Who did Claudius bet on for the fight between Hamlet and Laertes?

Claudius did not bet on either Hamlet or Laertes in the fight. This is because the fight was designed as a duel to the death, and Claudius, being Hamlet's uncle and the King, had a vested interest in Hamlet's death.

Claudius's plan was to manipulate the fight to ensure Hamlet's death, and he did this by:

* Poisoning Laertes's sword: The blade was coated with poison so that anyone who was touched by it would die.

* Poisoning a cup of wine: Claudius planned to have Hamlet drink from a poisoned cup if the sword failed.

Therefore, Claudius did not bet on either participant; instead, he orchestrated the whole situation to ensure Hamlet's demise.