Originally published on 60cards. Price data is from June 2013 – payouts and prices have since changed but those provided are a good example of a “normal” MTGO economy.

Introduction

One of the most famous articles on “going infinite” is Beginner’s Guide to Going Infinite on Magic Online by Brandon Large over at StarCityGames.com. On the surface, the advice he offers is solid; get a few tickets together, get into cheap formats such as Momir Basic or Pauper and then play Daily Events to build up a sizable stash of tickets in order to branch out into the more expensive Constructed formats. There is, however, one sizable flaw with his plan:

The bankroll.

In poker, one of the first concepts we try to drive into the minds of beginning players is the importance of bankroll management. If you had $100, you could quite happily go and enter a $100 poker tournament and there’d be nothing stopping you. After all, the prizes on offer would dwarf those of a $1 tournament. The problem, however, is that even as one of the greatest players on the planet you are still subject to the gods of variance and there’s no guarantee of winning any money. The risk of going broke is huge.

There has been quite a lot of talk in articles and discussions about going infinite around the concept of Expected Value (EV). A concept shared with poker and investment, EV in this context is simply the expected profit or loss from a wager or investment. When talking about Magic Online, we use EV to work out whether playing a particular event is profitable; however, no thought at all is given to whether the event is affordable. In Brandon’s article he suggests a starting “bankroll” of 15 tickets, from which the Momir Vig avatar has to come from as well as the entry fee to a Daily Event. If this advice was to be followed to the letter you’d be in exactly the same situation as the person with $100 to play poker with. This is where the concept of Risk of Ruin comes into play. In fact, you go broke 90% of the time using this strategy.

How can we not go broke?

The idea behind looking at our Risk of Ruin is to work out what a “safe” bankroll is for playing Daily Events on Magic Online. To calculate it, we need to know how much we expect to win from an average tournament. To make this easy to begin with, we’ll assume a win-rate of 50% – perfect for Momir Vig. (I’ve included the maths at the bottom of this article for those interested in how we’ve gotten to these figures)

Momir Basic DEs at Current Pack Prices

Risk of Ruin Tickets Required

50% 37

25% 75

10% 124

5% 161

2% 210

1% 248

0.5% 285

0.1% 371

0.01% 495

This table gives us both good news and bad news. The good news is that at the current pack prices it’s still profitable to play Momir Vig with the expected 50% win rate (a fairly safe assumption – even with excellent/awful play this won’t vary much due to the inherent randomness of the format). The bad news is that we’re vastly underestimating the number of tickets we need to safely play the format. As you can see from the table, a bankroll of 40 tickets still sees us eventually going broke half of the time. In poker we generally look to have a Risk of Ruin of 5% or less. From this, we can draw our first conclusion:

At the current pack prices Momir Vig DEs require around 25-40 tournament buy-ins (150-240 tickets) to be safe to grind.

The problem is that prize support varies immensely depending on the current set and how long that set has been out. A couple of months ago, just before the release of Dragon’s Maze, the support was 11-6 packs of Gatecrash which was at an all-time low value. The lowest value (2.49) would go as far as to make Momir Vig DEs unprofitable but that was very much a spike, so let’s instead take a look at how careful we have to be assuming an average pack price of 3.0 (which happens to be where Gatecrash boosters were for most of their time as a prize pack):

Momir Basic DEs at an Average Pack Price of 3.0

Risk of Ruin Tickets Required

50% 66

25% 131

10% 218

5% 284

2% 370

1% 436

0.5% 501

0.1% 654

0.01% 872

As you can see, the effect on bankroll requirements when the prize support becomes less valuable is huge. Our 30 buy-in bankroll just doesn’t cut it any more, going broke a whopping 17% of the time. In the cold wastelands of poor prize support it becomes necessary to have a much deeper bankroll stretching as far as 50-100 tournament buy-ins.

Bankroll requirements are incredibly sensitive to fluctuations in the value of the prizes.

So far we’ve looked at a simple model of winning 50% of our games represented handily by our good friend Momir Vig. But what of the big formats? We can bump our Match Win % (and thus our EV) which should present a rosier picture. Let’s pretend that we have a format-destroying Standard deck that allows us to win 70% of our matches.

Standard DEs with a 70% Match Win, Current Pack Prices

Risk of Ruin Tickets Required

50% 6

25% 12

10% 20

5% 26

2% 34

1% 40

0.5% 46

0.1% 60

0.01% 81

The bankroll requirements here become trivial. If you are confident that you can raise your win % this high (you probably can’t) there’s basically no chance of going broke as long as you keep 60 tickets in your account. Here we’ve made the situation more favorable by bumping our Match Win % but it would work just as well to bump the value of the prizes – either works to increase our EV and reduce our Risk of Ruin.

A high enough Match Win % (or prize support) makes correct bankroll management trivial.

It should be noted that this situation is in stark contrast to what happens in the poker world and is one big advantage Magic Online has over poker – the prize structures that exist in Magic Online have much lower variance than those in poker tournaments and as such there’s a lower risk of going broke.

Conclusions

So what have we learned from all of this?

Magic players may have taken the idea of EV on board but they are still likely to go broke because they don’t consider the size of their bankroll.

Momir Vig & Pauper are still very good ways to start accumulating tickets but the old ideas on the number of tickets required are really, really wrong

Having 160 tickets to play Daily Events is “safe” assuming the prize support is as it is currently

When prize support hits 33 tix/18 tix, it’s probably not worth playing Daily Events for profit, unless:

You’re one of the best players/best decks around then things are always peachy and you will rarely need more than 100 tickets behind you

In Part 2, I’ll be taking a look at bankroll requirements in the dark, scary world of Limited.

Thanks

Thanks to my partner and house stats geek Harriet Robinson for looking over my calculations and to numerous poker authors, forum posters and others for putting the hard graft in.

Calculations & Assumptions

Current pack prices: RTR 3.86, GTC 3.42, DGM 2.6

Current prize support in DEs: 4-0 = 3 RTR, 4 GTC, 4 DGM. 3-1 = 2/2/2

EV of a DE = (x^4 * 35.66) + (x^3 * (1-x) * 19.76) – 6, where x is your Match Win %

Risk of Ruin = e^((-2 * EV * BR) / (σ^2)), where BR is your Bankroll and σ is your Standard Deviation.

The Risk of Ruin formula is the one presented by DR Cox and HD Miller in The Theory of Stochastic Processes and was suggested as a solid approximation by 2+2 and EarnForex.