Okay, so 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 his methods. He’s also motivated to stay alive and kill more. For every person he kills, 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 pill 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.”
So initially he gives you a bottle. Your first instinct would probably tell you that he’s a threat, so he gave you the bad bottle, right? But what if it’s actually a bluff and he gave you the good one? What if he anticipated that too, and it’s a double bluff? Or a triple?
People would drive themselves mad trying to figure out what he’s thinking. They’re so eager to win, that they don’t make the game clever, they overcomplicate it.
“That’s your weakness. You always want everything to be clever.”
Sherlock took the bottle that wasn’t handed to him. He trusted his first logical instinct. The cabbie obviously knows how to bluff. But when Sherlock chooses his bottle, the cabbie takes the other pill out and stares at it. Why would he stare at it so intently if he’d done it four times before? Because this is something new? His right hand also remained steady throughout the entire game, but when he holds the pill up, it’s shaking. He’s under stress.
His demeanor changes slightly too. His attitude and tone towards Sherlock becomes more condescending. “A man like you so clever.” He gets sarcastic. His eyes are narrowed and his teeth are bared. Classic signs of aggression. He wouldn’t be angry if he weren’t beaten. He prides himself on being a proper genius. It’s a massive 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 he want to tell Sherlock if he was wrong? Prove to him who was more clever?
So in my opinion, Sherlock was right.