Most budgets do not fail because of bad math, they fail because they are built like restrictive diets, all-or-nothing systems that feel punishing and eventually get abandoned after one bad week.
Behavioral research suggests that flexible systems with some built-in slack tend to last longer than rigid ones. A budget with zero room for spontaneity is more likely to trigger a rebound of overspending once willpower runs out, similar to how strict diets often lead to overeating later.
Building in a guilt-free spending category, even a small one, tends to make the entire system more sustainable. A budget you can actually stick with beats a perfect one you abandon in three weeks. This is general education only.