Please only round at the very end and don't round while calculating, thank you

the professional basketball$$ league's draft lottery involves the $18$ teams that had the worst$$ won$-$lost records during the year. A total of $171$ balls are placed in an urn. Each of these balls is inscribed with the name of a$$ team: $18$ have the name of the team with the worst$$ record, $17$ have the name of the team with the$$ second$-$worst record, $16$ have the name of the team with the$$ third$-$worst record, and so on$($with $1$ ball having the name of the team with the $18$ th$-$worst $$record$).$ A ball is then chosen at$$ random, and the team whose name is on the ball is given the first pick in the draft of players about to enter the league. Another ball is then$$ chosen, and if it$$ "belongs" to a team different from the one that received the first draft$$ pick, then the team to which it belongs receives the second draft pick.$($If the ball belongs to the team receiving the first$$ pick, then it is discarded and another one is$$ chosen; this continues until the ball of another team is$$ chosen.$)$ Finally, another ball is$$ chosen, and the team named on the ball$($provided that it is different from the previous two$$ teams$)$ receives the third draft pick. The remaining draft picks $4$ through $18$ are then awarded to the $15$ teams that did not$$ "win the$$ lottery," in inverse order of their$$ won$-$lost records. For$$ instance, if the team with the worst record did not receive any of the $3$ lottery$$ picks, then that team would receive the fourth draft pick.