I have some tips to share:
1. In two player mode: To get rid of the low cards effectively and you knew which cards the other player have, play the cards in chain mode. For example you have 3, 4, 5, 6, 7 etc. Start with 4 later 6 or 3 later 5. If the other player collect the playing pile at the end (lowest is 4), put 3 and let see if the other player is willing to put 4 and you can just put the cards in chain if the other player is not using a counter for this.
2. If the playing cards pile is not that tall and the cards have high values like 8 or upper (the higher ranked cards, the thinner pile and the earlier game is better) and it might be reasonable to collect them.
3. And of course, manipulate the other player's choice of cards. Isn't it the main strategy of Palace?
There is a lot of useful strategies for Palace.
What is your strategies?