His demeanor also changes very slightly. He becomes more condescending toward Sherlock. ”A man like you, so clever”. He gets sarcastic. His eyes are narrowed and he’s baring his teeth. Classic signs of aggression. He wouldn’t be angry if he wasn’t beaten. He prides himself on being a proper genius, it’s a blow to his ego to be wrong.
He also knows Sherlock prides himself on being right. After being shot he refuses to tell Sherlock if he was right or wrong. Wouldn’t you think that he would want to tell Sherlock if he was wrong? Prove to him who the more clever man was?
So in my opinion Sherlock was right.