A one sided bet is a prize.
You are allowed to give prizes in Islam if the prize giver has the intention of encouraging a positive behavior.
For example, if you tell your son that if he gets an A in math your going to buy him a car. This is permissible.
The prophet Mohammad, peace be upon him, allowed prizes to be given to the winners of horse races. This is because he wanted to encourage the development of expertise in horse raising and breeding since horses were a vital tool of war.
On the other hand if the "prize" is being offered for intentions such as proving a point then its not permissible. Such as to say to your friend out of anger, if you make this basketball shot I'm going to give you my ipod. This "prize" is being given to diminish the other person and prove that your so confident they won't make a shot that you're willing to place something monetary at stake. This is forbidden as it creates enmity between people.