The slang bet appears to come from the everyday word bet, a wager  or to risk something of value.  By the 1850s, we were saying You bet! as an affirmative exclamation with the sense of Indeed!  This expression has the underlying notion of You can bet that it is so or That's a bet.

Dog  Short for underdog. Even  What you see next to a game when no team is given better odds. Short for even money. Sometimes called a pick 'em game. If you bet $10 and your team or player wins, you win $10.