This tourney finally convinced me of why BBs are worthy units for the AxA game. The basic analysis is that 2 fighters and a carrier give you more shots, more defense, more flexibility, more threat projection than either DDs or BBs, and therefore they are the bread and butter of your navy.
This is really, really true from a pure odds viewpoint. However, the problem is that the DD and BB both play different roles. The DD is too expensive to be the “infantry of the sea”. Really, its role is to be a blocker/screener (and to counter subs). In this capacity, I recommend buying 1 per turn in both G40 and G42 as Japan and at least 1 as Germany. If you are not sure how you will use that DD during the game, it will often become obvious why when you do not have one placed well before you needed it.
The BB really shines somewhere else; when you have plenty of $$, but only limited production spaces to create new units. This is the most powerful use of the BB I have found; to advance place them late game at an MiC or when you’ve been bombed. They are pretty much worse all around than buying carriers, odds wise, on attack or defense, because buying one big BB only lets you roll the dice 1 time per round. The other big benefit is unlike a carrier, when they take a hit, there are no drawbacks.
Usually, a carrier is better than an Airbase. they costs about the same, the carrier deploys 1 fewer plane, but it allows you to mobilize your defensive power and adsorbs same number of hits as destroyers do and the same cost.
The Airbase cant’ be sunk, and it can freely use your allies’ planes, so those are benefits. the carrier, in my opinion, is almost always the better choice than the airbase (or the battleship) unless you are planning something sneaky (often, these bases are only used once per game because they really make a difference at that one time).
The Cruiser is then, even worse than all of these options. It gets shredded by subs so if you are facing even a single enemy sub it would be better to have bought or kept a single DD in just one of your key fleets than have a Cruiser anywhere on the board. A strat bomber is the same price but much, much better threat projection. The support shot is really interesting, but it is extremely easy to block, and since it only goes 1 time, it only really shines when it is supporting a lone transport who needs just 1 punch to kill the defenders. Finally, with a 3 attack 3 defense (and vulnerable to subs) it cannot usually be relied upon to defend any fleet node by itself and so you will have to stack it with other ships, which tends to negate the independent power of the cruiser.
Several times I lost a cruiser in the first casualty round in last four games, and kept a sub instead; later when the subs acted I killed 2 tipped BBs and got a first strike retal on another cruiser…