Author

About the Author
@mfcrocker     -     Email     -   Articles Matthew Crocker is a full-time software developer and a part-time poker and MTG player. He has recently taken the knowledge gained through his experience as a poker player and applied it to the world of MTGO finance. He is also terminally addicted to Momir Basic.

BSB Classic: Brave New World

Editor’s note: Due to Thanksgiving, we’re taking the next couple days off. Enjoy this BSB classic and your holiday!

“All right then,” said the savage defiantly, “I’m claiming the right to be unhappy.”

On A Comedown

When Brian Kibler first started ranting about the November MOCS crashing, many Magic Online regulars rolled their eyes. We already knew that MTGO was a terrible piece of software: multiple MOCSs have crashed, PTQs die on a frequent basis, and Wizards is tightening the screws and milking every ticket from the player base (as I briefly discussed in my previous article). The thing is, many of us don’t want to listen to Kibler and quit Magic Online. We didn’t grow up with Hearthstone or Hex or SolForge. We like the instant gratifications (both playing and trading) that digital offers over paper. Heck, some players just don’t want or can’t handle in-person interactions. It’s not like the community has been silent, either; criticism has been loud and constant when these things happen, it’s just that nothing has improved.

However, I guess when you’re a two-time PT winner with nearly $250,000 of winnings important people start taking notice.

Wizards is making a high-risk, high-reward play, but it’s certainly a nuclear option. I’ll discuss my personal opinion of the changes towards the end of this article, but I’m not just here for opinions. I’m also here to provide some more cold, hard numbers.

We’ve got some new events to analyse!

Pay For Stability

As always, I’m calculating these based on current prices from supernovabots. At the time of writing:

Theros: Sell 3.6, Buy 3.49
Magic 2014: Sell 3.21, Buy 3.12

Constructed 8-Player Swiss (Standard, Modern, Legacy)

Entry: 6 tickets
Payout: Swiss (1 Theros pack per win)

50% Match Win = -0.765
55% Match Win = -0.242
60% Match Win = +0.282
65% Match Win = +0.805

Constructed 8-Player Single Elimination (Standard, Modern, Legacy, Block, Pauper, Momir Vig)

Note: only Pauper and Momir are new, but given that these are the stand-ins for DEs it’s worth visiting them.

Entry: 6 tickets
Payout: 5-3-2-2 Theros

50% Match Win = -0.765
55% Match Win = +0.056
60% Match Win = +0.952
65% Match Win = +1.928

Two-Ticket Tuesdays (Phantom M14 Sealed)

Note: These are only available for 2 days in November – 19th and 26th, but are now going to be on-demand queues.

Entry: 2 tickets (or 4 phantom points; not calculated here)
Payout: 6-4-2-1 M14 for Top 8

50% Match Win = -0.245
55% Match Win = +0.348
60% Match Win = +1.091
65% Match Win = +2.01

Conclusions

  • The days of printing tickets by playing constructed with a 50% win rate (read: Momir) are dead.
  • Constructed Swiss queues are terrible value.
  • If you need your fix, play 5-3-2-2s if you’re good and 2-man queues if you’re bad.
  • Two-Ticket Tuesdays are pretty decent value even if you’re just paying tickets. Paying phantom points make these a steal.

The Right to be Unhappy

“You’ve got to be hurt and upset; otherwise you can’t think of the really good, penetrating, X-rayish phrases.”

I want to wrap up my feelings on the matter in two parts: the financial impact and the wider health of Magic Online.

Financially, this blows for those of us who help to fund our Magic playing through daily events. This change by Wizards reflects a serious reduction in the equity of these events. To help put this into context, the current EVs for the old-style DEs are:

50% Match Win = +1.63 (change of -2.395)
55% Match Win = +3.78 (-3.72)
60% Match Win = +6.21 (-5.26)
65% Match Win = +8.90 (-6.97)

In the past, I’d have given Wizards the benefit of the doubt, but when the trend over the last couple of years is taken into consideration, I have to come to the obvious conclusion: This has been in the cards for some time. Kibler-geddon has simply provided an opportune moment to roll these out. If DEs ever come back (and it definitely is “if,” not “when.” See leagues.) I wouldn’t expect to see them paying 11-6.

