Bismarck recreates the British hunt for the German battleship, Bismarck, in 1941. Players are operating blind and are attempting to find (in the case of the British) or avoid (as for the Germans) each other, as the locations of each player's ships are hidden from each other. Searches are conducted à la Battleship by calling out target locations that search planes or ships can 'see'.
If and when the British successfully intercept the Germans, play can then be conducted in a fashion similar to miniatures, with counters laid out on a large space (the floor), and which then maneuver and fire at enemy ships.

In greater detail;

Avalon Hill's (AH) Bismarck 1979/80 edition, designed by Jack Greene, is a totally different game from the AH 1962 edition designed by Lindsley Schutz and Charles Roberts.

The game centered around the hunt for the KMS Bismarck and the KMS Prinz Eugen in mid-1941. The game has some similarities to the game Battleship, with both players having a hidden map-board and calling out co-ordinates to locate their opponent.

There are two players, German and British. The British player has the task of placing the Royal Navy vessels and search aircraft on his map-board before game play begins. Each map-board is on a grid, with letters on one axis, and numbers on the other. Each Royal Navy unit has a historically accurate starting point. The German setup takes but a moment, since the Germans have only a few bomber units and the task force with Bismarck and Prinz Eugen to place on their map.
Each turn the players move their respective units (cardboard counters), search for enemy units, and possibly engage in combat. In the vast spaces of the Bering Sea and North Atlantic, the search phase becomes vital. Each player calls out grid coordinates containing a ship or aircraft, and the opponent indicates whether a ship is located there, and if so what type. A player may choose not to search with a particular unit, thus keeping its location secret (common tactic for German player, obviously). Since the Bismarck is the only enemy Battleship on the map, British discovery of her is key to victory. As the British are unlikely to have a force sufficient to sink the Bismarck when they initially find her, they will need to "shadow" the mighty vessel. A fast unit, such as the heavy cruiser Suffolk, is able to keep up with Bismarck and follow her on radar without engaging in combat.

Eventually, British heavy units, such as the battle cruiser Hood, may be vectored into the same square as the German task force. At this point combat ensues. The British also have air units on the aircraft carriers Victorious and Ark Royal which can both search for the Germans and attack with torpedoes from a distance. The game has combat damage sheets with squares representing areas of each warship that can be damaged in combat. As combat is resolved, squares are checked off.

The Germans win by avoiding contact with the British, successfully "breaking out" into the Atlantic and ravaging merchant shipping there. They can also achieve victory by destroying any opposition they encounter and making their way to a friendly port in occupied France. Historically, either scenario would have grave consequences for the Battle of the Atlantic. The British have a tougher task, needing to intercept and destroy the Germans. Since most British vessels are no match for Bismarck, it is necessary to vector several vessels currently on convoy escort duties into the area to form a powerful task force. Poor planning by the British or clever moves by the Germans allow Bismarck to slip through.

The advanced rules of the game implement a weather system, combat using a miniatures-type system (with ship counters laid out on the floor), realistic damage to ships, etc. Alternate "what if" scenarios and ships are provided, such as the German aircraft carrier, Graf Zeppelin, breakout with the Tirpitz and others. U-boats are also represented (albeit in an abstract way) in the Advanced game.

Second edition changes included:

the square grid on the original map was replaced with a hexagonal overlay;
the single Bismarck ship unit was replaced by multiple German ships;
the relatively simple search, movement and combat systems of the original were replaced by more complex rules.
packaging was modified; the second edition coming in a smaller, standard-sized AH flat box (compared to the over-sized box of the first edition) and having alternative cover artwork.

They Come Unseen