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The Game Theory of Competitive Pokémon

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Strategic Element 4: Probability ManagementURL copied

The Damage FormulaURL copied

$$ \text{Damage} = \left\lfloor \left\lfloor \left\lfloor \frac{2 \times \text{Level}}{5} + 2 \right\rfloor \times \frac{A}{D} \times \text{BasePower} \div 50 + 2 \right\rfloor \times \text{Modifiers} \times \frac{r}{100} \right\rfloor $$

Where $r \sim \text{Uniform}{85, \ldots, 100}$.

The low-roll nightmare

Your attack deals just over 50% of their HP. One more hit wins the game. Next turn: the move deals just under 50%. You low-rolled. The situation is reversed.[Missing footnote: lowroll]

This is not bad luck in an isolated sense. At tournament level, players memorize exact damage ranges and avoid situations where a low roll costs them the match.