Ask HN: How will using containers save me money?

I am in a situation, where I am running multiple small independent apps in the cloud. They are each very low traffic with occasional traffic spikes, so they require very little resources on a day-to-day basis.

In the ancient world they would be running on a large colocated server under different users, perhaps using something like chroot, etc. The resources would be very well utilized but it would be a security and operations nightmare.

In the IAAS world I can rent instances of various sizes, one per my small application. This would improve on security and operations, but the resources are horribly allocated. I need every server to be sized so it can carry it's app at peak traffic, but otherwise they are all idling most of the time.

In the container (CAAS?) world security and operations are basically solved, but I am still not convinced about resource utilization.

Both AWS and GCE promise to deploy containers on top of their "compute platform" and charge me for used instances + some more for the management of the container platform.

So it seems by using containers to deploy my application I am still paying for the same underutilized resources, while giving the platform provider the possibility to optimize things behind my back. Basically I am saving THEM money.

I know could just pay for one big box and run all my applications on it, running docker and deploying containers by hand, but then I would be back managing things myself.

So how can I use containers to better utilize resources and save ME money?