Combustive formation of a first carbon ring is an important step in the growth of polycyclic aromatic hydrocarbons (PAHs) and soot platelets. Propargyl radical addition to but-1-ene-3-yne (vinylacetylene) can start this process, possibly forming 5-, 6-, and 7-membered rings. A variety of partially intertwined reaction pathways results from density functional theory (DFT), which indicates three C7H7 radicals, benzyl, tropyl, and vinyl-cyclopentadienyl, as particularly stable. DFT energetics forms a basis for a subsequent Rice-Ramsperger-Kassel-Marcus (RRKM) study at different combustion pressures and temperatures (P = 30-0.01 atm; T = 1200-2400 K). RRKM indicates open-chain structures and 5-rings as the most important products. Open-chain structures, whose main contributors are the initial adducts, are favored by lower T and higher P, while 5-rings are favored by higher T and lower P. The main feature is that the declining yield in open-chain structures with rising T almost mirrors, at all pressures, the growth with T exhibited by 5-rings (main contributor: fulvenallene). Thus, the two yield lines for open chains and S-rings cross at some T, and their crossing moves toward lower T values as lower P values are considered. Because the T dependence of the yields (slope of the lines) is more pronounced in the T range close to the line crossing, it also becomes less pronounced at the lowest P values considered because the crossing region falls at very low T values. Another constant trait is that 6-rings (mainly benzyl radical) are the third contributor, though they are present at most with a modest maximum yield of 2.4-2.7% in a T range which moves toward lower T as P is reduced.