Context. Uranus and Neptune have atmospheres dominated by molecular hydrogen and helium. In the upper troposphere (between 0.1 and 10 bars), methane is the third main molecule and condenses, yielding a vertical gradient in CH 4 . This condensable species being heavier than H 2 and He, the resulting change in mean molecular weight due to condensation comes as a factor countering convection, traditionally considered as ruled by temperature only. It makes both dry and moist convection more difficult to start. As observations also show latitudinal variations in methane abundance, one can expect different vertical gradients from one latitude to another. Aims. In this paper, we investigate the impact of this methane vertical gradient and the different shapes it can take, on the atmospheric regimes, especially on the formation and inhibition of moist convective storms in the troposphere of ice giants. Methods. We develop a 3D cloud-resolving model to simulate convective processes at the required scale. This model is nonhydrostatic and includes the effect of the mean molecular weight variations associated with condensation. Results. Using our simulations, we conclude that typical velocities of dry convection in the deep atmosphere are rather low (of the order of 1 m/s) but sufficient to sustain upward methane transport, and that moist convection at methane condensation level is strongly inhibited. Previous studies derived an analytical criterion on the methane vapor amount above which moist convection should be inhibited in saturated environments. In ice giants, this criterion yields a critical methane abundance of 1.2% at 80 K (this corresponds approximately to the 1 bar level). We first validate this analytical criterion numerically. We then show that this critical methane abundance governs the inhibition and formation of moist convective storms, and we conclude that the intensity and intermittency of these storms should depend on the methane abundance and saturation. -In the regions where CH 4 exceeds this critical abundance in the deep atmosphere (at the equator and the middle latitudes on Uranus, and all latitudes on Neptune), a stable layer almost entirely saturated with methane develops at the condensation level. In this layer, moist convection is inhibited, ensuring stability. Only weak moist convective events can occur above this layer, where methane abundance becomes lower than the critical value. The inhibition of moist convection prevents strong drying and maintains high relative humidity, which favors the frequency of these events. -In the regions where CH 4 remains below this critical abundance in the deep atmosphere (possibly at the poles on Uranus), there is no such layer. More powerful storms can form, but they are also a bit rarer. Conclusions. In ice giants, dry convection is weak, and moist convection is strongly inhibited. However, when enough methane is transported upwards, through dry convection and turbulent diffusion, sporadic moist convective storms can form. These storms should be more frequent on Neptune than on Uranus, because of Neptune's internal heat flow and larger methane abundance. Our results can explain the observed sporadicity of clouds in ice giants and can help us guide future observations to test the conclusions of this work.