Electrospray ionization mass spectrometry (ESI-MS) is found to gently and efficiently transfer small to large as well as singly to multiply charged [X+]n[A-]m supramolecules of imidazolium ion (X+) ionic liquids to the gas phase, and to reveal "magic numbers" for their most favored assemblies. Tandem mass spectrometric experiments (ESI-MS/MS) were then used to dissociate, via low-energy collision activation, mixed and loosely bonded [A- - - -X- - - -A']- and [X- - - -A- - - -X']+ gaseous supramolecules, as well as their higher homologues, and to estimate and order via Cooks' kinetic method (CKM) and B3LYP/6-311G(d,p) calculations the intrinsic solvent-free magnitude of hydrogen bonds. For the five anions studied, the relative order of intrinsic hydrogen-bond strengths to the 1-n-butyl-3-methylimidazolium ion [X1]+ is: CF3CO2- (zero) > BF4- (-3.1) > PF6- (-10.0) > InCl4- (-16.4) and BPh4- (-17.6 kcal mol(-1)). The relative hydrogen-bond strength for InCl4- was measured via CKM whereas those for the other anions were calculated and used as CKM references. A good correlation coefficient (R=0.998) between fragment ion ratios and calculated hydrogen-bond strengths and an effective temperature (Teff) of 430 K demonstrate the CKM reliability for measuring hydrogen-bond strengths in gaseous ionic liquid supramolecules. Using CKM and Teff of 430 K, the intrinsic hydrogen-bond strengths of BF4- for the three cations investigated is: 1-n-butyl-3-methyl-imidazolium ion (0) > 1,3-di-[(R)-3-methyl-2-butyl]-imidazolium ion (-2.4) > 1,3-di-[(R)-alpha-methylbenzyl]-imidazolium ion (-3.0 kcal mol(-1)). As evidenced by "magic" numbers, greater stabilities are found for the [(X1)2(BF4)3]- and [(X1)5A4]+ supramolecules (A not equal InCl4-).