If I get it right, you want to send 50K mails per 4 hours, that means 12.5 K per hour. In my case it allows me to set 12500 mails per hour into the max sending quota per hour field ... Maybe it's because you use smtp. In that case I would recommend using some service like MailGun because SMTP is reliable but I don't think 12.5K per hour is a good idea ...
Best Regards