In this note, we study large deviations of the number 𝐍 of intercalates (2 × 2 combinatorial subsquares which are themselves Latin squares) in a random 𝑛 × 𝑛 Latin square. In particular, for constant 𝛿 > 0 weAs a consequence, we deduce that a typical order-𝑛 Latin square has (1 + 𝑜(1))𝑛 2 ∕4 intercalates, matching a lower bound due to Kwan and Sudakov and resolving an old conjecture of McKay and Wanless. M S C ( 2 0 2 0 ) 05B15, 05C80, 60F10 (primary)1 † To see the analogy to permutation matrices, note that a Latin square can equivalently, and more symmetrically, be viewed as an 𝑛 × 𝑛 × 𝑛 zero-one array such that every axis-aligned line sums to exactly 1.