What does this idiom mean: "I'll eat my hat"?

[rumba]

Test No. incompl/advan-41 "Talking through his hat", question 6

I don't think she stands a chance in the election and if she does win, I'll ......... my hat.

(a) bite
(b) consume
(c) eat
(d) chew

Test No. incompl/advan-41 "Talking through his hat", answer 6

I don't think she stands a chance in the election and if she does win, I'll eat my hat.

Correct answer: (c) eat

Your answer was: incorrect
I don't think she stands a chance in the election and if she does win, I'll chew my hat.
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What does it mean?
I'll eat my hat

[Torsten]

I'll eat my hat if I'm wrong is a promise to do something impossible if you are wrong. This means, you declare absolute confidence in the correctness of your judgement.
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Test Of English for International Communication
TOEIC Preparation & TOEIC Vocabulary

[Guest]

[Alan]

Hi,

We use this expression either to express great surprise:

Well, I'll eat my hat!

or

We use it when we want to indicate that something will never happen:

If he wins the lottery, I'll eat my hat.

Alan
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English as a Second Language
You can read my ESL story Phrasal Verbs/run