I see the main problems with your code is that:
- You did not put your all of your dice-related code into the - if-block checking if the message is the- rollcommand.
 - 
- This causes the bot to reply when the number "rolled" is 6 even when the command is not invoked.
 
- You did not check whether the message came from a bot. - 
- It would reply multiple times since you did not check whether the message came from your bot.
 
Your code would look like this once you fixed all your errors:
//Dice Roll Game
bot.on('message', message => { // If theres only one parameter, you can omit brackets
    // Bot Check
    if(message.author.bot)return;
    // Even with useless parameters to the command, it will still run
    if(message.content.startsWith('!roll')) { 
        // Arrays are not needed
        // Gives a random int from 1 - 6, (~~) floors an integer 
        let random = ~~(Math.random() * 6) + 1; 
       message.reply(`You rolled a ${ random }!`); // ES6 Template Strings 
        // Please use strict equality signs to prevent bugs from appearing in your code
        if(random === 6){
            message.reply('You win!');
        }
    }
});
Side Note: If you do not want a mention prepended to your bot message, please use message.channel.send instead of message.reply.
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