Switch 16 (2001)

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Ages 7 and up, with nicely made and sturdy parts (the game, not the adults).

"Be the first player to discard the 16th card from the deck they control by rolling the numbers needed on the dice."

Each player has a card deck numbered 1-16. During your turn you roll 3 to 5 six-sided dice and can remove the top and subsequent cards if some combination of the dice add up to their number. You can choose to roll more than once, but a significant penalty is applied if you then can't remove a card. In addition to the number dice, another die is rolled that allows you to block other players or even switch decks with them.

You win if you're the first to remove all your cards.