a plurality of gaming machines, wherein each gaming machine can be in an active state or an inactive state, each gaming machine is associated with an accumulated bonus event pool which is based on any wagers placed at said gaming machine, and each gaming machine includes:

at least one processor;

at least one input device;

at least one display device; and

at least one memory device which stores a plurality of instructions, which when executed by the at least one processor, cause the at least one processor to operate with the at least one display device and the at least one input device to enable a player to play a primary game upon a wager; and

a controller configured to communicate with each of the gaming machines and programmed to:

(a) determine whether a bonus event is triggered; and

(b) if the bonus event is triggered:

(i) designate one of the gaming machines as a triggering gaming machine and each of the remaining gaming machines in the gaming system as auxiliary gaming machines; and

(ii) cause a bonus event participation gaming sequence to be provided for the designated triggering gaming machine and each of any of the designated auxiliary gaming machines in the active state, wherein:

(A) the bonus event participation gaming sequences provided for any of the designated auxiliary gaming machines in the active state determines which of any of the designated auxiliary gaming machines in the active state will participate in the triggered bonus event, for each designated auxiliary gaming machine in the active state,

(B) a probability of success in the bonus event participation gaming sequence is based, at least in part, on the accumulated bonus event pool of said gaming machine, and

(C) different accumulated bonus event pools greater than zero have different probabilities of success.