Heads Up Hold'em question

[PseudoPserious]

It's Thursday night. You are at home playing a heads-up Hold'em tournament against a friend. Your friend just dealt an unfavorable turn card, and you muck your hand face down in the burn pile after his pot-sized bet.

However, before your friend can discard his hand, the power goes out, placing the house in complete darkness.

You hear your friend fiddling with the cards. He tells you that he has picked up all 52 cards, leaving the board and his hand face-up in the deck with all of the other cards face-down as normal, and shuffled the deck.

He hands you the deck and offers you an odd bet: that you can't separate all 52 cards into two piles that both have the same number of face-up cards before the power comes back on. He generously lays you 2-1 odds.

Keeping in mind that you can not tell by sight or touch which cards are face-up or face-down in the deck, should you take the bet?

PP