What are the chances of Endure working three times in a row?

Question

That Falinks did not want to die...

Answer 1

Successfully using Protect, Detect, Endure, Wide Guard, Quick Guard, Spiky Shield, King's Shield, Baneful Bunker, Obstruct, or Max Guard consecutively now divides the chance of success of Protect, Detect, Endure, Spiky Shield, King's Shield, Baneful Bunker, Obstruct, and Max Guard by 3 for each consecutive use, with a minimum (1/3)^6 (1/729 or ~0.1%) chance.

The first Endure is guaranteed to work.

The second Endure has a 1/3 chance to work. You have a 1/3 chance to get this far.

The third Endure has 1/3 of 1/3 chance to work, which is 1/9.

1/3 x 1/9 = 1/27.

The Falinks you encountered had a 1/27 chance of using Endure three times in a row.

Source

Comments

Thanks.

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25% =/= 1/8. It should be 1 x 1/2 x 1/2 = 1/4.

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That is for the chance of the third Endure happening. Not for the second and third Endure to happen in succession. Because the second is not guaranteed, and the question asks what are the chances of Endure happening in succession.

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Oh crap you're right. I thought 3rd one also has a 1/2 chance of happening.

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But that's not how endure works in gen 8. The bulbapedia page you linked says: From
Generation VI onwards "Successfully using Protect, Detect, Endure, Wide Guard, Quick Guard, Spiky Shield, King's Shield, Baneful Bunker, Obstruct, or Max Guard consecutively now divides the chance of success of Protect, Detect, Endure, Spiky Shield, King's Shield, Baneful Bunker, Obstruct, and Max Guard by 3 for each consecutive use, with a minimum (1/3)^6 (1/729 or ~0.1%) chance."

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Now, that's what I thought it was. I didn't scroll down enough.