1. The Unexpected Intervention of Sherlock Holmes: Dr. Roylott's plan relies on the assumption that no one will suspect his involvement or intervene. However, Sherlock Holmes, with his keen observation and deductions, sees through the facade of the seemingly random "speckled band" and identifies the real culprit.
2. Helen Stoner's Resourcefulness: Dr. Roylott underestimated Helen Stoner's courage and intelligence. Though initially trapped, Helen finds a way to signal for help by cutting the bell rope, which alerts Holmes to the danger.
3. The Unforeseen Consequences of the "Speckled Band": Dr. Roylott's plan, focused on silencing Helen Stoner, leads to the unintended consequence of his own death. The venomous snake, meant for Helen, ultimately kills him when he tries to retrieve it after being alerted to the threat by Holmes.
4. The Unpredictability of the "Speckled Band": Dr. Roylott assumed the snake would act predictably and attack only Helen. However, the snake is attracted to the warmth of the bell rope, which triggers its unexpected attack on Dr. Roylott.
In essence, the plan backfires because it depends on a number of assumptions and factors that prove to be flawed:
* Underestimating Holmes's abilities: Holmes's sharp intellect and deductions completely dismantle Dr. Roylott's carefully crafted illusion.
* Underestimating Helen's resilience: Helen's resourcefulness and courage, coupled with her trust in Holmes, foil Dr. Roylott's plan.
* The unpredictable nature of the "weapon": The venomous snake, though intended for Helen, ultimately becomes the instrument of Dr. Roylott's demise.
Dr. Roylott's plan, driven by greed and malice, ultimately fails due to the unpredictable nature of events and the unexpected intervention of others. This serves as a powerful reminder of the limitations of control and the consequences of miscalculation.