De Finetti’s betting argument is used to justify finitely additive probabilities when only finitely many bets are considered. Under what circumstances can countably many bets be used to justify countable additivity? In this framework, one faces issues such as the convergence of the returns of the bet. Generalizations of de Finetti’s (Fundam Math 17:298–329, 1931) argument depend on what types of conditions on convergence are required of the bets under consideration. Two new such conditions are compared with others presented in the literature.