Missing MTG arena packs to complete rares

#!/bin/bash

# Calculate the number of packs to open to complete rares for a set
# Most recent sets have 53 rares. As a rule of thumb,
# 53 * 4 * (1-completion%) * 1.2 is the number of packs you want to have.
# The 1.2 accounts for mythic rares and wildcard upgrades.
ceil() {
echo "define ceil (x) {if (x<0) {return x/1} \
      else {if (scale(x)==0) {return x} \
      else {return x/1 + 1 }}} ; ceil($1)" | bc
}

packs=$( echo "53 * 4 * (1 - $1/100)" | bc -l )
packs=$(ceil $packs 0)
echo "$packs packs missing"