In Shakespeare's Hamlet, how many chances did Hamlet have to kill Claudius? Why didn't Hamlet do it?

In his
play , Shakespeare really only gives us one
moment prior to the final scene in which had an
opportunity to kill King . That moment is in Act III, scene iii, and happens soon
after Claudius has seen the play in which his murder is pantomimed.

In
Act III, scene iii, Claudius informsthat he is sending Hamlet to
England and they are to supervise him. Claudius's purpose is to have England execute Hamlet.
Later in this scene, when Claudius is alone, he delivers aconfessing his murder. He also kneels
to pray to ask for forgiveness. It's while he is praying that Hamlet happens upon him and, since
Claudius is alone and unaware of...