In the absence of other information, I think the plain language of the offer is that night #4 is free. The bill will probably show night #4 as costing $0.00, and the other nights costing exactly what they would have otherwise cost.

If the hotel tried to charge it another way that benefited them (e.g., comping the cheapest night), I would certainly complain, as the offer does not state that they may do that.