In this work, we explore different models formalizing half-duplex communicational systems. The half-duplex channel is the one where each party can either receive or send a message, and if both parties are sending the messages are lost. The typical example of such a system is a walkie-talkie. In some sense most models in communication complexity are half-duplex: usually, only one of the players is allowed to talk. But what if they can? At first glance, it seems like a useless option, but one can show that it can sometimes lead to better protocols. In this work, we will provide upper and lower bounds for equality in different settings as well as a potential application in circuit complexity.