Which booking request should you accept? The gap-night math
Short answer: accept the set of requests that leaves the calendar worth the most, not the single request that pays the most. A stay is worth its price, less what it costs to turn the place over, plus whatever the nights it leaves behind can still earn. Nights trapped in a gap shorter than your minimum stay earn nothing.
A worked example
You have a 7-night hole between two confirmed bookings (5 to 12 July), a 3-night minimum, $60 turnover and leftover nights worth about $50.
Request A, 7 to 10 July, $480. It pays the most per night, but leaves 2 nights before and 2 after. Both gaps are under 3 nights, so 4 nights are dead. Worth $480 - $60 = $420.
Requests B (5 to 9 July, $440) and C (9 to 12 July, $345) fit end to end. Worth $785 - $120 = $665.
Accepting the first request that arrived, or the one with the highest price, costs $245 here. The Booking Request Chooser finds that answer on any calendar, exactly, and lists the reason for each decline.
How the plan is found
Confirmed bookings are fixed. Any request overlapping one is out.
Between each pair of confirmed bookings, the tool considers every chain of non-overlapping requests (a stay may end the day another begins) with dynamic programming, scoring price minus turnover plus the empty-night value of every leftover gap at least as long as your minimum stay.
It compares that with accepting in arrival order and highest price first, and tries stays one or two nights longer or shorter at the guest's own nightly rate as counter-offers.
Pick the empty-night value honestly
That number is your estimate: your usual nightly price times how often a leftover night actually fills. Set it to zero and the tool only compares prices less turnover. The page also tells you whether the plan changes when leftover nights are worth nothing, half or double what you entered.
Questions
Should I accept the highest-paying booking request?
Not automatically. Compare what the calendar earns with and without it: its price, minus the cost of turning the place over, plus whatever the nights left on either side of it can still earn. If it leaves a gap shorter than your minimum stay, those nights are dead and the stay has to beat the alternative by more than their value.
How do I fill a one- or two-night gap between bookings?
Lower your minimum stay for just those dates, offer a discounted gap-night price, or send the guest a counter-offer that extends their stay a night earlier or later so it closes the gap.
Is it worth declining a request to keep a longer stay possible?
Only when the longer stays are realistic. Estimate what a leftover night is worth as your usual nightly price times how often leftover nights actually fill, and let the numbers decide.