PokéBase - Pokémon Q&A
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So I was on Showdown when I got hit by some bad rng. The opponent landed a hurricane (without rain/no guard) which then confused me. Right after that they hit me with a heat wave which burned me, after which I hit myself in confusion twice. What are the odds of this happenng?

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Hurricane has 70% accuracy without rain, and a 30% chance to confuse the opponent if it hits. Heat Wave has a 90% chance to hit and a 10% chance to burn if it hits. While confused, a Pokemon has a 30% chance to hit itself per turn.

So that's:
7/10 * 3/10 * 9/10 * 1/10 * 3/10 * 3/10 = 1,701/1,000,000, or approximately 1/588 or a 0.1701% chance.

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:O Thats...  rare man...