Heuristic solvers for general-sum extensive-form games produce a stream of iterates, and practice reports the NashGap of the returned profile. We ask what a solver can know about its own iterates from the regret accumulators and the terminal-distribution accumulators its updates already maintain. In two-player games the NashGap of a weighted average strategy equals, at the maximizing player, the weighted external regret plus a signed value correction. Bounding the regret by the running counterfactual-regret accumulator gives an online certificate whose cost per checkpoint is linear in the number of terminal histories. The certificate stays sound under alternating updates and in games with three or more players. The mismatch between what alternation evaluates and what the averages record enters as one signed comparator term, maximized in a single backward pass per player whose comparator weight is nonzero. The bound is read off the regret state, with no best response against the average. Run a portfolio of training-free regret-matching solvers, output the iterate with the smallest certificate, and verify that iterate once. On the benchmark's biased Leduc family a pool of sixteen training-free solvers, seven original and nine recent variants, solves
89% of the
64 instances at threshold
10−5 this way, matching the trajectory-minimum union of the solvers. The same protocol solves
92% of the
64 pre-registered held-out instances and
89% again on a third set of
64 instances that no earlier stage used. The zero-best-response certificate certifies all
57 in-sample solves and all
57 fresh ones, and
58 of the
59 held-out ones. Its exact-comparator refinement certifies every solve in the three sets. The certificate states both and attributes its bound. Code is available at https://github.com/lbn187/CertNE.