It isn’t all doom and gloom for grinders, however. This will force the majority of the player base to move to 5-3-2-2 queues which will be a lot more convenient and allow for much greater volume. From a purely personal standpoint, it’s wonderful to see some Momir queues worth playing, especially given many of the DEs started at 11pm where I live.

Regarding the long-term health of Magic Online, I don’t think these changes will actually have much of an impact. I return to the title of this section and the quote at the top from “Brave New World.” Although not a perfect analogy, we the userbase are choosing to be unhappy. We’re taking the crashes and the squeezing of prizes and the shitty beta because we love this game and are willing to put up with it. This is a damn shame – Wizards desperately needs the kind of shock Kibler calls for to actually improve Magic Online for the better but I just don’t see these issues or the competition hitting their bottom line. Growth might get hit as new players choose to take up Hearthstone or Hex instead, but those of us already addicted to digital paper crack are probably just going to keep trading our tickets over for another hit.

Maybe we all collectively need to check into rehab.

Matt Crocker – Brave New World

“All right then,” said the savage defiantly, “I’m claiming the right to be unhappy.”

On A Comedown

When Brian Kibler first started ranting about the November MOCS crashing, many Magic Online regulars rolled their eyes. We already knew that MTGO was a terrible piece of software: multiple MOCSs have crashed, PTQs die on a frequent basis, and Wizards is tightening the screws and milking every ticket from the player base (as I briefly discussed in my previous article). The thing is, many of us don’t want to listen to Kibler and quit Magic Online. We didn’t grow up with Hearthstone or Hex or SolForge. We like the instant gratifications (both playing and trading) that digital offers over paper. Heck, some players just don’t want or can’t handle in-person interactions. It’s not like the community has been silent, either; criticism has been loud and constant when these things happen, it’s just that nothing has improved.

However, I guess when you’re a two-time PT winner with nearly $250,000 of winnings important people start taking notice.

Wizards is making a high-risk, high-reward play, but it’s certainly a nuclear option. I’ll discuss my personal opinion of the changes towards the end of this article, but I’m not just here for opinions. I’m also here to provide some more cold, hard numbers.

We’ve got some new events to analyse!

Pay For Stability

As always, I’m calculating these based on current prices from supernovabots. At the time of writing:

Theros: Sell 3.6, Buy 3.49
Magic 2014: Sell 3.21, Buy 3.12

Constructed 8-Player Swiss (Standard, Modern, Legacy)

Entry: 6 tickets
Payout: Swiss (1 Theros pack per win)

50% Match Win = -0.765
55% Match Win = -0.242
60% Match Win = +0.282
65% Match Win = +0.805

Constructed 8-Player Single Elimination (Standard, Modern, Legacy, Block, Pauper, Momir Vig)

Note: only Pauper and Momir are new, but given that these are the stand-ins for DEs it’s worth visiting them.

Entry: 6 tickets
Payout: 5-3-2-2 Theros

50% Match Win = -0.765
55% Match Win = +0.056
60% Match Win = +0.952
65% Match Win = +1.928

Two-Ticket Tuesdays (Phantom M14 Sealed)

Note: These are only available for 2 days in November – 19th and 26th, but are now going to be on-demand queues.

Entry: 2 tickets (or 4 phantom points; not calculated here)
Payout: 6-4-2-1 M14 for Top 8

50% Match Win = -0.245
55% Match Win = +0.348
60% Match Win = +1.091
65% Match Win = +2.01

Conclusions

  • The days of printing tickets by playing constructed with a 50% win rate (read: Momir) are dead.
  • Constructed Swiss queues are terrible value.
  • If you need your fix, play 5-3-2-2s if you’re good and 2-man queues if you’re bad.
  • Two-Ticket Tuesdays are pretty decent value even if you’re just paying tickets. Paying phantom points make these a steal.

The Right to be Unhappy

“You’ve got to be hurt and upset; otherwise you can’t think of the really good, penetrating, X-rayish phrases.”

I want to wrap up my feelings on the matter in two parts: the financial impact and the wider health of Magic Online.

