I think the “$2 territory means a $4 swing” idea is balanced by the fact that even if you lose an entire continent, you don’t lose it all at once. In other words, let’s say Britain “loses” Africa. Does that mean that on Italy’s first turn, Italy literally sweeps down through Egypt into French West Africa and South Africa? Of course not.
Suppose Britain sends zero reinforcements to Africa, and America temporarily drops off one infantry and one artillery to Morocco on turn 2, which you can do at zero cost with your starting transport, kind of leaving them there to rest on your way to France or Italy or whereever. Suppose Italy unloads two transports (one into Transjordan, then one into Egypt), and Germany unloads one transport (to Egypt). Japan snaps up Madagascar on turn 3 but otherwise minds its own business.
Let’s say the Axis win all their battles effortlessly and steamroll through Africa at maximum speed, leaving a modest garrison in Libya. Here’s how the income might look.
Turn 1 – $5 for Axis (Morocco, Libya, Egypt, TJ), and $10 for Allies (TJ, Sudan, Ethiopia, Congo, FEA, FWA, Rhodesia, Madagascar, South Africa)
Turn 2 – $8 for Axis (Morocco, Libya, Egypt, TJ, Sudan, Ethiopia, FEA) and $9 for Allies (Morocco, Ethiopia, FEA, FWA, Congo, Rhodesia, Madagascar, South Africa)
Turn 3 – $11 for Axis (Libya, Egypt, TJ, Sudan, Ethiopia, FEA, FWA, Congo, Rhodesia, Madagascar) and $4 for Allies (Morocco, Rhodesia, South Africa
Turn 4 – $13 for Axis (Libya, Egypt, TJ, Sudan, Ethiopia, FEA, FWA, Congo, Rhodesia, Madagascar, South Africa) and $3 for Allies (South Africa, Morocco)
Turn 5 – $13 for Axis, $1 for Allies (Morocco)
Total income over five turns is $50 for Axis, $27 for Allies.
Now let’s flip the scenario around – suppose the Axis send the same three transports’ worth of forces to Africa, but this time the Allies bid one infantry in Egypt, build factories in South Africa and Brazil, send the entire British air force to Africa, have the Americans launch Operation Torch on turn 1 – basically the Allies just make Africa their absolute top priority. Assume both sides get average dice rolls. Japanese come on turn 3 to snipe Madagascar again.
Turn 1 – $5 for Axis (Morocco, Libya, Egypt, TJ), and $11 for Allies (Morocco, TJ, Sudan, Ethiopia, Congo, FEA, FWA, Rhodesia, Madagascar, South Africa)
Turn 2 – $5 for Axis (Libya, Egypt, TJ, Sudan), and $11 for Allies (Morocco, Libya, Sudan, Ethiopia, Congo, FEA, FWA, Rhodesia, Madagascar, South Africa)
Turn 3 – $7 for Axis (Egypt, TJ, Sudan, FEA, Ethiopia, Madagascar), and $10 for Allies (Morocco, Libya, Egypt, Ethiopia, Congo, FWA, Rhodesia, South Africa)
Turn 4 – $4 for Axis (TJ, FEA, Ethiopia, Madagascar), and $11 for Allies (Morocco, Libya, Egypt, Sudan, Congo, FWA, FEA, Rhodesia, South Africa)
Turn 5 – $2 for Axis (Ethiopia, Madagascar) and $12 for Allies (Morocco, Libya, Egypt, Sudan, FWA, FEA, Ethiopia, Congo, Rhodesia, South Africa)
Totals this time are $23 for Axis, $55 for Allies.
I think these are fairly extreme scenarios – in most games, making a big investment in Africa would swing Africa a little more slowly or a little less completely. But even in this extreme scenario, the total swing over 5 turns is 45 IPCs. It’s possible my math is wrong, but I’m pretty confident that you shouldn’t double that figure – that 45-IPC budget already includes the gains you can make as the Allies and the losses you can inflict on the Axis by investing in Africa.
But it really doesn’t take that much to spend 45 IPCs – if you build one factory in South Africa on turn 1 and fill it with 2 tanks on turns 2, 3, and 4, and 5, that’s 15 + 10 + 10 + 10 = 45. If you send any fighters or lose any men during Operation Torch or land any additional transports (let alone start going crazy with a Brazilian IC or a dedicated African shuck-shuck), you’re now over-budget.
I expect people will argue that (1) national objectives help increase the budget, and (2) you can make up any shortfalls in the budget by continuing to hold Africa after turn 5. Here’s my counter-arguments:
Italy’s NOs require it to hold Morocco and Gibraltar. The Anglos can and should rapidly take those territories just as a side effect of establishing Atlantic naval supremacy – you don’t need to be running any particular African campaign to be able and willing to retake those territories. Similarly, Britain’s NOs require it to hold Egypt and Australia and South Africa all at once – if you’re fighting hard in north Africa and also working on some kind of naval buildup in the Atlantic, then you’re going to lose Australia to Japan before you can retake Egypt – if you try to hold Egypt and South Africa and Australia in the opening, you’re going to run out of IPCs for the European campaign, and Germany will turn into a monster.
Income after turn 5 can be useful as a kind of ‘tiebreaker’ to see who would win the game hours and hours down the road if you’re in a tight stalemate, but it’s not going to help you seize a capital. Let’s say Britain is trying to reinforce Moscow with income collected from Africa on turn 6. If you collect it on turn 6, you can build fighters in London on turn 7, move them to Scandinavia on turn 8, and move them to Moscow on turn 9 – after Germany and Japan have already made their turn 9 attacks. So the income you collect on turn 6 is useful to stop a turn-10 German attack on Moscow. 90% of the time, a capital has already fallen before turn 10, and your reinforcements will be too late.
There are obviously exceptions – if Germany holds Africa and the Allies are laying siege to Berlin, then Germany’s African IPCs can help drop infantry right into Berlin. But I think these are pretty rare cases – usually one nation on a team gets rich and another nation on that team has to worry about defending its capital, if for no other reason than that smart players will make a point of focusing on the poorest (and therefore weakest) capital to attack.