Sorry to resurrect an old thread but I’ve been exploring purchase combinations and offensive probabilities by IPC spent.
Using 24 IPC as an upper bound (this is divisible by both 3 and 4, more on that later), you can buy 8 Inf or 6 Artillery. In pure attack odds, the probably mass functions appear as so:
With 8 infantry dice rolls, you have about ~25% chance of no hits, ~35% chance of one hit, ~25% of two hits, ~10% of three hits, and so on. On average, you’ll hit a little better than once per 8x rolls.
With 6 artillery dice rolls, you’ll hit 1 about ~25% of the time, ~35% chance of two hits, ~22.5% chance of three hits, and almost 10% chance of 4 hits! Clearly superior to Infantry alone.
You can get the same overall probability as 6 artillery for only 21 IPC by buying 3 Infantry + 3 Artillery.
This figure is showing the per-unit type group roll probabilities, not global probability per round of combat but you can figure in your head that 6 rolls for 2 attack is going to have the same probability as 6 rolls for two attack.
So, what would I purchase and use, when, and why? If your intention is to defend only, then Infantry is clearly superior as you can get 8 hp for 24 IPC or 7 hp for 21 IPC. If there is any possibility of attacking, then try to split your purchases so that your group has even amounts of Infantry and Artillery. Lastly, if you have an odd number of IPC that is not equally divisible by 3 and 4, then weight your purchases towards trying to even out Artillery with Infantry. If you already have Infantry on the board in a position to attack, then for 1 additional IPC you are buying the same probability that the 3 IPC Infantry purchase would grant to you.
In my play, only the Russian player has had to worry about these things. Once you get enough IPC you should not need to worry about optimizing absolutely every purchase. With those 24 IPC, the German player will be buying 4 tanks, with a 25% of 3 hits. Ouch!
Hope this helps