Question: In Tamil, there is a proverb that translates to something like this:

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> A tiger will not eat grass, no matter how hungry it is.
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It essentially is used to describe a situation in which no matter how dire of a situation you're in, you will not use your last resort. In this case, it's used to describe that even if a tiger is starving to death, it won't eat grass (because it's a carnivore). I really couldn't find any sort of English idiom that can accurately describe this Tamil proverb. **Please post all related English idioms as answers, even if they are only partially accurate.**

A possible situation I might use this in: Alice was a hardworking student who believed that she could receive an A in her class without using extra credit. 

I might use the idiom to describe Alice in this situation, as she refuses to use her last resort (extra credit), no matter desperate she is (because she believes she can earn an A without extra credit.)

Answer: 
**"a tiger won't change his stripes"** is a saying, with some variations like: "a **tiger/leopard/zebra** can't change its stripes to spots".

* a person's character, especially if it is bad, will not change.
* certain personal traits are unchangeable.

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> It means that [a person's character, especially if it is bad, will not change, even if they pretend it has changed.](http://idioms.thefreedictionary.com/A+leopard+can%27t+change+its+spots)
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> * "I doubt very much that marriage will change Chris for the better. A leopard doesn't change its spots."
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**EDIT** - If you mean that Alice has an advantage that other people don't know about, you may say that **"she keeps an extra ace up her sleeve"** or **"...a card up her sleeve"**. (keeping it back until the time is right)
If you are willing to loosen your requirement from *will not use* slightly, consider the phrase *Mexican standoff*:

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> A **Mexican standoff** is a confrontation between two or more parties in which no participant can proceed or retreat without being exposed to danger. As a result, all participants need to maintain the strategic tension, which remains unresolved until some outside event makes it possible to resolve it.
>  [- wikipedia](https://en.wikipedia.org/wiki/Mexican_standoff)
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Here, the idea is that although there may be a weapon of last resort, using it would lead to a situation no better than not using it. Hence it is not used. A large-scale example of such a situation was the [Cold War](https://en.wikipedia.org/wiki/Cold_War), where although the Western Bloc and Eastern Bloc both possessed weapons that could be classified as *weapons of last resort*, neither side used them.