There are several synonyms for the phrase "make book on." One of the most common is "place a bet on," which is often used in the context of gambling or sports betting. Other synonyms include "wager on," "gamble on," "back," "lay money on," and "put money on." These phrases all refer to the act of staking money or placing a prediction on the outcome of an event or situation. While the specific words may differ, the shared meaning remains constant: a willingness to risk something in the hopes of gaining something more valuable.