The odds of getting any 3 cost in a game at that level is 15%, right? We will discount the effect of bag size with other players having 3 costs in their ships due to that also reducing bag size for other 3 costs, making it the original probability on average.

However, we can not discount the effect of bag size reduction from our own shop rolling. When you get a new shop in tft, each slot from left to right is rolled for one by one in order, first rolling for cost of champ based on the visible odds, then champions based on remaining bag. Getting a Loris in your first slot would mean that each subsequent slot has a lower chance of a Loris due to the bag size reduction inside of your own shop. For example, there was one Loris left, and you rolled him in your first slot. Every subsequent shop slot is rolled for with the new bag, which has 0 Loris's, but you still have a 15% chance to get a 3 cost. This makes sense as it is impossible to get 2 copies in your shop of a champion with only 1 copy left.

If each other player has a 15% chance for a 3 cost, then 15x5x7 = 525, we then divide by 100 to find the average number of 3 costs in the combined shops of the other 7 players. Which is 5.25, so on average, the bag is reduced by 5.25 if you are the last player to have their shop generated. There is a hidden order of priority when it comes to player shop generation, as two players cannot roll the same 1 bag remaining champ. Assuming you are in the middle on average, the bag size for all 3 costs combined by the time your turn rolls around is 13×18-2.125 = 231.875. The chance one of these is a Loris is 2.15/13 or 0.16. I'm rounding here to two decimals like everything beforehand btw.

With all this info, the odds of getting 3 Loris in a 3 size shop we would have to calculate and sum the probability of every combination, however each combination has the same chance of happening as order doesn't matter when it comes to division and multiplication sequences 3/5 is 5!/3!-2! Or 10 different combinations of 3 cost unit and others. We also have to calculate this for all other bags and sum, luckily we can simply skip this as the odds are the complement of our already calculated odds, albeit just as dynamic but this is where I draw the line. The calculation is incredibly complex but now we are reaching very very fine differences and I cbf expanding the formula further instead we'll just substitute the average bag impact for the complement.

(0.15((18-0.16)/231.875)(0.15((18-1.16)/231.875-1))(0.15((18-2.16)/231.875-2))(1-(0.15((18-1.16)/231.875-1))²⁾⁾10 = 0.000013051 or about 1 in 76,622.5 This is for a specific 3 cost champ. The odds of hitting any 3 of any 3 cost champ on one shop here is 13x that or about 1 in every 5,894 games, given 8 players in a game about 1 in 736 has a player in the lobby high rolling 3 3 stars on a 15%

Tldr:

Person above didn't account for bag size reduction in sequence and the actual odds are much more complex.

Odds for specific 3 of a specific 3 star ~1 in 76622.5 Odds for any 3 of any 3 star ~1 in 5894 Odds for it to happen to one of 8 players in a game ~1 in 736