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When I say those words that begin with 'ad', how do I pronounce 'd' sound? Sometimes "advice" sounds to me like 'avice' and "advocay" 'avocasy'.
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Perhaps the speaker is not enunciating carefully. Even though the "d" may be pronounced quickly, it is (or should be) pronounced. (In other words, it's not like the "d" in "Wednesday", i.e., silent!)

CJ
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The stopped /d/ in an unstressed syllable will be slightly less obvious when followed by another consonant sound-- so that the /d/ of advice and adventure may be less audible than the /d/ in adamant or even advocacy, or certainly even addenda-- but as Jim says, it should be there if the speaker is enunciating clearly.