Master Key System Depth and Change Key Capacity

ScopeThe theoretical count is a power, and powers grow fast enough to be misleading: six positions with six usable depths is 46,656 combinations, which sounds inexhaustible. Then master two positions with a two-step progression. Each mastered position yields ceil(usable depths / 2) - 1 change values (every other depth in the master's parity group, the larger one when the count is odd, less the one the master claims) -- two here -- so the system holds 2 x 2 = 4 CHANGE KEYS, not 46,656. A facility with 40 doors and a plan to expand has already outgrown it before the first cylinder is pinned. Master three positions instead and capacity rises to 8, better, at the cost of a master key that differs from every change key in only three places, which is a weaker system. The theoretical figure is not merely optimistic; the usable count is smaller by an order of magnitude or more, because the master claims one value at each mastered position, adjacent-cut and MACS rules eliminate a large fraction, keyway restrictions cut it again, and the requirement that change keys not accidentally operate other cylinders cuts it further. THE FAILURE THIS PREVENTS IS EXPENSIVE. A system designed without a proper progression eventually issues a change key whose cuts, combined with the master wafer stack, operate a cylinder it was never meant to -- a cross-keying accident -- and discovering that in a building with a thousand cylinders means rekeying the building. The design decision is how many positions to master: more gives more keys and less security, fewer gives a tighter system with less capacity, and the trade should be made deliberately at the start rather than discovered at key three hundred. A capacity estimate for a simple two-level, two-step progression. Multi-level systems with grand masters, selective keying, cross-keying, constant cuts, keyway families, and manufacturer-specific restricted keyways all change the arithmetic substantially, and the usable depth count itself depends on the manufacturer's cut specification. It does not generate a bitting list, check for cross-keying conflicts, or verify that no change key inadvertently operates another cylinder, which is the actual work of system design and is done with a bitting chart. The manufacturer's system specification, a qualified locksmith or system designer, and the facility's key control policy govern.

Formula or tabletheoretical combinations = usable depths raised to the number of cut positions; a two-step progression yields ceil(usable depths / 2) - 1 per mastered position (every other depth in the master's parity group, the larger when the count is odd, less the one the master claims), so change keys = that raised to the number of mastered positions.

Source and editionThe progression capacity relation as standard master keying practice, by name, with the lock manufacturer's system specification named as governing the usable depth count, the cut rules, and the keyway restrictions.

Free accessA power and a product on counts the user supplies; no manufacturer bitting specification is reproduced.

What governsEstimate. AHJ and licensed professional govern.

API field namescut_positions, usable_depths, mastered_positions, alternative_mastered_positions, change_keys_required, theoretical_total, per_mastered_position, change_keys_available, alternative_change_keys, margin

• The usable count is far below the theoretical by an order of magnitude or more once the master, the cut rules, and the keyway are appliedmaster keying practice
• Mastering more positions trades security for capacity and the decision is made before the first cylinder is pinnedmaster keying practice
• Cross-keying is the failure mode a change key that operates a cylinder it was never meant to means rekeying the buildingmaster keying practice