Trying to understand a prize distribution from a Reddit comment: https://www.reddit.com/r/mtgjudge/comments/6y1e9u/simple_flat_prize_structure_at_fnm_leads_to_bad/dmkf3io/

packs_given.py

#Packs = ((points - rounds) - (rounds - 3))
#Take one point off for a perfect record.

def points(record):
	"""Give the number of points a certain record is worth."""
	w, l, d = record[:3]
	return 3 * w + 1 * d

def packs_awarded(record, rounds):
	"""Calculate the number of packs to give someone with a given record."""
	total = points(record) - 2 * rounds + 3
	return total - 1 if points(record) == 3 * rounds else max(0, total)

def nice_show(record):
	"""Display a record in w-l-d format."""
	w, l, d = record[:3]
	return str(w) + '-' + str(l) + '-' + str(d)
	
def show_pack_distribution(rounds):
	"""Show how many packs each possible record gets. No ties or drops."""
	possible_records = [(i, rounds - i, 0) for i in range(rounds + 1)]
	for records in possible_records:
		print '*', nice_show(records), 'gets', packs_awarded(records, rounds), 'packs'
	return None

def compute_records(rounds, records):
	"""Give how many people of each record there will be, assuming 2^rounds many players.
	Doesn't work for 5+ rounds because it doesn't take into account pair-up/pair-downs.
	"""
	if rounds == 0:
		return records
	records.append(0)
	for i in range(1, len(records)):
		#print records
		winners = records[-i-1]
		#print winners
		records[-i] += winners / 2
		records[-i-1] -= winners / 2
	#print rounds-1, records
	return compute_records(rounds-1, records)

def total_packs_given_out(rounds):
	"""Compute how many total packs are given out."""
	records = [(i, rounds - i, 0) for i in range(rounds + 1)]
	total_packs = 0
	for i in range(rounds + 1):
		total_packs += packs_awarded(records[i], rounds) * compute_records(rounds, [rounds ** 2])[i]
		print '*', nice_show(records[i]), 'gets', packs_awarded(records[i], rounds), 'packs', compute_records(rounds, [rounds ** 2])[i], 'total people'
	return total_packs

r = 4
#print compute_records(r, [2 ** r])
print total_packs_given_out(r)