Financially, this blows for those of us who help to fund our Magic playing through daily events. This change by Wizards reflects a serious reduction in the equity of these events. To help put this into context, the current EVs for the old-style DEs are:

50% Match Win = +1.63 (change of -2.395)
55% Match Win = +3.78 (-3.72)
60% Match Win = +6.21 (-5.26)
65% Match Win = +8.90 (-6.97)

In the past, I’d have given Wizards the benefit of the doubt, but when the trend over the last couple of years is taken into consideration, I have to come to the obvious conclusion: This has been in the cards for some time. Kibler-geddon has simply provided an opportune moment to roll these out. If DEs ever come back (and it definitely is “if,” not “when.” See leagues.) I wouldn’t expect to see them paying 11-6.

It isn’t all doom and gloom for grinders, however. This will force the majority of the player base to move to 5-3-2-2 queues which will be a lot more convenient and allow for much greater volume. From a purely personal standpoint, it’s wonderful to see some Momir queues worth playing, especially given many of the DEs started at 11pm where I live.

Regarding the long-term health of Magic Online, I don’t think these changes will actually have much of an impact. I return to the title of this section and the quote at the top from “Brave New World.” Although not a perfect analogy, we the userbase are choosing to be unhappy. We’re taking the crashes and the squeezing of prizes and the shitty beta because we love this game and are willing to put up with it. This is a damn shame – Wizards desperately needs the kind of shock Kibler calls for to actually improve Magic Online for the better but I just don’t see these issues or the competition hitting their bottom line. Growth might get hit as new players choose to take up Hearthstone or Hex instead, but those of us already addicted to digital paper crack are probably just going to keep trading our tickets over for another hit.

Maybe we all collectively need to check into rehab.

Matt Crocker – Dealing With Draft Addiction

Cracking Packs

Going infinite in Momir Basic DEs is all fine and good (and a lot better now that M14 has rotated out of prize payouts) but let’s face it, it’s not that glamorous. Momir is fun but it doesn’t add cards to your collection and doesn’t give you that lovely addictive mp3 of a pack being ripped open.

It’s time to talk about drafting.

Feeding the Bots

If you have any interest in “going infinite,” you’ll already know that you should be avoiding 4-3-2-2 queues like the plague. However, EV is difficult to calculate for all draft queues because we need to assign a value to the cards we pull. At the time of writing, Theros was just released so card prices are artificially inflated. As a result, we are better off trying to calculate the value of a stable format like triple M14.

It’s very unusual on MTGO for a money common or uncommon to really blow up, so I think it’s reasonable to only model rares and mythic rares when it comes to pack value. We’ll take the 1-in-8 probability of getting a mythic as read and ignore foils – with the probability of a foil rare or mythic being so low their effect on the EV calculation is absolutely minimal. We’ll also assume that all players are playing greedily (i.e. they always take the rare/mythic first pick in every pack). This is not the optimal strategy and some extra EV can be achieved by getting good at deciding when it is better to raredraft and when it is better to draft for a better deck – more on this later.

(Author note: these prices are from before the Pro Tour. Everything blew up!)

Pack value = 7/8 * (mean rare price) + 1/8 * (mean mythic price)

Using current M14 buy values from supernovabots:

Pack value = (7/8 * 0.438) + (1/8 * 4.77)
Pack value = ~0.98

Using this figure and current M14 pack prices (sell 2.83, buy 2.74):

EV Event = (Expected prizes) – (3 * (2.83 – 0.98) + 2)
EV Event = (Expected prizes) – 7.55

50% win rate

4-3-2-2 queue EV = -3.78
Swiss queue EV = -3.44
8-4 queue EV = -3.44 (NB: this is expected – the number of packs paid out is the same and this theoretical player has no edge over the field so the top heavy payout neither hurts nor harms their EV (although is higher variance))

55% win rate

4-3-2-2 queue EV = -3.25
Swiss queue EV = -3.03
8-4 queue EV = -2.41

60% win rate
4-3-2-2 queue EV = -2.69
Swiss queue EV = -2.62
8-4 queue EV= -1.24

65% win rate (Probably near the top win rate that can be expected)
4-3-2-2 queue EV = -2.08
Swiss queue EV = -2.21 (!)
8-4 queue EV = +0.09

70% win rate (Starting to enter Magical Christmas Land)
4-3-2-2 queue EV = -1.43
Swiss queue EV = -1.80
8-4 queue EV = +1.58

Limited Value

As you can see, it is very difficult to be a winning player in drafts. Sadly, the value just isn’t there. However, from running the figures we can still draw some interesting conclusions that may not be obvious:

  • As everyone already knew, you shouldn’t be playing 4-3-2-2 queues. Ever.

