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I think you've muddled up the cause and effect, possibly not helped by our tendency to misuse particle & parcel terms.
Think about the basics.
Turbulence is random and it's effect will change with time. Ie the eddies form, move and break up etc. To avoid modelling every eddy we can use a RANS approach. So we now have a single (hopefully) solution with modelled values for the turbulence field.
We now add particles. They follow the flow. Good, but the flow should vary due to turbulence: we're modelling that as a constant value because we're using RANS so there's no variation. If we use Stochastic tries, we add a random kick to particles based on the turbulence field. As it's random and we often want a meaningful particle distribution we need lots of tries so the kick is random to each track in each cell and that probably evens out with sufficient tries. One try is not statistically meaningful: 100 tries is probably excessive.