The Care and Feeding of Glasshoppers (Article by Missingtoez and Kartoffel)

The Care and Feeding of Glasshoppers (Article by Missingtoez and Kartoffel)

The following article was written by SPG’s Missingtoez and Kartoffel. 



Hey, everybody it’s Toez, I’m back. Some of you will be like “oh cool, Toez hasn’t written anything in forever” and some of you will be like “I have no idea who that is”. Both of those responses are valid. So for those who don’t know me: I’m a long time Eternal player with varying degrees of lack of success under my belt. My E-Peen would be on fire if I was vain enough to spend $25 on such nonsense.

Occasionally, when the planets align or I’ve lost a bet, I etch symbols on my cave wall for the education and amusement of others. So a bit like Ilya’s reddit posts, just with better spacing. Today we’re going to talk about the latest bad guy. A deck so bland it became interesting. A synergy deck so light on synergy that it actually functions at a high level in Eternal: Praxis Pledge.


Part One: Inception, Revelation and Desertion

Our story begins as all stories begin, in a Discord server. The Monday after the release of Homecoming, and the blasted hellscape that was playing through that campaign, my fellow members of SPG and I were doing what all card gamers do with new cards, brewing. Or in our case watching Bruised By God play a Hooru based deck on ladder and calling it brewing. The deck in question was TJP Pledge, light on the T because it’s BBG. Despite the deck’s weaknesses it quickly became clear that Glasshopper was a real card, and that Korovyat Palace probably shouldn’t exist.

At some point in the day our team dad Paradox posted a message in our competitive ideas channel saying that he thought he’d found a tier 1 deck. Statements of that nature aren’t often made in SPG chat because we are a band of (mostly) heathen savages looking to dunk on each other at any opportunity. This was the list Paradox posted:

https://eternalwarcry.com/decks/details/AzI7yKkGw50/paradoxs-praxis-pledge-tokens-4-2-19

Our team had already fallen in love with Glasshopper from our experiments with TJP, so the group of us that were in the call that day stopped watching BBG as he was discovering the extremely interesting interactions of Palace and whatever units happened to be alive on turn six, and started playing Paradox’s deck on ladder… and it was good. It was very good. We were both elated that we had a new toy to play with and let down because we couldn’t dunk on Paradox.

As is tradition in SPG we quickly split into two camps. Those who wanted a Fire market to help push damage and close out games, and those who wanted a Time market to… help push damage and close out games WITH VALUE. The core of the deck was set though. Praxis has 16 good pledge cards and a couple mediocre ones. We decided to play the good ones, because we’re very smart. Glasshopper was a must because it was new, shiny and our actual payoff for playing Pledge. The Teacher of Humility and Amaran Stinger package is one of the strongest openings aggressive Praxis can manage, might as well throw those in too. Heart of the Vault and Torch are two of the best cards in the game, no reason not to play four of each.

https://eternalwarcry.com/decks/details/W9FgnItuDKA/the-core

The core 36 cards of this deck are so strong that I think you could fill the rest in at random and still win games in the right meta. The deck was fun in that way that all shared secrets are fun, but it was far from perfect, like the odds of keeping a secret once shared. At some point the question of the optimal number of Pledge cards was raised and Kartoffel aka Saddemo aka A10 aka Lucky Handz spent several hours with childroland verifying what some of us enlightened primates just knew instinctively 16 Pledge cards is a good place to be. Now, since I’m fully committed to scratching out these pictographs by the light of a dying fire I’m going to let Kart give you a quick rundown of the voodoo he calls “mathematics”.  


Kartoffel Does the Math

Hello and welcome to the Potato corner of this article. For those of you deathly afraid of numbers, those of you who would rather concede than do blockers math and those of you needing a head start to hide your prized pictographs from toez, feel free to skip to the pretty results section at the end of this paragraph. For those of you who are still with me, I will detail our progress in the next five sections: Our goal, our constraints, our model, the results and finally a few warnings.

The goal, or “what is this even about”

Back when Homecoming released and our team frantically raced each other to finish the campaign, a question emerged in the wake of all the new Pledge and Pledge payoff cards: “How many pledge cards do you need to reliably pledge at the start of your games?”. While the cavemen tried to divine the correct number through hitting their clubs against their screens, childroland and I decided to find a more mathematical approach. We ended up reframing the question as: “How many pledge cards do you need to have in your deck to reliably pledge at the start of your games, without going to 6?”. Quite obviously, a pledge deck will have a higher chance of finding a pledge unit by exhausting all their mulligan options. However, it was our belief that a deck should not be built with the expectation of being down a card every game just in order to function properly.

The constraints or “the rules of the game”

The constraints were born out of the mechanic behind the opening hand and the mulligans. You can find them for yourself in the Eternal wiki, but I will list them here again for convenience sake:

  • Opening hand (7 cards): You are guaranteed at least 1 power card and at least 1 non-power card.
  • First mulligan (7 cards): You will have either 2,3 or 4 power cards in your hand. Each of those three options is equally likely.

