mtga_completion

The goal of this repo was to answer the ultimate MTGA question: how many packs do you need to purchase to buy a playset of each mythic?

• 10k.csv shows how many packs to complete each set
• rare10k.csv shows how many packs to get a full playset of rares of each set
• 10k-completionist-sequential.csvshows how many packs to complete every set (this is different from the sum of totals in 10k.csv as after each set there would be residual resources, thus running them sequentially is needed)

Factors Considered

• Rare -> mythic upgrade rate varies on set
• Wildcards (both wheel and pack replacement rates) and the optimal strategy of holding them until completion at that rarity is within reach
• The vault system
• The pity system, which sets upper bounds on how many 'misses' you can get on a certain upgrade event
• Excess cards at a certain rarity can be converted to gems and serve to buy packs (hence the difference between opened and purchased packs)

Strategy

The easiest way to solve this is via Monte Carlo. mtga_set_completion.py implements an object-oriented abstraction for a players collection. stats.py serves as a driver for this: averaging results over multiple sets and calculating standard dev, percentiles, and writing out results.

Verification

We could also verify these results with a system of equations which would consider everything but pity timers and the case where Mythics become the limiting factor (which is very improbable). Let column vector x solve for the dollar value of the following variables x = (common, uncommon, rare, mythic, gems, vault). As expected, multiplying these values by the number of cards in each rarity for a set gets us very close, and slightly above our experimental results

import numpy as np

A = np.array([
    [5, 2, (7/8+3/24), (1/24+1/8), -200, 0],
    [1, 0, 0, 0, 0, -1/1000],
    [0, 1, 0, 0, 0, -3/1000],
    [0, 0, 1, 0, -20, 0],
    [0, 3, 2, 1, 0, -1],
    [0, 0, 0, 0, 200, 0],
             ])
b = np.array([0, 0, 0, 0, 0, 1])
x = np.linalg.solve(A, b)

x = array($.005, $.016, $.1, $5, $.005, $5.298)