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So, I had a Iron Crown against a damaged Heatran. I used Calm Mind, and the Heatran used Lava Plume, crit, and Burned. Then the Heatran got a QUADRUPLE Protect, which allowed the burn to kill me. Just how unlucky was I?

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If you already successfully used 3 protects, the chance of the fourth one succeeding is 1/27. The chance of all 4 succeeding is 1 * 1/3 * 1/9 * 1/27 = 1/729.
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Thanks for resuming my typical luck!