No matter what I pick (yes or no), I'm getting the default return....

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var user = prompt("You look like you're in shape, I may let you pass to my kingdom. Are you brave, yes or no?").toLowerCase();

 

 

switch(user) {

    case user == "yes":

        var strong = prompt("Are you strong?");

        var smart = prompt("Are you smart?");

        if(strong === yes && smart === yes){

            console.log("You may pass!");

        }

        else {

            ("You cannot pass, it is much to dangerous for you in there!");

        }

    break;

    case user == "no":

        var swift = prompt("You coward! You may not pass! Are you swift enough to escape my sword!");

        var strong2 = prompt("Are you strong enough to take a hit/ get past the barrier to escape me?");

        if(swift === yes || strong2 === yes) {

            console.log("The knight charges for you, you duck and run away");

        }

        else{

            console.log("The knight slices you in half, you lay dead on the kingdom bridge");

        }

    break;

    case user == "maybe":

        var friendly = prompt("You seem confused, have my sword, IF, you feel you have the power to wield it?");

        if (prompt === yes){

            console.log("Take it, it is of no use to me against most of the people who pass through here!");

            console.log("A troll passes by and you slice him in half, well done!");

        }

        else{

            console.log("Be gone then.");

        }

        break;

    default:

    console.log("You weren't even brave enough to put yes or no, shame on you!");

}

You're using case incorrectly. 

switch (user) {
    case "yes":
        ...
    case "no":
        ...
    case "maybe":
        ...
    default:
        ...
}