The model, or “the model”

Pretty much all the underlying math of this is done through hypergeometric probabilities. Explaining that whole concept fully would go far beyond the scope of my paragraph, so I will offer you a quick introduction and signpost you to some more in-depth reading material.

Merriam-Webster defines “hypergeometric” as something “involving, related to, or analogous to operations or series that transcend ordinary geometrical operations or series” which basically means it is not just math, it is advanced math.

To fit the criteria of being a hypergeometric experiment, two specific conditions must be fulfilled. I will attempt to illustrate them using a standard Eternal deck (75 cards) as an example:

1)      A sample of size n is randomly selected without replacement from a population of N items.

Consider Eternal: At the start of your game, you randomly draw 7 cards from the top of your deck, which contains 75 cards. In this case, your initial 7 cards would be your sample size n, 75 cards your population N.

Moreover, you do not draw one card, shuffle it back, and then draw the next one, but draw them all one after the other. This fulfills the criteria selecting your sample without replacement.

2)      In the population k, items can be classified as successes, and N – k items can be classified as failures.

What you label as successes and failures can obviously vary wildly for different experiments, but if you recall the goal of this section, we can label our number of pledge cards as successes, and every other card as failures.

Or, in short: The probability of a success changes on each draw, since each draw decreases the population.

Moving forward, we can use a hypergeometric formula to compute our probabilities. I will not go further into how the formula works in this bit, but will ask the interested reader to consider reading through this page if they are interested to dive in further.

To finish this section, this is how our modeling ended up looking (We are also assuming a deck with 75 cards, 50 of which are non-power cards, the remaining ones being power):

i. Opening hand:  To fulfill the constraint given we divided the original starting hand into three sections:

  • Group A: The 1 guaranteed power card
  • Group B: The 1 guaranteed non-power card
  • Group C: 5 random cards

 

Since we were looking to find at least one pledge card, we used the approach of computing the probability of neither group having any pledge cards. The complement to this event is then in fact the probability of finding at least one pledge card. The formula roughly looks like this:

100% – (% chance no pledge card in A)*(% chance no pledge card in B)*(% chance no pledge card in C)

ii. First redraw: In this case we took a similar approach, but for each 2,3 or 4 power option. Since it is known that each option is equally likely, we sum each complement and divide it by 3. The rough formula:

{[100% – (% chance of no pledge card with 2 guaranteed power)] +

[100% – (% chance of no pledge card with 3 guaranteed power)] +

[100% – (% chance of no pledge card with 4 guaranteed power)]} * 1/3

    iii. “Finding at least one pledge card when redrawing once”: To find our most important statistic we again take the approach of using complements for i and ii respectively, multiplying them and the complement of that result is what we are looking for:

100% – [100% – (% chance of no pledge cards in opening hand)]*[100% – (% chance of no pledge cards in first mulligan)]

The results or “The hard math part is over, now look at this pretty graph. It has colors, weeeeeeeeeeeeeeeeeeeee”

(You may have to open this image in a new tab in order to see the numbers more clearly.)

In this table you will find the odds of finding at least one pledge card within your opening hand (“no redraws”) and within your first 2 hands (“redrawing once”) while being on the play. Being on the draw your odds improve slightly since you get to see one more card. Recalling our stated goal at the beginning of this side piece, the important part at this stage is to find a number that properly represents “reliable”. It was our belief that a success rate bigger than 95%, or put differently, a failure rate of less than 5% within your first two hands, would fulfill that requirement.

Notably back then the instinctual players surmised the sweet spot would lie somewhere between 12 and 16, so they felt rather vindicated when we announced the sweet spot being 16 pledge cards, some even wrote an article.

Warnings, or “Numbers don’t lie, but…”

  • As Eternal players or card game players in general we have likely met our fair share of variance at some point. Maybe you were looking to close your game out but ended up drawing 4 basic sigils in a row, losing you the game.

My point is that 5 percent is still 1 in 20 games and depending on how much the shuffler likes you, it might be worse over a small sample size of games.

  • One issue this model has is that it does not account for “playable” hands. An opening hand of 6 sigils and one pledge card for example would fall into “at least one pledge card” but would very likely be a mulligan.

Keep in mind that your standalone odds past your opening hand get progressively worse, since there is more guaranteed power in your hand and then even one less card in your final mulligan. If you want to know what your odds are to have at least one pledge card in your opener, regardless of previous hands, here is one more graph for you:

(You may have to open this image in a new tab in order to see it more clearly.)

Your takeaway from this should be the following: If your first/second hand has a pledge card but is a “questionable keep”, you should be aware of the mathematical risk of not finding a pledge card at all.

