Going Infinite drafting on Magic Online... A Myth?

The dream

Lately you've been crushing your local draft club. This is no fluke! You're a very good player and you have a good grip on the format. So you decide it's time to go international and beat up on those online foes. How can those Mexicans, Kazachstani and Lichtensteiners ever match up to your skills? You switch on your laptop and fire up Magic Online. Hey, what do you know, they released a new version! Actually you don't care about those shiny features as long as you can draft.

A few hours and multiple megabytes downloaded later you sign up for your first 4-3-2-2 draft. Conveniently Magic Online v3.00 has a built in store where you buy four draft sets and a few tickets because you figure you need a cushion to prevent going broke before you go infinite.... That's right: INFINITE. You expect never to buy another virtual piece of cardboard again and keep drafting with your winnings until your grandchildren say "please no more virtual magic cards for my birthday, grandpa!" (Magic is dead while Yugimon vs. Pokeyo:the Brainwashing is all the rage by then)

Doing it

The first draft is on the rails and you're so excited you almost take the 9-mana rare that's worth about 4 tix. Settling down you notice the common that won't commit you yet and can always be splashed. So you pass the rare and continue to draft a deck that you know from experience to crush most other decks.

First round is against a total n00b with a rating of 1560 and you smile. Your opening hand makes your smile into a grin so you send it back. Oops, the next six have no land, so you go to five and have to keep that one. Your opponent keeps his seven. The game drags on for a while despite your mulligan and the numerous mistakes of your opponent. Unfortunately he then plays that 9-mana rare you passed and you have no more answers. You don't worry and make some good sideboard decisions and crush his dreams as expected in the next with a great curve. The last game starts up and you have a perfect hand: five cheap spells and two lands on the draw. Six turns later all you have on the table are those two lands and you're discarding every turn while your opponent is beating you down with his motley crew of overcosted vanilla creatures. You slam your laptop shut in disgust.

A yoga session later you're ready for revenge. You draft another solid deck and this time the mana gods are kind to you and you win the entire thingy. You jump right into another and win that one as well AND the next! That's it, you're doing it! You're living the dream! You're going INFINITE!

Waking up

The following day you lose two in a row in the first round because of mana screws and slightly inconsistent decks (curse that shuffler!). You follow those up with two more sweeps and then another crushing first round loss against the worst player ever who gets rainbow mana by turn 5 two games in a row. You swallow it down and just sign up for the next draft when a weird pop-up appears: ‘You need to purchase these items'... You stare in amazement. "How's that possible?", you wonder. "I swept half of my drafts!?". Then you realize those first round losses meant 3 boosters and some tix gone and the swept drafts only gave you half a booster of profit (remember it costs 2 tix to draft). Still, no need to worry because you remember you picked up a few very valuable rares in those drafts. Those will certainly keep you in the running and help you go infinite.

You open up the Classifieds tab and start trading. Ten minutes later you only managed to trade away 4 of your 25 rares and 2 uncommons to get a massive 14 tix in return. You trade those back for a draft set and sign up to draft... You immediately lose to a player with a 1900 rating who has a better deck, better sideboard and better brain. Why the hell is that guy messing around in the lowly 4-3-2-2 queues you ask yourself while broke and realizing you failed your dream of going infite???

...

This little anecdote must be familiar to most players and raises the question if it's actually possible to go infinite drafting Magic Online!? I decided to find out. I jotted some ratings in rows and columns, added a few formulas and charts in Excel and there was my answer. I'm kind of a number guy, so if you're not, just skip to the bottom of this article and find out the answer.

