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  "body": "\n## Summary\n\nThe total variation distance between two probability measures is the largest difference between the probabilities they give to the same event.\nIt is half the [[total variation|EPBND51CR5]] norm of their difference.\nIt is the natural distance for questions of distinguishing two distributions: it controls the best possible success probability of a test between them.\n\n## Explanations\n\n### L1 human\n\nTwo distributions are close in total variation if no event at all has very different chances under them.\nFor two coins with heads probabilities $p$ and $q$, the distance is $\\abs{p - q}$.\nFor densities, it is half the area between the two density curves.\nA distance of $0$ means the distributions are equal, and a distance of $1$ means they live on disjoint sets.\n",
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