Mixed Strategy

Also known as: mixed strategies, randomized strategy, frequency play, mixing

Playing the same hand multiple ways at set frequencies, used at equilibrium when two actions share the same EV.

A mixed strategy plays a given hand more than one way at specific frequencies — e.g. AhKh checks 40% / bets 60% in a spot. A pure strategy always takes one action. Mixing appears at a Nash Equilibrium for a precise reason: a player only randomises between actions that have equal EV. If betting were strictly better than checking, you'd always bet; the moment they're equal (because the indifference principle forces it), any mix is fine and the equilibrium picks a frequency that keeps the opponent indifferent too.

Why it matters: mixing is how a solver keeps ranges balanced and unexploitable across all your hands at once. A hand that mixes bet/check lets you show up with both value and bluffs in each line, so no single line is cap-able.

Practical reality: humans can't execute 63/37 splits reliably, and you don't need to. Most solver mixes exist because the difference is near-zero EV — pick the cleaner pure action by blocker logic or board read. Reserve genuine randomisation (card suits, a watch's second hand) for high-stakes spots against opponents tracking your frequencies. Against the pool, exploit beats mixing.