This rule can be used with any Pig Tickler variant, but it must be used with Team Pig Tickler.
Instead of each player taking a turn in a pre-arranged order, a deck of initiative cards is used. A regular deck of cards can be used, with each lancer associated with a specific card (such as the Ace of Hearts or the Queen of Spades). Since decks of cards are cheap, you could buy one specifically for the game and write the player's name on the card in indelible ink. A deck made up of blank business cards could also be used.
Each lancer gets 2 cards. The deck is shuffled and the cards are turned over one at a time. The card indicates the lancer that is activated that turn.
Whenever the rules state that something happens "next turn", the "next turn" occurs the next time a lancer's card turns up.
Design Notes
This rule adds some randomness to the game. Players often place the pig and/or the stoker in order to maximize the difficulty for the next player. This strategy is reduced with an initiative card system.
The disadvantages of this system are the lack of planning that it produces due to the random picking of players, and the gaps that sometimes appear between player activations. The advantage of this system is the tension it creates.