I’ve been looking at the proposed solution from Krieghund: if we neglect the US attacking BC, then the odds are improved a little:
Using the numbers from vonLettowVorbeck1914 earlier on in this thread, Japan has:
16 inf, 1 mech, 6 art., 1 tank, 11 ftrs, 8 tact., 3 bombs + bombardment (2 cruisers and 2 battleships).
US has 17 inf., 1 mech, 1 art., 7 tanks, 8 fts, 1 tact., 2 AA guns. As you might recall, this battle had a 97% win ratio for Japan.
But now the US had a bonus 30 IPCs to spend. So far, the best combo I used got If the US uses the additional 30 IPCs to buy 1 ftr and 4 AAA, then the win % goes down to 67% (when 1 land unit must survive).
However, with the additional units purchased, the US now has the good option of attacking BC filled with Japanese land units only (16 inf. 4 art, 1 tank) with its units (in my case, 9 inf., 1 mech, 4 art., 2 tanks, 6 fts, 1 tact) with a 85% win chance and an average of 7 units left.
In this case, US purchases are: US1 2 art., 1 tank, 1 inf. (17 IPCs), US2 1 AA, 4 inf., 1 art., 2 fts (47 IPCs, 9 units, using the 30 bonus IPCs).
BC is critical to the strategy outlined for the Japanese in this thread, because it is in BC the air units must land after attacking WUS. If the US takes BC, even with heavy losses then the Japanese are left with few land forces and the UK, ANZAC and China dominating the south and west of the map. The US production is now 57 and they can quickly punish Japan for such a bold move. Note that without the bonus 30 IPCs the US win chance in taking back BC is 42% (using US1 purchases for US2 again). And with the Japanese airforce parked in the Aleutians, the Japanese still have a ridiculously high chance of taking WUS.
Of course, the Japanese can use this to bluff and instead take Hawaii (since the US moved everything out of there to protect WUS), but this is extremely costly in China and SE Asian territories.
Perhaps we could term this the “American Opening” for the Japanese player :-)