A Bait Hive Sized by Arithmetic: A Capture-Odds Model and the Cheapest Specification That Reaches a Stated Probability

Bait hives, empty boxes set out to attract honey bee swarms, are usually built by copying a traditional size without asking how much each feature contributes or what a cheaper box gives up. This paper builds a simple multiplicative capture-odds model over cavity volume, entrance area, mounting height and comb presence, with every preference parameter stated as an assumption drawn from well-known bait-hive literature values, and searches 240 candidate specifications for the cheapest that reaches a stated capture probability. The reference box, at 40 litres with old comb mounted at 5 metres, is assigned a capture probability of 0.5. Only 8 of the 240 specifications reach the target probability of 0.4. The cheapest that does so is a 30 litre box with a 12.5 square centimetre entrance, mounted at 3 metres, containing old comb, with modelled relative odds of 0.693, a capture probability of 0.409 and a stated-assumption cost of 73.0 dollars, against 94.0 dollars for the reference box. This study is simulated, not measured; the model is assumption-driven in the precise sense set out in the text, and its probabilities are relative comparisons between boxes, not forecasts for any real site.