Strategy for the game: I Doubt It, also known as cheat, B.S
Cheat! without bluffing is entirely deterministic
In the variant you've described (assuming I've understood it correctly), all the Aces will be played, then all the 2s, then the 3s, etc.  In theory, someone could withhold playing a card during the proper round, but there is zero benefit to doing so, and an enormous penalty (if you do so and nobody else does, you're guaranteed to lose), so in practice nobody would.  This means that the person who wins will be the one who has the lowest high card.  (ie, if my highest card is a Queen and your highest card is a Jack, then you will beat me.)
The strategy in Cheat is entirely in knowing when to bluff or call bluffs in order to minimize your chance of getting new cards while maximizing the chance of other players calling you out mistakenly, and using the bluffs to get rid of the cards that wouldn't be played for a long bit of time.