Just played two games of Regicide solo, after being inspired by the PBF here. What a nifty little game. Definitely some luck involved, as if you have a bad draw, there is not much you can do about it (barring the solo rules for Jokers).
I lost the first game after getting to the first King, but managed to win the second. Took both of the Jokers, but got a lucky draw near the end of the game, getting the King of Clubs in hand, with enough other cards to finish off the King of Hearts, revealing the final card as the King of Spades. Finished it off with the King of Clubs for the win. Definitely pays off to try to defeat the castle cards exactly so they go to the top of the tavern deck.