The Big Bet is the eighteenth episode of Season 3 of The Brady Bunch, and the 67th overall episode of the series. Written by Elroy Schwartz and directed by Earl Bellamy, it first aired 28 January 1972 on ABC.
After Greg boasts that he can do twice as many pull ups as Bobby, the youngest Brady brother demands he put up or shut up, betting that the loser has to do everything the winner says.
Greg dismisses an excited Bobby's ability to do more chin ups than anyone else in his class as being good for a kid his age, but nothing compared to what an older guy like he can do. Irked at Greg's response, Bobby decides to bet Greg - that Greg can't do twice as many chin ups as him - a bet which Greg readily accepts, with the loser having to do what the winner says for an entire week.
The bet gets the entire family involved, with specifically Marcia and Cindy rooting for one person in the battle of the ages. Beyond the swelled head the winner ultimately gets from the challenge, the question becomes if there is a limit to what the winner can tell the loser to do, especially if it directly impacts other important things going on in the loser's life, and has consequences on others not involved in their bet. Bobby wins and soon becomes a tyrant. He invites himself along on Greg's date with Rachel. Bobby is annoying and disruptive through the date, and through his intentionally silly antics rips the soft top of Mike's convertible, leaving himself with a large debt to Mike for the repairs.
Meanwhile, Mike has been invited to his twenty year high school reunion. Carol's task at the reunion ends up being to figure out who was Mike's senior year crush, Carol armed only with the knowledge that her nickname was "Bobo". Taking a play from Greg and Bobby, they make a bet that Carol cannot on one guess figure out who Bobo is of the reunion attendees.