More than seven, rounded down
In the base game, a player with more than seven resource cards discards half, rounded down, when a seven is rolled. Nine cards means discard four and keep five before any theft. Seven cards means discard zero. Development cards are not resource cards and do not count toward this hand limit.
Count rolls, not rounds
With fair independent dice, a seven has probability 1/6 each roll. Across three rolls, the chance of at least one is 1 − (5/6)^3, about 42.1%. That is a dice event, not your probability of losing cards: production, spending, trades and earlier discards can change the hand before the event occurs.
Resolve the roll before making trades
If seven has already been rolled, you cannot first trade down to seven to avoid the discard. The spending figure is useful for planning before a future roll. Discard once for that event, even if the remaining hand is still above seven. A knight moving the robber does not trigger this seven-roll discard. Variants and Colonist modes can change thresholds; this tool deliberately uses the base seven-card threshold.
Rules, assumptions & further reading
Check the official CATAN rulebooks and Colonist’s base-game rules for the rules at your table. These calculations and worked examples are original mathematical models, not measured win rates. They do not read a live game or establish that a move is legal.