This answer will focus on the RN's wargames of the 1920s and 30s. These generally had two components; a strategic game, carried out on paper, and a tactical game, carried out either with models, or with actual ships. The strategic game attempted to replicate a situation with which the RN felt it might be faced, and was used to set up the condition for the tactical game. While the strategic games were relatively free-form, tactical exercises were governed by a set of rules, laid down in Admiralty publications. The most studied ruleset is CB 3011, titled ‘War Game Rules, 1929’. This provided rules for estimating the effects of gunfire, torpedoes and anti-aircraft fire.

CB 3011 divided hits on ships up into three categories. 'Vital hits' were hits to magazines or turrets, which might blow the ship up. 'Speed hits' represented hits to engine or boiler rooms, and reduced the ship's speed. All other hits were ‘Non- Vital Hits', which had a cumulative effect on the ship. These non-vital hits were used as the basis for determining the survivability of ships, with ships given an appropriate number of these hits needed to sink them (or render them useless in battle). 15in gunfire was used as the typical yardstick for this. A modern battleship, like Nelson, was expected to sink after 18 hits from these guns, while an older one like Iron Duke or a battlecruiser would take 15 to sink. Cruisers would survive just three or four hits, and a destroyer would be sunk after just one. Lighter gunfire was calculated in terms of their 15in equivalent, with the precise value depending on the target. Against heavily armoured targets, a 15in hit was seen as the equivalent of six 8in or twelve 6in hits, but against cruisers and smaller, it equalled three 8in or six 6in. As a result, a cruiser that took four 15in hits to sink would sink after 24 6in hits. However, serious damage would be caused by fewer hits. A modern battleship would be 60% effective after nine hits from a 15in gun, while two hits from this gun on a heavy cruiser would halve its effectiveness.

The chance of hitting and doing damage was based on exercises carried out in 1922-26, with an estimated reduction of 30% to reflect the stresses and problems introduced by the reality of battle. The calculation was simplified by ignoring the possible effects of near-misses, especially splinter damage to upperworks. The resulting percentages are shown in the table below:

| Modern Battleships or Battlecruisers | Old Battleships | Heavy Cruiser | Light Cruiser | Destroyer ---|---|----|----|----|---- 12in gun and above | 1.2 | 1.0 | 0.8 | 0.6 | 0.3 6-8in | - | 1.2 | 1.0 | 0.8 | 0.5 4-4.7in | -| -| 2 | 1.6 | 1.0

It should be clear that larger guns were seen as being less effective against smaller targets, due to their greater manoeuvrability. Similarly, smaller guns were ineffective against larger ships due to their armour, though they were more likely to score hits. Variations on this table were used to take into account the effects of weather, aircraft spotting, and other factors. The values in this table were then weighted by the range of fire and the fire rate of the gun to give a 'hits per gun per minute' table. This gave the expected number of hits each gun would score in a minute. Typically, this gave a lower hit probability than in the table above, as it was used for the early stages of an engagement, when firing solutions were still being calculated. It was multiplied by the number of guns firing and by the number of minutes before the range was found (3 minutes at 20,000+ yards, two between 10-20,000 and one below 10,000) to work out the total number of hits scored. After the time was up, the accuracy reverted to that in the table. Each hit had a 1/30th chance of scoring a 'vital hit', and an umpire-decided chance of causing a 'speed hit'.

Similar tables were used for anti-aircraft gunnery. These were generally optimistic, assuming that more hits would be scored than actual experience would show. An octuple mount for the 2pdr 'pom-pom' was expected to score four hits every minute, with a 50% chance of scoring a hit in the first minute, before full accuracy was achieved. Real experience showed that the real value was more like 5%. Torpedo tables were equally optimistic for the battleship. These tables showed the percentage of full speed that a ship would be capable of making after a hit, depending on the warhead of the torpedo. A modern Nelson-class ship would be slowed by 50% after six hits, while a Queen Elizabeth or 'R' class would take four or five hits to reach the same state. In reality, the Barham, a Queen Elizabeth class ship, would sink after just three hits. In general, there was no need to go through the steps of actually 'firing' the guns. Gunnery training was done against real targets, usually large scaffolds towed behind tugs. Anti-aircraft gunnery was done against radio-controlled drone aircraft. Real torpedoes with dud warheads were, however, more common.

As an example of a game played under this ruleset, we can look at Exercise MZ, carried out in March 1929. This was intended to simulate a possible British war with Japan, with a weaker force ('Blue') attempting to draw out and defeat a portion of a larger enemy battlefleet ('Red'). The strategic part of the game was played out at the Naval Staff College in Greenwich, setting up the starting conditions of the tactical exercise. The Red Fleet had eight battleships, three battlecruisers, two carriers and supporting elements available, but had to cover two important convoys. Blue had a smaller fleet in the strategic game, but maintenance requirements of Red ships had given them temporary equality; this, combined with political pressure from above, led to the need to attack the convoys, or the enemy battlefleet, if encountered.

The two convoys would sail on the 17th-18th March 1929, each covered by a division of Red battleships. The rest of the Red force was kept at anchor, but on short notice to sail. Air reconnaissance soon spotted Blue ships approaching. The convoys were dispersed, and the rest of the fleet set sail, hoping to combine with the battleships at sea. Blue's aerial forces sighted the convoys and the covering forces, but did not initially sight the rest of Red's fleet. As a result, a short engagement ensued, with Blue's battlecruisers and aircraft attacking the Red battleships at long range. One Red and one Blue capital ship were damaged, mainly by air attacks, as Red attempted to draw Blue away from its main bases. Shortly afterwards, though, Blue aircraft sighted the main Red fleet. Realising that achieving their main goals would soon be impossible, Blue disengaged.

A more exciting exercise would come in 1934, during the main Naval Manoeuvres. The Home Fleet, operating as Blue, was tasked with 'establishing' a base for commerce raiding on the Iberian coast, while the Mediterranean Fleet, Red, had to stop them. The two fleets had five battleships each, but Blue had one carrier and two battlecruisers, while Red had two carriers and no battlecruisers. Admiral W. W. Fisher, commanding Blue, correctly reasoned that Red was likely intending to set up their base in Spain's Arosa Bay. He set up his fleet in a position to intercept them at close range in a night engagement, taking advantage of bad weather that grounded both sides' reconnaissance aircraft. Splitting the Red fleet into two pieces, Blue was able to fight a brief, successful action.

Sources:

Royal Navy Strategy in the Far East, 1919–1939: Planning for War against Japan, Andrew Field, Frank Cass, 2004

The Battle of the River Plate: A Tactical Analysis, Alan D Zimm, in Warship 2018, John Jordan, ed., Osprey, 2018