  • Unless you lose more often than you win, theoretically you also shouldn’t ever play in Swiss queues.

  • In reality, the line for this is slightly higher because Swiss queues have worse players and so your Match Win % will be better in Swiss than in 8-4s.

  • In a strange twist, top players should be avoiding Swiss events more than 4-3-2-2s despite the higher total pack payout.

  • If you’re not the Kenji Egashiras and Brian Wongs of the world drafting will always cost you money, and you should accept this.

On that last point, I mean it. An important part of bankroll management is keeping yourself in check and honest. If you are able to go infinite from drafting you are either one of the top Limited players in the world or the singles market is completely busted and pack value is through the roof. For us mere mortals, drafting will cost us money and tix.

And that is fine.

As long as we know this is the case, we can handle it elsewhere. The main thing to do is to budget for it. I suggest either having a dedicated cash budget for drafting or funding it through Constructed DEs. If you are choosing the latter option, set yourself a line in the sand for your bankroll under which you don’t draft at all – have a look at Part 1 of this article series and set the line at 5% risk of ruin or lower.

Stopping the Rot

The other thing to do is to squeeze as much EV from each draft as possible. Others have discussed this in the past, but it’s always good to refresh the basic principles:

Play 8-4s: I covered this already, but unless you’re outclassed as a player it is always correct to play 8-4 queues over every other format.

Learn how to rare draft: There’s a balance to be struck between taking the rare or mythic in a pack and taking the best card to improve your Match Win %. As the figures above show, a 5% increase in Match Win % is worth around 1-1.5 tix (increasing as your Match Win % gets higher). In practice, this means it’s certainly not worth raredrafting bulk and probably not worth it unless that card is worth a ticket or two (in which case it’s probably helping your deck as well).

Split: If you make the final of an 8-4, always split the packs unless you legitimately feel your deck is the absolute nuts. This doesn’t improve your EV but it does significantly reduce your variance.

Play your A game: A common suggestion in poker is to avoid playing when you’re not playing your best. In reality this isn’t practical, but the spirit of it should be taken on board – avoid the draft queues when it’s obvious you’re not at your best.

Improve all your games: This can come in many forms. Reading articles and learning more about the format will improve your best games. Learning to handle tilt properly will improve your worst games. I highly recommend reading The Mental Game of Poker by Jared Tendler for more information on this – the wisdom contained within is easily applied to Magic.

Keep an eye on the market: Drafting provides you with a lot of cards, which means you’re inadvertently catapulted into the world of Magic finance. You can easily improve your drafting EV by making sensible decisions about when to sell cards. For example, I recently ripped a Chandra, Pyromancer and flipped it immediately for 11.5 tickets. Mono-Red has continued to be a force in Standard and I could now get 16.8 from a bot. That’s nearly the cost of a whole draft down the drain because I didn’t feel out the market correctly or (and!) was impatient.

Sell to humans where you can: You can squeeze out some extra parts of tickets if you sell directly to people rather than bots. I actually quite like bots for the convenience but it obviously comes at the cost of not getting full value. This will take time and your time is worth something, so make a sensible decision based on your view of it and remember that you can always quickly compare the buy prices of various bots.

Play the value formats: Not all formats are created equal. Your Match Win % may be better in DGR block drafts than in triple Theros. M14 pack values may stomp all over both. It’s not that difficult to calculate EVs and in the future I might release a quick online calculator to show you the best online draft formats. Pay special attention to “retro” draft formats – there are often some disgusting chase money rares in these that absolutely warp the expected pack value. Roll on Mirage…

The Elephant in the Room

It needs to be said – the big winner when it comes to drafting is Wizards of the Coast. Drafts are so unprofitable because they cost so much to enter. Assuming that the values of cards would stay the same if nix tix drafts were brought in (a faulty assumption but necessary for simplicity) it would reduce the necessary Match Win % to be profitable from ~64% to ~57%, which is far more attainable.

Sadly, this will never happen. Wizards have quite clearly set their stall out to extract as much value from their customer base as possible and I don’t see them giving back $16 per draft, regardless of how many extra packs nix tix queues would shift. I’m not an economist, but I doubt the increased sales would make up for it.

Matt Crocker- You Are Going Broke, Not Infinite

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.