This is an 'adverb infinitive'. It is not a participle, either present of past, because it doesn't end in -ing. And it is not an 'adjective infinitive' since its meaning is adverbial, 'you must capture or trap the other king' IN ORDER 'to win a game of chess'. Adjective has to modify a noun, which isn't the case in this sentence.
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The coordinating conjunction in the sentence is NOR.
There are only seven coordinating conjunctions. Remember the terms FAN BOYS in relation to coordinating conjunctions.
F - for
A - and
N - nor
B - but
O - or
Y - yet
S - so
Coordinating conjunctions connect words, phrases, and clauses. Giving equal emphasis on two main clauses.
Here are the patterns for using coordinating conjunctions:
1) connecting two main clauses
main clause + coordinating conjunction + main clause
2) connecting two items
item + coordinating conjunction + item
3) connecting three or more items in a series
item + item + coordinating conjunction + item
I don’t think you need a comma after old
