The Dark Knight

A gang of criminals rob a Gotham City mob bank, double-crossing and murdering each other until there is only one left: The Joker, who escapes with the money.
Batman, District Attorney Harvey Dent and Lieutenant Jim Gordon form an alliance to rid Gotham of organized crime. Bruce Wayne is impressed with Dent's idealism and offers to support his career; he believes that, with Dent as Gotham's protector, he can give up being Batman and lead a normal life with Rachel Dawesâeven though she and Dent are dating.
Mob bosses Sal Maroni, Gambol and the Chechen hold a videoconference with corrupt accountant Lau, who has taken their funds and fled to Hong Kong. The Joker interrupts, warns them that Batman is unhindered by the law, and offers to kill him in exchange for half of their money. Gambol puts a bounty on the Joker, but the Joker kills him instead and takes over his gang. The mob ultimately decides to take the Joker up on his offer.
Dent arrests the entire mob, while Batman finds Lau in Hong Kong and brings him back to Gotham to testify against them. The Joker threatens to keep killing people unless Batman reveals his identity, and starts by murdering Police Commissioner Gillian B. Loeb and the judge presiding over the mob trial. The Joker also tries to kill Mayor Anthony Garcia, but Gordon sacrifices himself to stop the assassination. Dent learns that Rachel is the next target.
Bruce decides to reveal his secret identity. Before he can, however, Dent announces that he is Batman. Dent is taken into protective custody, but the Joker appears and attacks the convoy. Batman comes to Dent's rescue and Gordon, who faked his death, arrests the Joker and is promoted to Commissioner. Rachel and Dent are escorted away by policemen on the mob's payroll. Batman interrogates the Joker, who reveals that Rachel and Dent have been trapped in separate locations rigged with explosives. Batman races to save Rachel, while Gordon goes to save Dent. Batman arrives at the building, realizing that the Joker sent him to Dent's location instead. Both buildings explode, killing Rachel and disfiguring half of Dent's face. The Joker escapes the jail with Lau.
Coleman Reese, an accountant at Wayne Enterprises, deduces that Bruce is Batman and tries to go public with the information. After observing the unpredictability of the Joker, Maroni informs the Joker's location to Commissioner Gordon. The Joker sets fire to the mob's money, burning Lau alive in the process and kills the Chechen. Not wanting Reese's revelation to interfere with his plans, the Joker threatens to destroy a hospital unless someone kills Reese. Gordon orders the evacuation of all the hospitals in Gotham and goes to secure Reese. The Joker finds Dent in Gotham General and manipulates him into seeking revenge for Rachel's death. The Joker then destroys the hospital and escapes with a busload of hostages. Dent goes on a killing spree based on a coin flip, targeting people he holds responsible for Rachel's death. This includes two corrupt cop-detectives (Michael Wuertz and Anna Ramirez) who worked for Maroni in kidnapping Dent and Rachel. While in car with Maroni, Dent kills his driver, which presumably killed Maroni as well.
After announcing Gotham will be subject to his rule come nightfall, The Joker rigs two evacuating ferries with explosives; one containing civilians and the other containing prisoners. He says that he will blow them both up by midnight, but will let one live if the passengers of anyone blows up the other. Batman finds the Joker with a sonar device that spies on the entire city, with the reluctant help of Lucius Fox. Both the civilians and the prisoners refuse to kill each other, and Batman apprehends the Joker after a fight. Before the police arrive to take the Joker into custody, he gloats that Gotham's citizens will lose hope once Dent's rampage becomes public knowledge.
Gordon arrives at the building where Rachel died, where Dent judges his fate, along with his own and Batman's, by flipping a coin. He spares himself, shoots Batman, and tries to kill Gordon's son. Before he can, Batman, who was wearing body armor, tackles Dent off the building to his death. Batman persuades Gordon to preserve Dent's heroic image by holding Batman responsible for the killing spree. As the police launch a manhunt for Batman, Gordon destroys the Bat-signal, Fox watches as the sonar device self-destructs, and Alfred Pennyworth burns a letter from Rachel about her choice to marry Dent.

Question: How did Dent judge Batman's fate?
Answer: By flipping a coin