The Battle of the Denmark Strait was one of the most dramatic episodes in World War II, which had no shortage of drama. As such it's one of the most popular topics for wargames, dating all the way back to Avalon Hill's original Bismarck game in 1961.
As an operational game the Bismarck campaign has a lot of potential and has successfully been made into games several times. The Battle of Denmark Strait, however, presents somewhat of a problem. It's really hard to fit it into a wargame format.
Today, for example, I played out the Denmark Strait matchup three times with two different players using Axis & Allies War at Sea. Now, WAS is admittedly not the first word in simulation. But the four ships involved in the historical battle are explicitly represented int he game, and most of them have special abilities that are explicitly modeled on what happened at this battle. And still there was really no context, as the Bismark and Prinz Eugen were handily defeated thrice. In game terms this isn't surprising, because the two German ships add up to 70 points while the British pair top out at 102 points. Yet one has to wonder whether this is a problem with the game or actually a reflection of the historical improbability of the actual result.
In the Avalanche Press Second World War at Sea series game Bismarck the Bismarck and Prinz Eugen add up to 151 points while the Prince of Wales and Hood are 165 points -- closer, but still showing an edge for the British. (And also not including the two shadowing British cruisers). Considering that all the British need do is achieve significant damage to the Bismarck and they win and the straight point value seems to understate the British edge.
Mongoose Publishing's Victory at Sea rules have Fleet Allocation Points. If we consider the Denmark Strait to be a "Raid" level scenario than the German fleet is worth 5 FAP and the British squadron is worth 8 FAP. Another way to look at the matcup is to note that the two German ships will be rolling a total of 12 dice with a potential maximum of 28 damage dice (24 of which are 'AP') contrasted with the British battle line salvo of 18 dice with 44 potential damage dice (all AP).
At the high end of the realism scale with the Command at Sea system there's no point system at all, but the design notes for the Denmark Strait point out that the chance of the hit that blew up the Hood happening under the CaS rules comes out to .00016! That's a 1 in 6,250 chance. They say" This is small comfort for the crew of the Hood, but it demonstrates the difficulty in duplicating a historical result."
So the bottom line is that by any reasonable measure of likelihood the Bismarck's sortie should have come to an abrupt and aborted end that early morning inf May, 1941. The British strategy for dealing with a potential raid would had worked perfectly. The raiders were spotted before they even left Norway. Appropriate and effective deployments were made. The cruiser pickets successfully detected the German breakout attempt and shadowed it superbly. A more than adequate countering force intercepted just as the British planned and was literally a few minutes away from closing the range enough that the Hood's weak deck armor would no longer be an issue. Most wargame refights of Denmark strait -- whether using the super detailed Command at Sea or the highly abstracted War at Sea -- will reflect this reality. The Bismarck should lose.
Had it played out that way in reality, the Bismarck affair would have played a much smaller role in the lore of World War II, probably ranking somewhere below the exploits of the Graf Spee and Scharnhorst.
But one shell hit changed all that. The dramatic destruction of the Hood instantly changed the odds in the battle and combined with the Prince of Wales teething troubles and the mental shock of the Hood's loss allowed the Bismarck to break out and created the high drama that captured the public imagination.