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I have been playing Pokémon Sword and I am hunting a shiny litwick through Masuda breeding and am not sure if it’s ok to close the software after saving your progress. I think I might reset my built up chances of getting shiny litwick and have to start over again

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I think you're misunderstanding how Masuda Method works. Each Egg has an individual chance to be a shiny -- there are no chains, no combos, nothing that will boost an Egg's chance of being shiny. Therefore, it's perfectly fine for you to close your game -- your "built up chances" won't reset, as they never existed in the first place.

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Hope I helped!

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Thanks for the help! I was taking the B(n,p) thing into consideration, and that’s what made me think that and get lost
No problem! Please click the green checkmark in the top right of my answer if it helped.