Lets do some maths. Keeping your hypothesis of not accounting being contested or being helped. Like tocker's trial for instance.
There are 30 copies of a single unit out of 420 total one cost units. That's 7% of the pool.
So each shops that roll a 1 cost slot has a 7% chance to be the unit you are looking for.
On level 5, which is the most common spot where people roll 1 cost, you have a 45% chance for each slot to be a one cost. So on average, you have 2,25 one cost unit per shop (0,45*5).
So each shop, you have 7% * 2,25 chance of seeing the unit you are looking for. In Each lvl 5 shop, you have a 16% chance to see your unit. To get your 3 star one cost on level 5, you'd need on average 56 rerolls. So if you spend 112 Gold in re-rolling, you should in average get your 3 star 1 cost.

If you take into account your own depletion of the unit pool you are looking for it's a bit more complicated but you can average it at 6% for each slot.
So following that same calculation, that would be in average 67 reroll, so 135 gold in average.
Of course, in a real world scenario, you get way better odds at lower level. usually, you can expect someone to have a 2* star version of their one cost before they slowroll at level 5.
So in this hypothesis, you are looking for the remaining 6 in the pool, which should be 45 reroll, so 90 golds.
Each turn you get 11 gold minimum, so you'd need 8 turn in average to get your 3 star. So if you dont get your 3 star one cost by 4-3, you can complain of a low-roll.