Linking of S, T and H

As far as i have observed, T after S will sound like D instead of T itself alone, like "STudy, and first H of the following word is often ignored.

So, for " He may cast himself as the king", normally would native speakers pronounce it like "cast Dimself", or "cast Timself", or "cast Simself"? Which one sound better or correct? Thx.