In Particles addon it should be possible to set creation (not only simulation) speed randomiser when the game is already running.
wouldn't it be the same thing if you created the particle, and set the simulation speed in the same event?
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I already tried setting sim. speed rand. to 1000, then, after one tick, to 0, but it gives non-linear spread, because some particles are randomized more than once, and some aren't randomized at all. It's chaotic.