Blackjack is a common noun, along with golf, chess, football, and darts. Therefore, "blackjack" is not capitalized. It is not capitalized even when referring to the blackjack hand, the ace of spades paired with a jack of spades or the jack of clubs.
All proposed revisions are correct.
Any well established, modern dictionary may be used as an authoritative guide as to whether a noun is proper or not.
Some nouns, particularly those based on brand names and the names of people, evolve in classification from proper noun to common noun. So, for relatively new words, it is possible for current dictionaries to be out of step with each other at any one time. But generally, you will find unanimous agreement in most cases of noun classification. Words recognized as being in transition are often flagged with the remark "often cap." or "freq. cap."
Some nouns are capitalized only for certain usages. All modern dictionaries flag such entries with a similar remark, usually "cap."