Learn Spanish (Latin America): El oponente tiró el dado, así que es tu turno. - The opponent threw the die, so it is your turn.

Así que means 'so' or 'therefore' and is used to introduce a consequence. Because the opponent threw the die (the cause), it is now your turn (the effect). It works very similarly to por lo tanto, but así que is much more common in everyday spoken Spanish.

Doesn't tirar usually mean 'to throw away' or 'to pull'?

It can mean both of those things, but tirar is also the standard verb for tossing or rolling objects in games. So, tirar el dado is the natural way to say 'to roll the die' in Spanish.

Why do we use es for es tu turno? Shouldn't a turn be temporary and use estar?

Even though a turn is temporary, Spanish treats it like an event taking place in time (similar to stating the hour or the date). Events always use ser (es) rather than estar. You are identifying whose moment it is, not describing a physical state.

Since English often uses 'dice' for both singular and plural, how strict is el dado in Spanish?

It is very strict! You must use the singular noun el dado for one die, as shown in this sentence, and the plural los dados when rolling two or more.