You’ll find though that people will commit 2 Inf on the retake whether you have 1 or 2 Inf there.
And the extra Inf does not net you the full 2 IPCs of the territory. It boosts your chance by 30-40% maybe. So that increase is worth 1/3 of 2 IPCs, or 2/3s of an IPC, not 2 IPCs. So committing the extra 3 IPC unit to “ensure” taking a 2 IPC territory only brings a return of about 1.7 IPCs.
Run it on frood.net and see the avg. IPC losses for both sides, you’ll see. I like to trade 1 more Inf preserved over against an additional 1/3 chance to capture a territory. Unless the territory has tactical importance of course. But if it’s just for the money, I’d rather risk a 39% chance of not taking the territory than send an extra front-line unit to certain death.
I know the feeling of kicking myself when I fail to take a territory (“Why didn’t I send 2 Inf?”) but then I console myself with the fact that I saved one more Inf in my main stack. That’s 3 IPCs not only in the bank, but right on the front line, and in itself is worth more than the 3 IPCs gained from taking the territory PLUS the avg. 1 IPC damage it will inflict on defense.
It’s counter-intuitive though, not many people understand it.
There are however reasons to put more units in: if you have the unit lead, and want to whittle down both sides so your lead becomes proportionally larger, or if you want to tie up enemy air units to distract them from other targets.
I remembered why I do like to take territories, so let me expand on the reasons you hint at for wanting to take a territory. First, you are not sending your inf to certain death, bad luck can happen to the enemy too, they might send 2 inf 2 figs and come out with 2 figs. Second, if you console yourself with “well I saved an inf” you have to realize you saved the enemy an inf too, if not 2 inf, since he only has to send 1 inf there to prevent a free taking. Third, some territories are worth more than 2 IPCs.
Fourth and best, sometimes you don’t want to allow the enemies after you to be able to reinforce that area with figs. You can’t land figs in areas you just captured or cleared, but if allow for 39% of not taking a territory that could really mean the next turn you see 10+ figs from the powers that come after you land there to reinforce his buddies. I wouldn’t be too happy if say I were Russia and didn’t take Ukraine, then suddenly wtf is this 6 German figs land there along 6 Japanese fighters with the pile of inf? Or the opposite if I were Germany and didn’t take Ukraine, now UK has 6 figs there, compounded with a pile of 20 Russian inf and 3 figs and America’s figs. Or if I were Russia and didn’t Novo, now I see 8 inf + 6 fighters on defense there. All because I didn’t take a territory. It is usually difficult to reinforce an ally’s front territory with fighters due to the limitations on fighters landing and also because sometimes you simply don’t have land forces to clear the area for your buddies, but if the enemy doesn’t take the territory then it becomes very possible.
Your math is good and pure and I got it when I saw the concept, and I would definitely do it (and have had it done to me) in small consequence areas, but one simply must be think about which is the better of the options at the time, not choose to use one theory in all situations. Using 1 inf + airforce is more economical in terms of pure math for some territories, but there are other very important considerations to keep in mind.
