I tried:
UPDATE giveaways SET winner = \'1\' WHERE ID = (SELECT MAX(ID) FROM giveaways)
But it gives:
#1093 - Yo
This is because your update could be cyclical... what if updating that record causes something to happen which made the WHERE condition FALSE? You know that isn't the case, but the engine doesn't. There also could be opposing locks on the table in the operation.
I would think you could do it like this (untested):
UPDATE
giveaways
SET
winner = '1'
ORDER BY
id DESC
LIMIT 1
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