Completing sets through Standard: The Metagame Challenge

At the end of my final report on completing sets through limited, I mentioned wanting to try completing a set through constructed next and considered that this was possible through the Standard Metagame Challenge. In this report, I detail my attempt to do so with the Theros Beyond Death set that just released a week ago. I show that this event can be very profitable if you can manage the win rate needed.

A quick aside on what it means to “complete a set”

Based on previous experience, it takes about 22 ranked drafts to manage being almost rare complete by the beginning of the next expansion. This was what I learned from Throne of Eldraine. I am still missing 5 rares from the set, but none that I need. I believe something around 22 drafts is just the right number; it’s high enough for you to not use too many of your wildcards crafting your decks but low enough so that you will not reach the point where you are rare complete and future packs you open from the set only give you 20 gems (which is a huge waste considering that a pack is valued at 200 gems).

Thus, if we consider that each ranked draft gives at least 4 packs (three draft packs and one prize pack), then we are aiming to get at least 22 x 4 = 88 packs from doing the Standard Metagame Challenge.

Expected value of the Standard Metagame Challenge

The Metagame Challenge is the most difficult event apart from qualifiers that MTGA has to offer. You play best-of-3 games on a queue until your 7^th win or your 1^st loss. The event costs 2000 gold to enter but has very competitive prizes. Below is a table showing the prizes and the net gain/loss of achieving each number of wins on one run of the event.

Wins	Prizes	Net Gain/Loss (in gold)
0	500 gold	-1500
1	1000 gold	-1000
2	1500 gold and 1 pack	500
3	2000 gold and 3 packs	3000
4	2500 gold and 5 packs	5500
5	3000 gold and 10 packs	11000
6	4000 gold and 20 packs	22000
7	5000 gold and 30 packs	33000

As shown from the table, you need to get to at least 2 wins in order to break even. Every run at 2 wins actually nets you 500 gold in value, since you paid 2000 gold for the event and get1500 gold plus one pack (valued at 1000 gold) back. The ceiling for the prizes of the event is huge, with a perfect record netting you 33000 gold in value. However, this should be understood in the context of your win rate. We define win rate as the probability that you will win versus an opponent who is in the Standard Metagame queue and is matched against you. Obviously, you do not know what your true win rate is. Consider if your win rate is 50%. In this case, the expected value of the event can be computed in the succeeding table (for a more thorough discussion of what an expected value is, see here).

Wins	Probability (win rate 50%)	EV	Probability (win rate 55%)	EV	Probability (win rate 45%)	EV
0	0.5	-750	0.45	-675	0.55	-825
1	0.25	-250	0.2475	-247.5	0.2475	-247.5
2	0.125	62.5	0.136125	68.0625	0.111375	55.6875
3	0.0625	187.5	0.07486875	224.6063	0.05011875	150.3563
4	0.03125	171.875	0.041177813	226.478	0.022553438	124.0439
5	0.015625	171.875	0.022647797	249.1258	0.010149047	111.6395
6	0.0078125	171.875	0.012456288	274.0383	0.004567071	100.4756
7	0.0078125	257.8125	0.015224352	502.4036	0.003736695	123.3109
	Total	23.4375	Total	622.2145	Total	-406.986

Based on these computations (probabilities are computed using a truncated geometric distribution), a win rate of 50% has a total expected value for the event of 23 gold. This shows that if your true win rate is 50%, then over a large number of runs, you will experience a net gain of about 23 gold per run. This is practically negligible, and so it can be strongly argued that this event is quite fair. That is, you need to be better than average in order to get something reasonable out of it. As can be seen in the next column of the table, if you have a win rate of 55%, you actually net 622 gold on average per run. On the other hand, if your win rate is 45%, then you will actually lose 407 gold on average per run. I caution interpretation of these values since they should be understood in the context of the law of large numbers. That is, you must be doing a large enough number of runs to actually realize these outcomes. Thus, in attempting to complete the set this way, your gold reserve must be deep enough to weather out the variance.