The numbers

How I simulated the drafts (*):

First I made a sample draft pool: you can expect to have about half the players in a 4-3-2-2 draft to be inexperienced (-1700 rating) and the other half having some experience (1700-1800). Often there will be one really good player of +1800 rating. Then I calculated the average outcome of the first round of matchups for differently rated players. The probability of someone with a 1750 rating to survive the first round against that pool of opponents is 60%. This is simply the average of the winning probabilities against the individual players in the field according to this formula:

Expected Win Percentage = 100 / ( 10 ^{(opponent's rating - your rating) / 400} + 1)

This is the actual formula used by the DCI, so it should be sufficiently accurate. (You might want to check out this article for more info on ratings and how to calculate them:

http://www.starcitygames.com/php/news/article/9198.html)

Then I made a pool for the second round consisting of the two best players and one beginner who got lucky and again calculated the probabilities of surviving that round for the different ratings. A 1850-rated player should expect to survive that round about two times out of three.

For the finals I picked the average rating of the best and second best player in the previous round as opponent (it's quite unlikely the beginner has survived again). Once more I calculated the winning percentages for the various ratings.

When all that was done it was time to multiply those win percentages with what you win in a draft (boosters). Finally I subtracted the cost of entering a draft to find out the expected profit for the different players. That cost is 3 boosters and 2 tix, but on average you should expect to draft rares worth 2 tix each draft so I set the cost at 3 boosters. Here's the chart for the 4-3-2-2:

(the first column contains the pool of players in the draft and the top row has the rating for which we want to find out the expected playtime).

4-3-2-2 Chart

First round	1600	1650	1750	1850		1920	2000
1800	24%	30%	43%	57%	67%		76%
1730	32%	39%	53%	67%	75%		83%
1700	36%	43%	57%	70%	78%		85%
1660	41%	49%	63%	75%	82%		88%
1650	43%	50%	64%	76%	83%		88%
1600	50%	57%	70%	81%	86%		91%
1600	50%	57%	70%	81%	86%		91%
WIN	39%	46%	60%	72%	79%		86%
LOSE	61%	54%	40%	28%	21%		14%
PRIZE	0	0	0	0	0		0
Expectation	0	0	0	0	0		0
Second Round	1600	1650	1750	1850	1920		2000
1800	24%	30%	43%	57%	67%		76%
1730	32%	39%	53%	67%	75%		83%
1620	47%	54%	68%	79%	85%		90%
WIN	34%	41%	55%	68%	75%		83%
LOSE	66%	59%	45%	32%	25%		17%
PRIZE	2	2	2	2	2		2
Expectation	0,52	0,55	0,55	0,47	0,39		0,29
Finals	1600	1650	1750	1850	1920		2000
1750	30%	36%	50%	64%	73%		81%
LOSE	70%	64%	50%	36%	27%		19%
PRIZE	3	3	3	3	3		3
Expectation	0,29	0,36	0,49	0,53	0,49		0,41
WIN	30%	36%	50%	64%	73%		81%
PRIZE	4	4	4	4	4		4
Expectation	0,16	0,27	0,65	1,25	1,74		2,30
	1600	1650	1750	1850	1920		2000
Total Expectation	0,97	1,18	1,69	2,25	2,63		3,00
Cost	3	3	3	3	3		3
Profit	-2,03	-1,82	-1,31	-0,75	-0,37		0,00
	1600	1650	1750	1850	1920		2000
DraftWin	4%	7%	16%	31%	44%		57%
Playtime	1,5	1,7	2,3	4,0	8,0		INFINITE

What does it all mean?? The bottom two lines are the most interesting: a beginner should expect to sweep the draft about 1 time in 25 (4% in the DraftWin row) . The 1850 will win it 1 time in 3 and the 2000-rated player crushes more then half of his drafts. This seems reasonable, but it doesn't really tell us anything about infinity. The bottom row gives the ratio of how long someone will be able to play if he buys one draft set (three boosters). So if the absolute beginner were to purchase 10 draft sets he should expect to draft 15 times before running out of boosters (10 draft sets X 1,5 playtime = 15 drafts). The good player will squeeze out a nice 40 drafts with those same 30 boosters (10 draft sets X 4 playtime = 40 drafts).

