The recent development of the smartphone Global Navigation Satellite System (GNSS) chipsets, such as Broadcom BCM47755 and Qualcomm Snapdragon 855 embedded, makes instantaneous and cm level real-time kinematic (RTK) positioning possible with Android-based smartphones. In this contribution we investigate the instantaneous single-baseline RTK performance of Samsung Galaxy S20 and Google Pixel 4 (GP4) smartphones with such chipsets, while making use of dual-frequency L1 + L5 Global Positioning System (GPS), E1 + E5a Galileo, L1 + L5 Quasi-Zenith Satellite System (QZSS) and B1 BeiDou Navigation Satellite System (BDS) code and phase observations in Dunedin, New Zealand. The effects of locating the smartphones in an upright and lying down position were evaluated, and we show that the choice of smartphone configuration can affect the positioning performance even in a zero-baseline setup. In particular, we found non-zero mean and linear trends in the double-differenced carrier-phase residuals for one of the smartphone models when lying down, which become absent when in an upright position. This implies that the two assessed smartphones have different antenna gain pattern and antenna sensitivity to interferences. Finally, we demonstrate, for the first time, a near hundred percent (98.7% to 99.9%) instantaneous RTK integer least-squares success rate for one of the smartphone models and cm level positioning precision while using short-baseline experiments with internal and external antennas, respectively.