OK, I changed the hose. The old one wasn't as bad as I thought.. I think the real culprit might have been a sticky idle control valve. Yesterday I cleaned it out with carb cleaner and lubed it with WD-40. The car starts right up, idles fine and takes off without hesitation after the first start of the day. I'll know for sure whether or not it's "fixed" after a few days and I'll post another update.

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2000 c280 Sport (looks like an upgrade, feels like a downgrade)
1991 190e 2.3 (sold)