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The rules state Any player with more than 7 resource cards must chose and discard half of them. SO, does this mean that anyone with eight or more cards discard half or does it mean that anyone with 7 ore more cards discard half?

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    "Seven or more" and "more than seven" are trivially distinct and separate statements. – Nij Dec 27 '16 at 3:01
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If x is the number of resource cards in your hand, and x is greater than 7, discard half of them. If x is equal too or less than seven, do nothing.

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The rules state Any player with more than 7 resource cards must chose and discard half of them. SO, does this mean that anyone with eight or more cards discard half or does it mean that anyone with 7 ore more cards discard half?

You actually answered your own question when you asked the question. As you said:

The rules state Any player with > 7 resource cards...

But then, in the very next sentence you asked whether:

... anyone with >= 7 cards discard half?

"7 or more" is another way of saying "greater than or equal to 7".

Here's how it works:

  • If you have 8 cards you must discard 4 and keep 4.
  • If you have 9 cards, you must discard 4 and keep 5 (With an odd number of cards the advantage always goes to the player).

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