Are ultraspinning Kerr-Sen-${\mathrm{AdS}}_4$ black holes always superentropic?

We study thermodynamics of the four-dimensional Kerr-Sen-AdS black hole and its ultraspinning counterpart and verify that both black holes fulfil the first law and Bekenstein-Smarr mass formulas of black hole thermodynamics. Furthermore, we derive new Christodoulou-Ruffini-like squared-mass formulas for the usual and ultraspinning Kerr-Sen-${\mathrm{AdS}}_4$ solutions. We show that this ultraspinning Kerr-Sen-${\mathrm{AdS}}_4$ black hole does not always violate the reverse isoperimetric inequality (RII) since the value of the isoperimetric ratio can be larger/smaller than, or equal to unity, depending upon where the solution parameters lie in the parameters space. This property is obviously different from that of the Kerr-Newman-${\mathrm{AdS}}_4$ superentropic black hole, which always strictly violates the RII, although both of them have some similar properties in other aspects, such as horizon geometry and conformal boundary. In addition, it is found that while there exists the same lower bound on mass ($m_e\ge 8l/\sqrt{27}$ with $l$ being the cosmological scale) both for the extremal ultraspinning Kerr-Sen-${\mathrm{AdS}}_4$ black hole and for the extremal superentropic Kerr-Newman-${\mathrm{AdS}}_4$ case, the former has a maximal horizon radius $r_{\mathrm{HP}}=l/\sqrt{3}$, which is the minimum of the latter. Therefore, these two different kinds of four-dimensional ultraspinning charged AdS black holes exhibit some significant physical differences.