This paper studies when a market-making firm should place orders to maximize their expected net profit, while also constraining risk, assuming orders are maintained on an electronic limit order book (LOB). To do this, we use a model-free and off-policy method, Q-learning, coupled with state aggregation, to develop a proposed trading strategy that can be implemented using a simple lookup table. Our main training dataset is derived from event-by-event data recording the state of the LOB. Our proposed trading strategy has passed both in-sample and out-of-sample testing in the backtester of the market-making firm with whom we are collaborating, and it also outperforms other benchmark strategies. As a result, the firm desires to put the strategy into production.