A system for monitoring the play at gambling games is disclosed. The preferred embodiment comprises a system for monitoring the play at blackjack as that game is played in casinos. The system typically will comprise video monitor means for generating a digital representation of the bets made by the players and of the cards dealt to the players and to the dealer, so that an output can be generated indicating whether the correct payouts are made and bets collected. An alarm signal is generated if an error is made in the play of the game. An alarm signal may also be generated if the long-term statistics of the game indicate that the odds ordinarily applicable to the game have been departed from over a period of time.