Put ethane out and increase the stake (2,3,4)

I believe the answer is:

up the ante

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'increase the stake' is the definition.
I know nothing about this answer so I can't tell whether this works.

'put ethane out' is the wordplay.
'out' indicates an anagram (out can mean wrong or inaccurate).
'put'+'ethane'='putethane'
'putethane' anagrammed gives 'UP THE ANTE'.

'and' acts as a link.

Can you help me to learn more?

(Other definitions for up the ante that I've seen before include "Demand more" , "Lift stakes" , "Pet tuna he used to raise poker stakes" , "Increase the stakes" , "increase risks" .)

I've seen this clue in The Daily Express.

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