Apparently this was a local variant that I grew up with, and I couldn't resist sharing. It's kind of a ghetto cross between battleship and just blowing things up on paper.
You're going to need paper (not too thin!), a sharp regular pencil, and a willing friend.
Step 1: Draw Your Terrain
You can't fight without something to fight over! Draw some wacky, overexaggerated terrain on your paper. Have cliffs, spots for lakes, airspace, anything!
Step 2: Add Yer Vehicles Ye Be Shooting With!
It may be called Tanks and Subs, but you can have anything you want. I've got choopers, fighters, bombers, subs, tanks, and jeeps! The sky's the limit, but remember, they all have the same strength. Or do they?
The game I'm going to show you will have a Jeep, tanks, subs, a chopper, and a fighter.
Give your factions an even number of vehicles. Maybe one's all air force, and one's got subs and tanks, but make sure you both have the same number. Or do you? This is another variation you can add in.
Mark your vehicles so you can tell whose is whose.
Step 3: The Reds Started It!
Bullets, shells, and torpedoes can do amazing things in this universe. They seem to move in stop-motion, and can follow the most improbable paths. Torpedoes can leave water, for example.
Put the tip of your traditional (not mechanical) pencil against the tip of one of your guns. In this version, all guns have the same power, from the Howitzer to the Luger. Just start at the tip of one of your guns, place the pencil straight up, and push down until the pencil slips. Hold onto the paper. The sharper your pencil is, the longer the potential trails. My pencil is really dull, so they're pretty short.
Pencils have a habit of going flying and landing in the land of the lost like mine just did. Keep an eye or two on the sneaky little buggers!
Step 4: Damn the Torpedoes!
They blew up my tank!
Draw a dot where the line breaks (this will be a point of contention). On your next turn, you may continue the shot from this point. You may also start a new shot. A shot is considered over when the line crosses a vehicle or the ground. Make sure you don't klutz up and draw the line over part of the shooting vehicle. That's a backfire or a jam, and blows up the unlucky chunk of iron.
You can have however many shots going at one time as you have guns. Your tank can be shooting its main gun and its .50 caliber at the same time. Et cetera.
Step 5: Make It Your Own
Make modifications. Shoot with your eyes shut. Make it so you can only continue the shot you just started, but cna't start another one without the one that was already in the air "falling out of the sky" or something. Assign various weapons various powers and various vehicles various stamina points. Put three, four, five factions all on one paper (make it a big one.) Make it so there's such a thing as a ground-penetrating effect, and when a projectile hits the ground, it leaves a certain sixe crater.
Anything you want!