largest-deck-id.js

function factorial(n) {
  let result = BigInt(1)
  while (n > 0) {
    result *= BigInt(n)
    n--
  }
  return result
}

var deck = []
for (let i = 1; i <= 52; i++) deck.push(i)

var outstanding = 0xffffffffffffffffffffffffffffffffffffffffffffffffffffffffn
var counter = 51
var multipliers = []
var result = []

while (counter > 0) {
  var divisor = outstanding / factorial(counter)
  outstanding %= factorial(counter)
  
  multipliers.push(deck[divisor])
  deck.splice(parseInt(divisor), 1)
  counter--
}

deck = {
   1:'AC',  2:'2C',  3:'3C',  4:'4C',  5:'5C',  6:'6C',  7:'7C',  8:'8C',  9:'9C', 10:'TC', 11:'JC', 12:'QC', 13:'KC',
  14:'AD', 15:'2D', 16:'3D', 17:'4D', 18:'5D', 19:'6D', 20:'7D', 21:'8D', 22:'9D', 23:'TD', 24:'JD', 25:'QD', 26:'KD',
  27:'AH', 28:'2H', 29:'3H', 30:'4H', 31:'5H', 32:'6H', 33:'7H', 34:'8H', 35:'9H', 36:'TH', 37:'JH', 38:'QH', 39:'KH',
  40:'AS', 41:'2S', 42:'3S', 43:'4S', 44:'5S', 45:'6S', 46:'7S', 47:'8S', 48:'9S', 49:'TS', 50:'JS', 51:'QS', 52:'KS'
}

for (let i = 0; i < multipliers.length; i++) result.push(deck[multipliers[i]])

console.log(result.join(','))