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You can get 4-6 hostile encounters in Sector 1. While I have no idea what the chances are to get each type of hostile encounter, in Sector 1 they seem to be mostly Rebel, Auto-Ship, or Pirate. Again I'm generalizing and assuming some even distribution, if you have 6 hostile encounters drawing from 3 categories including Pirate, the odds are ~32% that at least 3 of the 6 would be Pirate (using the Dice Probability Calculator[www.omnicalculator.com] to figure that out).
I'm making some generalizations and estimations, I think sounds rare but not astronomically improbable, and the kind of thing you might eventually ecounter if you play enough games.
There are other events that lead to fights, and I think some may even be unavoidable fights (not sure).
Rolling 18 on 3 different six-sided dice do happen. I've seen it in real life. I've also seen a triple pirate spawn in game before (although I'm pretty sure it's not 1 in 6 since many of the Slug events can only spawn as filler events). I have never seen 3 ZS pirated or otherwise ships in a row in Sector 1 or 3 ZS in any order in Sector 1 and as I said I am glad when playing the Slug B that it doesn't happen.
I had one Crystal B run where I took a first-jump store, to sell the augment and buy a shields buffer; and the next beacon was a regular fight that got me two shields, and the next five fights or so were Autos and Zoltans, culminating in a horrible Artemis + Heavy Laser Zoltan fight.
... where the Artemis hit my shields.
If I hadn't taken that first jump store, I wouldn't have gotten two shields up for that fight, and there would have been a moderate chance of dying to that Artemis into shields.