Choosing a crystal for a long-running synchronizing application between two microcontrollers
Garden-variety crystals only have an initial accuracy on the order of 100 ppm, before you even start to consider thermal and voltage effects. You can spend more money and push things down to on the order of 10 ppm, or you can spend a LOT more money for temperature compensated or even ovenized crystals to do even better than that.

Two 22.1184 MHz crystals whose frequencies differ by exactly 100 ppm will have a phase difference of 2211.84 whole cycles after just one second. Crystals 1 ppm apart will have drifted by 22.1184 cycles in that period.

So no, you can't rely on "blind" synchronization for any meaningful length of time. You need to design your system so that the subsystems remain in sync despite the inaccuracies of their individual clocks. Basically, they need to communicate with each other in some way on a continual basis.



Of course, it isn't at all clear why a laser tag system would require that kind of global synchronization in the first place. Sounds like some sort of X-Y problem. What problem does that sort of approach solve for you?