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General Troop Allocation Advice

Let’s say you’re in a situation where you have two separate fronts. One front has 10 enemy units on it, the other has 4. You have 16 troops to allocate to either border. Where should you put them?

Keeping symmetry would dictate that you should put 11 troops on one front, and 5 troops on the other. However, it must be remembered that when you have large number of troops, the distribution of possible outcomes is much less dependent upon pure chance. So you want to maximize the buffer you have in the battle with fewer troops.

For example, if you flip a coin 4 times, the odds of getting all heads or all tails is (1/2)^4 or 1/16. If you flip a coin 4,000,000 times, odds are mathematically impossible that you’ll get all heads or all tails.

So, back to the troop allocation. It’s better to put both of your extra troops on the border that only has 4 enemy troops (not considering what the enemy could do on their next turn). This is because to maximize the chance that you’ll win both battles, you’re better off having both of your “extra” units (units above the 14 that your opponent has) in the smaller battle. So you should allocate all 10 to face off the opponent’s 10, but 6 to face off the opponent’s 4.

This assumes that your main goal is to defend both fronts equally.

Furthermore, this prevents your opponent on their next turn when they have some additional troops to allocate from putting them on the border with the fewest troops and overwhelming your forces. For instance, if your opponent had 3 units to allocate on their next turn and is interested in “cracking” one of your 2 borders, their best chance is to dump them all on the front that would give them the greatest statistical advantage. In this case, they would put all 3 units on the front that only had 4 units initially, giving them either a 7-6 or 7-5 advantage (depending on what you had allocated on your turn), as opposed to putting them on the 10-10 unit border, which would give them a 13-10 advantage.

This is similar to an argument about nuclear proliferation. If you have 1 nuke, and your opponent builds 2, then they have a 100% advantage over you. If you have 1,000,000 nukes, and your opponent builds one more, then they only have a .0001% advantage over you. Now don’t you feel safer about widespread nuclear proliferation?