How low is the ideal first offer? Prior to any negotiation, decision-makers must balance a crucial tradeoff between two opposing effects. While lower first offers benefit buyers by anchoring the price in their favor, an overly ambitious offer increases the impasse risk, thus potentially precluding an agreement altogether. Past research with simulated laboratory or classroom exercises has demonstrated either a first offer’s anchoring benefits or its impasse risk detriments, while largely ignoring the other effect. In short, there is no empirical answer to the conundrum of how low an ideal first offer should be. Our results from over 26 million incentivized real-world negotiations on eBay document (a) a linear anchoring effect of buyer offers on sales price, (b) a nonlinear, quartic effect on impasse risk, and (c) specific offer values with particularly low impasse risks but high anchoring benefits. Integrating these findings suggests that the ideal buyer offer lies at 80% of the seller’s list price across all products—although this value ranges from 33% to 95% depending on the type of product, demand, and buyers’ weighting of price versus impasse risk. We empirically amend the well-known midpoint bias, the assumption that buyer and seller eventually meet in the middle of their opening offers, and find evidence for a “buyer bias.” Product demand moderates the (non)linear effects, the ideal buyer offer, and the buyer bias. Finally, we apply machine learning analyses to predict impasses and present a website with customizable first-offer advice configured to different products, prices, and buyers’ risk preferences.