This game is a more interesting enhancement of the old pencil-and-paper battleships game that you may have played as a child. It's still a pencil-and-paper game: all you need to play is some squared paper and a pen or pencil.
I found this version of the game sometime in the 1960s in an old book by Hubert Phillips called More Indoor Games for Two Players. It was a library book, and I was never able to buy a copy, so these rules (devised by Hubert Phillips) are what I remember from decades ago.
Each player starts with an empty 21 × 21 grid that the other player can't see (use squared paper). The columns are lettered from A to U; the rows are numbered from 1 to 21. Or the other way around, it makes no difference.
You're advised (but not required) to make a second map on which you can note what you've discovered about your opponent's map — and the squares you've hit, so that you don't hit the same square twice.
Laurie Dunkin Wedd has provided me in February 2007 with a ready-made game map in a PDF file: download by right-clicking here.
Each player starts with 160 points that must be spent before play starts. You must spend between 60 and 100 points on ships.
Draw each ship on the map with a solid outline around the squares that it occupies. Ships don't move during the game (neither does anything else). Ships may not touch each other, not even at corners. However, they may touch land or the sides of the map.
A submarine occupies one square and costs one point.
A destroyer occupies two squares in a horizontal or vertical line, and costs two points.
A cruiser occupies three squares in a horizontal or vertical line, and costs three points.
A battleship occupies four squares in a horizontal or vertical line, and costs four points.
An aircraft carrier occupies four squares in a square shape (2 × 2) and costs four points. It can carry aircraft but not anti-aircraft guns.
One block of land is nine squares in a square shape (3 × 3). Land is free and you can have as many blocks of land as you want. Ships can't be placed on land; weapons can't be placed on water, or on ships (except that aircraft can be placed on aircraft carriers). Draw land on the map with a solid outline. If you feel artistic, you can use one colour for ships and a different colour for land; but it's not necessary.
All weapons can be used once only. All weapons except salvos must be placed on your map and can be destroyed by enemy fire before being used.
When one of your weapons is used by you, mark it as used with a circle around it. When one of your weapons or ships is hit by your opponent, mark a cross on that square on your map. It's necessary to distinguish between used and hit because, if you have an aeroplane on an aircraft carrier, a hit affects both plane and ship, but using the plane affects only the plane.
A salvo costs one point. It's the only thing not placed on the map. You make a note beside the map of how many salvos you've bought; whenever you fire a salvo, reduce the number by one.
A salvo consists of three shots. You tell your opponent which three squares on his map you want to hit. They can be anywhere on the map; they don't have to be close to each other. He tells you the total damage resulting from the three shots: for instance: "One hit on a cruiser, and one recce plane." He doesn't tell you the effect of each shot separately. Hitting a weapon that's already been used has no effect, so he doesn't tell you about it. A ship is sunk when you've hit every part of it; he tells you when you've sunk a ship ("Two hits on a cruiser, sinking it.").
A recce plane costs one point and does no damage. When you buy it, you place it on your map (on land, or on an aircraft carrier). Mark it with an R. When you use it, you send it to any square on your opponent's map, and he tells you what's in that square, and what's in all the adjacent squares. In other words, he gives you a full description of everything that's in a 3 × 3 area: land, ships, and weapons (and their exact locations). A recce plane can be shot down by an anti-aircraft gun, in which case you get no information from it. When you've used it, put a circle around it.
A bomber costs three points and works in the same way as a recce plane, except that it destroys everything in a 3 × 3 area. Mark it on your map with a B. Your opponent tells you the damage done (as with a salvo), but gives no other information. A bomber can be shot down by an anti-aircraft gun only if the gun is in the exact square to which the bomber has been sent.
A nuclear bomber costs ten points and works in the same way as a bomber, except that it destroys everything in a 5 × 5 square and can't be shot down by anti-aircraft guns (though it can be destroyed on the ground before being used). Mark it on your map with an N.
An anti-aircraft gun costs one point and can shoot down bombers that appear on its square. It can also shoot down recce planes that appear on its square or on an adjacent square. Place it on your map, on land, marking it with an A. When you've used it once, put a circle around it.
Playing the game
You must spend all your points and place all your ships, aircraft, and anti-aircraft guns on your map before play starts.
In your turn, you can send an aircraft or fire a salvo. When you've done that, it's your opponent's turn. Your anti-aircraft guns are used during your opponent's turn.
Winning the game
The game ends when both players have used all their aircraft and salvos.
Each player then counts the total value of his ships that are still afloat. A ship is not sunk until all of its squares have been hit. Thus, a battleship with three hits is still afloat, and still counts four points.
The winner is the player with more ship points still afloat.
As far as I remember, destroyers and cruisers are the most useful ships. A submarine is sunk with a single hit; but if your opponent finds one end of a battleship with a recce plane, he knows immediately where the rest of it is, which gives him a lot of free information.
Recce planes and salvos are the most useful weapons. You can sink your opponent's fleet efficiently with them if he has no anti-aircraft guns.
Bombers are inefficient against ships but can destroy concentrations of enemy weapons quickly.
I doubt that nuclear bombers are cost-effective, but you can buy one or two if you feel like it. If you buy ten of them, you'll destroy about half your opponent's ships and aircraft, but he'll still have half his aircraft and all his salvos, and you'll probably lose.