Держу пари, ты забудешь ...
My girlfriend often uses this phrase in IMs as well as in conversation. The indeclinable noun "пари" seems to be a borrowed word from French, and in French the phrase "je parie que ... {I bet that ...}" is commonly used in conversation.
She has lived near Paris (no pun intended) for ten years in her teens, so I have always wondered if this phrase might actually not be as commonly used among Russian speakers who don't speak French. Is this quite an informal expression?