Another way to look at how profitable or not this event is for you is to consider what win rate is needed to achieve each of the possible number of wins on average. Estimates of this are given by the table below (I say estimates because I computed this based on a plain geometric distribution rather than a truncated one, and so the win rate needed for average 7 wins computed in the table is slightly higher than the truth). As shown from the table, you need a very high win rate to even average 4 wins at the event. To average 3 wins, you need to be someone who wins 3 out of every 4 matches consistently.

Average Wins	Win rate needed
0	0
1	0.5
2	0.666666667
3	0.75
4	0.8
5	0.833333333
6	0.857142857
7	0.875

My experience

The next table shows my experience with the Standard Metagame Challenge. I did the event 16 times and used four different decks. However, the main decks I used were Rakdos Cats and Rakdos Knights. The table shows the number of wins I got each run, the net gain or loss from that event, and a running tally of the total net gold I spent (not counting prizes). This last column is important to see how you need a deep gold reserve to pull this off. As can be seen from the cumulative gold cost column, the total net cost of the event for me increased steadily. After switching to Rakdos cats and getting my first 6-win run followed by a mediocre 3-wins, I did four consecutive 0-win runs, increasing the total gold cost to 8000. However, after going 5 wins twice with Rakdos Cats and then having a nice string of 4-win runs with Rakdos Knights, finishing with another 6-win run, my total gold cost was down to 2000 gold. That is, the entire 16-run exercise which net a total of 79 packs ultimately cost me only 2000 gold.

Wins	Deck	Net Gain/Loss	Cumulative gold cost
1	Bu Devo	-1000	1000
1	Bu Devo	-1000	2000
6	Rakdos Cats	22000	1000
3	Rakdos Cats	3000	1000
1	Rakdos Cats	-1000	2000
0	Rakdos Cats	-1500	3500
0	Rakdos Cats	-1500	5000
0	Rakdos Cats	-1500	6500
0	Rakdos Cats	-1500	8000
5	Rakdos Cats	11000	7000
2	B Devo	500	6500
5	Rakdos Cats	11000	5500
4	Rakdos Knights	5500	5000
4	Rakdos Knights	5500	4500
4	Rakdos Knights	5500	4000
6	Rakdos Knights	22000	2000

Obviously, my experience with the event was a very fruitful one. I won about 2.6 matches on average per run which means that my estimated true win rate is 72.4%. This is consistent with our previous tabulation. The total of 79 packs is very close to our target of 88 packs, and I decided to stop here because I still want to do a few runs of ranked draft and I did not want to overshoot and end up being rare complete too early. I expect that 4 ranked draft runs should suffice to get the same result as I did in Throne of Eldraine. It is also worth noting that using a combination of Metagame Challenge and Ranked Draft is an efficient way of completing a collection. The cost of the former is the same regardless if you are paying in gold or in gems but the cost for ranked draft is much higher in gold (5k gold) than in gems (750 gems). Thus, it is efficient to pay gold for the Metagame Challenge and then pay gems for Ranked Draft. Also, the Metagame Challenge is only available for a very limited period of time (3 days?) while Ranked Draft is available for the set throughout the seasons where it is the latest set. Thus, one can play the Metagame Challenge for as many times as one’s schedule allows and then use Ranked Draft for the rest. As always, do not open prize packs until you have drafted all you want of a set in order to maximize duplicate protection.

Concluding remarks

The Metagame Challenge is certainly a viable option for completing the set early if you have a strong enough win rate and enough gold to play a sufficiently large number of runs in order to realize the actual expected value of your win rate. As I mentioned in the previous article, the paradox of the challenge is that you want to use it to complete the set, but you may need cards from the set to have a good enough deck to compete in it. This is only partially true, as the most success I have had was from a deck that did not have a single card from THB. I look forward to using this event again in future sets.

May the shuffler be with you.