5 ideas
Cardano calls the total set of equally possible results of a throw the 'circuit': 6 for one die, 36 for two, 216 for three. The chance of an event is the number of outcomes in the circuit that favor it, set against those that do not. This turns luck into arithmetic by listing every way the dice can fall.
Cardano calls equal conditions the most fundamental principle of gambling: equal opponents, money, situation, and honest dice. A bet is just only when each player's stake is in proportion to the number of outcomes favoring them.
Cardano sees that a few throws can stray wildly from the computed odds, but over many trials the results come close to what the circuit predicts. Calculation therefore describes the aggregate, not any single throw. He still keeps room for personal 'luck' to explain short-run streaks that seem to defy the numbers.
Cardano argues that even a player who knows the odds loses more in time, reputation, temper, and health than he can win in money. He tolerates gambling only as brief relief from anxiety or grief, played for small stakes against honest opponents. By his account, the rational best move at the table is not to sit down.
Calculated odds hold only if the game is honest, so Cardano catalogs the ways they are corrupted. These include loaded or shaved dice, marked or soaped cards, mirrors, and collusion with onlookers.