When luck adjustment creates chips: choosing the freeze point in all-in equity adjustment

Luck-adjusted performance measures replace an observed outcome with its expectation at a chosen moment, and conditioning on events that occur after that moment biases it. Such biases (post-treatment, collider or look-ahead bias) are well understood in theory but have mostly been quantified in simulations or against experimental benchmarks, because the true value is seldom observed. We measure one in a real evaluation system where it is observed. In poker, all-in equity adjustment averages a player's result over the cards still to come; when one player is all-in while others keep betting, a natural implementation would freeze the cards at the all-in but take the contenders from the showdown. Writing a hand's result as a Doob martingale, we show that it corresponds to no stopping time, characterize the valid alternatives, and derive a necessary condition, conservation of chips within each hand, that exposes the rule without computing any equity. In 1,312 hands from 410 players in three-handed online tournaments, where every outcome is observed, the rule overstates the player all-in first by 4.5 to 6.8 chips per hand and violates conservation in almost every hand. As predicted, the bias is several times larger when the decisive fold follows an all-in.