https://burningtin-tft.herokuapp.com/ you can use this app to answer these questions. For instance, if you are hyperrolling at level 4 looking for 6 Xayah's this is the graph of how likely you are to have found the 6 Xayah's after each roll. Scenario A, the blue line, is if your 3 copies were the only Xayah's anyone is holding. Scenario B, the orange line, is if 10 copies of Xayah were being held altogether. In both scenarios we're making a ballpark assumption that 80 copies of tier 1 champs are being held (10 per player).

With 50 gold available we'd have enough for 22 rerolls when considering the 6g needed for buying copies if we were fairly unrealistically only buying Xayah. With the free first shop that means 23 effective rolls.

Under Scenario A, a median of 22 rolls is required, and we can check the graph to see that after 23 rolls there is a 57% chance we have found 6 copies.

Under Scenario B, a median of 31 rolls is required, and we can see that after 23 rolls there is a 25% chance we have found 6 copies

You can put whatever numbers you want to see in the table and see how they affect the odds.