How do American sports betting odds work?

Positive odds (+150) show profit on a $100 bet — +150 means $150 profit. Negative odds (-200) show how much you must bet to win $100 — so $200 to win $100. The implied probability: for +150 it's 100/(100+150) = 40%; for -200 it's 200/(200+100) = 66.7%. The gap between true probability and implied probability is where the sportsbook makes its margin (the vig).