Guest Article - Tournament Maths – How to Make a Profit on Magic Online Part 2

By Sebastian Parker (RisingSun000 Online)

Ok, now that my last post has been up for a few days, I’d like to discuss how calculating the EV of entering events can affect your strategic decisions.

Case 1: Hourly EV
Consider, if you will, a hypothetical metagame consisting of red aggro decks (think goblins, red deck wins, burn etc.), blue control decks (mystical teachings, monoblue counterspells etc.) and some other decks. The red aggro decks only take about 10 minutes to complete a whole match whereas the blue control decks sometimes win by timing out the opponent and take 40 minutes on average to complete a single match.

After playing a hundred 2 man queues with each, you find that the red deck is winning 60% of the time and the blue deck is winning 80% of the time. Which one is more profitable?

On a per-match basis, obviously blue is winning more so blue should be most profitable right? Well, that’s not the whole story. Our equation from last time:

EV = expected prizes – costs

For a 2 man queue, the expected prizes are 1 booster*P(win) and the cost is 2 tix.

EVblue = 0.8*booster -2
EVred = 0.6*booster -2

But, the red deck is 4 times faster than the blue deck so the EV of 40 minutes of 2 man queues is

EVblue,40 = 0.8*booster -2
EVred,40 = 4*(0.6*booster -2)

To work out when it is more profitable to play red:

EVred,40 > EVblue,40
4*(0.6*booster -2) > 0.8*booster -2
2.4*booster – 8 > 0.8*booster -2
1.6*booster > 6
Booster > 6/1.6
Booster > 3.75tix

So when a booster is worth more than 3.75tix, you make more profit playing the red deck than the blue deck, even though the blue deck is more likely to win a round.

This theory only really works for 2 man queues (and sometimes to 8-4 drafts, where you sometimes split the finals) because during a daily or premier event you have to wait for everybody to finish a round before the next one starts so playing a less winning, but faster deck will not increase your EV.

Another interesting point arises here, the fast red deck and the slow blue deck are hypothetical extremes but this sort of calculation can affect how you build your deck. If the most reliable win condition for your control deck is gaea’s blessing, so be it, but if you could put in meloku to take a hit to your win% and finish your matches in half the time, it may be profitable to do so even though you win less of the time.

Case 2: Cost of Investing in Cards
Last time, I discussed the loss of value during the act of opening a booster pack. This is part of the cost of playing in drafts and there’s nothing you can do to avoid that loss other than win lots more packs to make up for it.

A similar thing happens in constructed, you have to invest into a deck before you can play. You can sell the deck when you’re done, but usually you make a loss on the transaction. (You did buy the cards to play with after all – not to speculate on an increase in price.)

I’ll be working on the assumption that by this point you’ve done enough drafting to have a playset of commons and uncommons, which you can’t sell to a bot. So the loss on a bought/sold deck is basically going to be the rares.

This year’s block constructed UW control contains some number of the following rares:

Card	Buy	Sell	Diff
Elspeth Tirel	10.5	10	0.5
Venser, the Sojourner	13.95	13	0.95
Sunblast Angel	0.3	0.2	0.1
Myr Battlesphere	1.5	1	0.5
Seachrome Coast	1.3	1.2	0.1
Contagion Engine	0.4	0	0.4
Indomitable Archangel	3.25	2.8	0.45
Wurmcoil Engine (promo is cheap)	2.5	2	0.5
Precursor Golem	0.6	-	0.6

(Buy prices taken from cardbot, sell prices taken from ads in the Classifieds)
The diff column is essentially how much it costs you to buy the card, put it in your deck, play for a while and then resell it. For this decklist
4 Glimmerpoint Stag
3 Sunblast Angel
3 Origin Spellbomb
2 Trinket Mage
3 Venser, the Sojourner
3 Elspeth Tirel
2 Contagion Clasp
2 Tumble Magnet
4 Revoke Existence
2 Volition Reins
4 Stoic Rebuttal
1 Myr Battlesphere
1 Contagion Engine
1 Precursor Golem
4 Seachrome Coast
10 Island
11 Plains

Sideboard:
4 Necropede
4 Halt Order
4 Wurmcoil Engine
2 Trigon of Thought
1 Volition Reins

The ‘buy and immediately sell’ cost is 7.55tix. Compare that to the 92tix you need in your account to actually buy the cards and it comes off quite favourably. To make back the “cost” of the deck, you only need to win about 4 more 2 man queues than you lose (so even if your win% is only 55%, you’ll eventually make it back).

Since UW control is posting solid results in daily events, I’d expect it's winning something like 60-70% from the strength of the deck. A very strong pilot could probably steer toward the top end of that, along with the certain level of randoms playing their draft cards in 2 man queues, you can expect to win back your 7.55tix by entering

EV2man = 0.7*3.93 – 2 = 0.75
7.55tix/EV2man = 10

Ten 2-man queues, which will take approx. 4-5 hours with a control deck.
These are just a couple of the ways I use maths to help me make decisions in what to play online. I’m sure that a lot more people will want to play 2 mans when they release higher stakes. Hopefully this has been enlightening and as always,

Thanks for reading.