We compute the minimum one-minute peak of a battery with power and energy limits by bisection with an exact greedy test, to within 10−4 kW, and compare an online threshold rule with it over 119 seven-day windows of one household. With the threshold at the training 99th percentile and a 4 kWh, 3 kW battery, the median relative gap is 34.5% (95% CI 20.4–43.7%), rejecting H1 (median below 10%). Whenever the threshold is achievable, the rule’s peak equals it, so the gap mainly measures how the threshold is set. The bisection runs over ten times faster than a linear programme.