The most important decisions are before starting a war, and there the mistakes have very different costs. Overestimating your enemy results in peace (or cold war) which basically means that you just lose out on some opportunistic conquests but underestimating your enemy results in a bloody, unexpectedly long war that can disrupt you for a decade or more—there are many nice examples of that in 20th century history.
Peace or cold war are not the only possible outcomes. Surrender is another. An example is the conquest of the Aztecs by Cortez, discussed here, here, and here. Surrender can (but need not) have disastrous consequences too.
Overestimating can be costly too. That’s why bluffing can work, in poker as in war.
Examples/articles:
Empty Fort Strategy
100 horsemen and the empty city (gated). Here are two articles summarizing the original paper: Miami SBA and ScienceDaily
The most important decisions are before starting a war, and there the mistakes have very different costs. Overestimating your enemy results in peace (or cold war) which basically means that you just lose out on some opportunistic conquests but underestimating your enemy results in a bloody, unexpectedly long war that can disrupt you for a decade or more—there are many nice examples of that in 20th century history.
Peace or cold war are not the only possible outcomes. Surrender is another. An example is the conquest of the Aztecs by Cortez, discussed here, here, and here. Surrender can (but need not) have disastrous consequences too.
Generals are not the people who decide whether or not a war gets fought but who decide over individual battles.