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It happened this morning...I was only at 5 and I was really confused myself as to how I got this lucky...oh well a shiny Pokemon is a shiny Pokemon. But I'd like to know the exact chances of this happening - I know it was improved from the nearly 1/8200.

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What game were you chaining on?
Anyways with the DexNav after each encounter your chance is upped but sometimes you can get really lucky, so I dont really know if there is an EXACT chance
once I got a Pokemon on my 2nd on PokeRadar
I KNEW there was a tag I was's in OR.

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Best answer

PokeMath time!

Here's the formula for chaining a shiny Pokemon:

… where n is the number of encounters that you have made within the chain. In this case we consider it as 5.

And after some math, I got this to be a 0.01541456% (approx) chance of finding a shiny. That's a really low chance, so you got very lucky indeed!

Source: Smogon, the walnut between my ears.

Hope I helped!

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Can you make an approximate fraction for me? (Any other answers with this will get a vote)
4849⁄31457280 is the least fractional form. It doesn't reduce any further. It just looked more intimidating to me, so I avoided it.
Does that mean it goes up to 100 percent after 41 chains? (I suck at Math)
Oh right I think I forgot to mention that after 40, the value of 'n' does not go any higher. Meaning 40 is the cap, and 41 would still be counted as 40 (otherwise the denominator will become zero and the world would explode xD). And the chance for getting a shiny at 40 is *ahem* 0.50151824951172% , approximately 1 out of 20 pokemon.