As you can see there's only one very happy player: the guy with the 2000 rating. He will probably go infinite, but last time I checked there are only a handful of players with a +2000 rating and I don't think they're messing around in the 4-3-2-2 queus so NOBODY is drafting for free in the 4-3-2-2 queues. Shocked? I must admit I was a bit surprised by this. But what kind of money would a 2000+ be making? If you look at the Profit-row you'll see he's just breaking even (this is due to roundings...he's actually winning about 3/1000 of a booster/draft). Here's a little graph to make things clearer:

One conclusion is that even the worst players are getting some extra value out of these drafts (50% more than if they were to open their boosters).

...

Now the advanced queue:

8-4 Chart

First Round	1600	1650	1750	1850	1920	2000
1900	15%	19%	30%	43%	53%	64%
1850	19%	24%	36%	50%	60%	70%
1850	19%	24%	36%	50%	60%	70%
1800	24%	30%	43%	57%	67%	76%
1750	30%	36%	50%	64%	73%	81%
1700	36%	43%	57%	70%	78%	85%
1650	43%	50%	64%	76%	83%	88%
WIN	27%	32%	45%	59%	68%	76%
LOSE	73%	68%	55%	41%	32%	24%
PRIZE	0	0	0	0	0	0
Expectation	0	0	0	0	0	0
Second Round	1600	1650	1750	1850	1920	2000
1900	15%	19%	30%	43%	53%	64%
1850	19%	24%	36%	50%	60%	70%
1800	24%	30%	43%	57%	67%	76%
WIN	19%	24%	36%	50%	60%	70%
LOSE	81%	76%	64%	50%	40%	30%
PRIZE	0	0	0	0	0	0
Expectation	0	0	0	0	0	0
Finals	1600	1650	1750	1850	1920	2000
1870	17%	22%	33%	47%	57%	68%
LOSE	83%	78%	67%	53%	43%	32%
PRIZE	4	4	4	4	4	4
Expectation	0,17	0,24	0,43	0,62	0,69	0,69
WIN	17%	22%	33%	47%	57%	68%
PRIZE	8	8	8	8	8	8
Expectation	0,07	0,14	0,44	1,10	1,85	2,91
	1600	1650	1750	1850	1920	2000
Total Expectation	0,24	0,38	0,87	1,72	2,54	3,60
Cost	3	3	3	3	3	3
Profit	-2,76	-2,62	-2,13	-1,28	-0,46	0,60
	1600	1650	1750	1850	1920	2000
DraftWin	1%	2%	5%	14%	23%	36%
Playtime	1,1	1,1	1,4	2,4	6,5	INFINITE

You should expect tougher opponents in the 8-4 drafts so I made a pool of one beginner (1650) who probably misclicked or was feeling lucky, two +1700, three +1800 and one pro (+1900). The second round will probably consist of mostly sharks (+1800) and in the finals you'll either face the pro or the second best player. Notice that if you're below 1800 you're completely over your head and should be playing the 4-3-2-2's. The beginner will need to be extremely lucky to ever win one of these and even the 1850's are only winning 1 in 7. The most interesting observation is that even the best players are getting more playtime out of the 4-3-2-2 than the 8-4 and you need at least 1940 to switch to 8-4 for more value!!! Now the 2000+-rated guy is actually making a profit of about 2/3 of a booster each draft (about $1/hour) and you still need around 1970 to actually go infinite (last time I checked the Hall of Champions in Magic Online only the top 20 limited players are going infinite). Here's the graph:

It's a lot flatter in the beginning than the 4-3-2-2-graph which means the pros are getting most of the value out of these (stealing from the poor scrubs and wannabes).

The Verdict

• Expect to be buying virtual packs on a regular basis if you draft Magic Online
• If you're a very good player you should still be playing the 4-3-2-2 to get the most value for money. And you shouldn't be ashamed about it!
• If you're a pro drafting online don't throw away your VISA after buying a few packs. You're probably going to need it again!
• When some hot shot tells you he's been drafting forever without buying packs, smile and give the poor guy a hug... he's probably kidding himself

• Going infinite drafting Magic Online is just a dream for all but a select few!

Still wishing you happy drafting!

Jeroen

(*) Disclaimer: these simulations are not meant to be 100% accurate (not even 90%), but they should give a pretty good estimate of the real situation!!