In Particles addon it should be possible to set creation (not only simulation) speed randomiser when the game is already running.
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wouldn't it be the same thing if you created the particle, and set the simulation speed in the same event?
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.