If I understand your architecture correctly, your client has to wait for the network roundtrip before being able to see the result of the die roll, correct?
Yes. This is over websockets though, and in all of my testing/profiling (pretty shitty ISP in West Africa, game server is currently hosted in the US) I haven't had an exchange take longer than one second. Also the mandatory wait is just for the die - for picking a move, for instance, the client can go straight into rendering the selected move while sending it to the server.