I am in war with USA as UK (1920 start).
As USA sent almost whole fleet to Europe and I plan invasion in the Caribbean and Prime Minister wanted fleet in the Mediterranean counter Italy aggresion just before starting war with USA, my fleet was distributed between 3 regions.
Northern Europe: 8 BB, 1 BC, 2 CV, 1 CVL (148 aircrafts)
The Caribbean: 5 BB, 3 BC, 2 CV (168 aircrafts - inexperienced)
America Northeast coast: 9 BB, 2 BC, 1 CV (84 aircrafts, brand new, pilot inexperienced)
In other areas: 3 BC, 2 CVL (52 aicrafts with experienced pilots - could not get in time into Atlantic from Pacific)
However USA has sailed from Europe to Northeast coast and clash between both fleets started.
My fleet:
5 battleships of Resolution class
4 battleships of Mars class
2 battlecruisers of Admiral class
1 carrier of Furious class (84 aircrafts)
USA fleet:
15 battleships (13 of them around 40000 tons with 16" guns)
3 battlecruisers
2 ligh carriers
Resolution class battleship
designed 1932
8 battleships commissioned in 1934-1936
35000 tons as they were done as cheap as possible to counter USN superiority in number of battleships
speed 27 knots
2x4x16" guns (the solution was found as not exactly good one, as during battle 2 of 5 battleships were hit disabling both turrets together leaving them without any firepower of main guns)
14" inclined belt armour, 4.5" deck armour, 15" face turret armour (they armour was vital as at first stage of battle they dominated)
TDS lvl 4 protection (quite important and during battle no torpedo hit did significant damage)
Mars class
designed in 1913 by AI (legacy fleet)
4 ships commissioned in 1916
all ships heavily modernized in 1936
27500 tons
speed 23 knots after refit
4x2x15" guns
after modernization:
12" belt, 3" deck, 15" turret face armour (the increased deck and turret armour was vital in battle but their main task was punch as there were too small and not heavily armoured to withstand heavy shelling)
TDS lvl 1
Admiral class
designed in 1922
4 ships commissioned in 1924-1925
39800 tons (largest capital ships built till this date - 1939)
speed 30 knots
4x2x15" guns
12.5" inclined belt, 3.5" deck and 14.5" turret face armour (their armour was still reasonable even after almost 20 years and one of the 2 ships received 11 hits from 16" guns with minimal damage)
Battle started by contact reported by one of my cruisers and scout torpedo plane from HMS Glorious at same time.
My battlecruisers open fire on USN battlecruisers and starts hitting enemy ship but precise fire. Because of too many USN ships they just turn around and lure USN fleet towards mine. After some time USN battlecruisers were damaged, disengaged and has no effect on the rest of the battle. I started air strikes but my unixeprience pilots achieved minimal success (HMS Glorious was brand new carrier with uneperienced pilots).
After some time I was able to cross T to enemy main battle force. At that time firing was at distance about 18-22000 yards which was ideal for RN as their most modern capital ships were armoured quite well. After some time 2 USN battleships were severely damaged, one of them started sinking. However the second one with displacement over 40000 tons still continue to sail against my battleships. This distracted my fleet as they focused on this wreck and rest of USN fleet get a little attention. At this time I was winning as 2 USN capital ships were sinking or expect to sink. Another 2 was damaged and my fleet received only minor damage. But situation started to change as USN charged against RN and started to use her numerical superiority. Soon of my battleships was damaged to rudder leaving main battleline. The situaton of my first battle division (4 Resolution class battleships) started to be critical. At that time the second battleship divison (4 Mars class battleship) started to cover retreat of the first divison. The battlecruiser division continued north and was split from rest of the fleet for rest of the battle. But their speed helped them remain out of danger and they were able sink 2 heavily battleships trying to escape. So my situation was that 4 USN battleship was in sinking condition but the rest 11 battleships started do massive damage on my fleet. HMS Mercury (Mars class) got hit into machinery allow her only 3 knots. She was left behind hoping that enemy will focuse on her and allow my fleet to escape. However it was not possible as many of my ships were unable do more than 18 knots.
The situation started to be even worse when 2 of my modern battleships were hit in turrets disabling and destroying their all main armament. As one of Resolution class battleship has been already out of battleline situation started to be critical as only 2 Resolution battleships and 3 Mars battleships remain battleworthy and were fighting 11 USN battleships. I was able to sink another battleship but it was clear I need to run for the life.
HMS Venus (Mars class) was hit and shell penetrated her magazine, she blew up with all hands. Luckily remaining 2 Mars battleships were able to get west where only heavily damaged USN battleship was trying to escaped. But the rest of USN battleline was fighting my 2 criplled battleships. It was clear that they will be overhelmed so I ordered 2 remaining modern battleships to escape. One did do it but the other get one shell after another and stop death in water. Both cripled battleship did not made it too.
So I lost 5 battleships, 3 modern ones, 2 Mars class. However USN lost 5 battleships too, 4 of them modern around 38000-39000 tons. So at the end it was victory of Royal Navy as overall I have more battleships than USN.
note: all the time of 20s and 30s, USN had much more battleship however with construction program of Resoluton class I had 22 battleships against 21 of USN. However a lot of USN battleships were old 13" guns battleship and USN have just scrapped them just before war. From 22 battleships I have 9 old battleships, however all have 8x15" guns armament making them quite usefull, especially Mars class which all 4 ships be refitted extensively withing budget of one new battleship. This made them most costs effective weapon at start of war.
After the battle comparison of USN and RN is:
Number of ships RN/USN
First class battleships (build after 1920): 10/10
Second class battleships (heavily refitted): 2/0
Third class battleships (15" guns, no main refit): 5/0
First class battlecruisers (build after 1920): 6/7
Second class battlecruisers (13" guns): 3/1
Carriers: 5/1
Light carriers: 3/4
Carriers planes estimate: 452/119
Carriers under construction: 3/1 (RN first armoured carriers with 60 airplanes capacity, 3" armoured flight deck, 1.5" hangar sides, 2" belt, 1.5" hangar deck, TDS lvl 4)
Battlecruisers under construction: 0/2