Now then, I hope you enjoyed this brief excursion away from the madman’s grasp, but I will need to hand you back over. Before I do, I will once again thank childroland for his help and while I will not ask you to pledge allegiance, I’d ask you to follow carpola1 on twitter, he needs to impress his date.


I understood nothing that Kart just said, but those graphs sure were colorful. I like colorful things. Anyway, back to our story.

An ongoing tradition in SPG is participation in the Tuesday Night ECL, in part because we like the good folks at TGP and want to support their efforts at building a stable community tournament scene apart from the ETS and in part because Kaelari has encoded something called “Team Terror” into his site. We don’t know what “Team Terror” is, we don’t know precisely how we acquire it, we just know we want it. Like I said, we’re savages.

For the first Tuesday Night ECL of the new season several of us brought varieties of Paradox’s original list and did well with them, Jarboe and Carpola played the Fire market version. Paradox and I played the Time market version, though I swapped out the Grenadin Drones for a playset of Initiate of the Sands and titled my deck “I Don’t Think This is a Tokens Deck”. Not my best work humor wise, but a bit prophetic. Interestingly, a month later Sardaukar99 would make day two of ECQ: Dark Frontier playing a list that was one card off this early version. In the end though it was BBG who took down the Tuesday tournament with TJP Pledge, because having a unit and six power is a fair win condition.

Soon after Homecoming the ladder became infested by owls, and Praxis isn’t usually the place you want to be in a Hooru meta. That coupled with the fact that it was a Praxis deck and no one could stand working on it for very long caused us to abandon it. For no reason other than lack of interest we left a tier 1 deck by the wayside. This wouldn’t last long.


Part Two: This business will get out of control. It will get out of control and we’ll be lucky to live through it

For the next couple of weeks SPG focused on ECQ: The Winter Crown, and neglected to give our Glasshoppers any serious thought. We focused on tuning or beating Hooru and FTP, and our little experiment was all but forgotten. I was personally committed to sniping SecondBlue during his run using a deck that hard counters his. This is a tactic he’s used on other members of our team in the past. It worked, in that I sniped him and got a nearly free win and qualified for the top 64 in the process. It also failed in that he learned nothing from the experience and my deck was poorly positioned for a run on day two. Then a simple twist of fate sparked renewed interest in the Pledge deck.

On April 7th the ECL, Shiftstoned and EternalWarcry sponsored the Opal Waystone classic, hosted by and on EternalTournaments.com. The unique format and prize pool drew a record crowd and the site couldn’t handle the added traffic. The resulting crash left a lot of folks feeling frustrated, and forced Kaelari to make some changes on the backend. On April 18th Kaelari held a stress test to see if his changes held up. This wasn’t an actual tournament, no one played any games. We did however, register decks, and the one I registered happened to be Praxis Pledge. It was a hard fought tournament, but I manage to pull out a glorious victory going undefeated… also winless. One of my finer Eternal achievements. Because Warcry automatically pulls the top finishing decks from Kaelari’s site the test tournament results ended up on the front page.

Then a strange thing started to happen.

Over the next couple of days I started getting messages about the deck I’d used to win a tournament that never happened. It also started popping up on ladder. People were playing and refining it to suit their own purposes. Magikarp took second in a Sunday ECL using a Fire market version that cut Amaran Stinger in favor of a split of Trail Maker and Dawnwalker, he also added Jawbone Greatsword to the deck which combos exceptionally well with Gunrunner. This got me thinking about the deck again, and I started pulling the team in with me. This round of testing was more focused and we quickly came to a list we were comfortable with. During this period we flirted with the Fire market and Jawbone Greatsword. We also added Shugo Standard to push damage, a card that should have been in our lists from the start. Eventually we settled on the ramp of the Auralian Merchant and the girthy thickness of Sandstorm Titan over Jawbone, which while letting us do a fabulous Kurt Russell impression wasn’t pulling its weight where we needed it. Then disaster struck. Sunyveil gave away the shop.

At some point Suny started streaming his version of Praxis Pledge and someone sent me his list. His early version was very close to where we ended up on ours, a bit heavier on power and Pledge units. The main thing we took from this list was the Glasshopper in the market, it was a strong value play with the bonus of adding consistency and a touch of psuedo ramp.  ChiCityShogun used an early version to take second in the impromptu SPG 11th Hour Open tournament. Then the two of them did a podcast claiming it was the deck to beat in ECQ: Dark Frontier. The only consistent thing about the last three ECQ metas is that the deck Suny plays will be the most prominent deck. The size and openness of the Friends of Eternal, plus Suny’s role as one of the game’s more prominent voices cause his ECQ predictions to manifest into reality. So among the Hojan’s Oathkeepers and set one stock Rakano you’ll play a fair amount of whatever deck Suny has willed into existence. Several members of SPG have made the day two cuts just countering whatever deck Suny plays. We’re not proud, because we’re gorillas.  

https://eternalwarcry.com/decks/d/yOh4vWBAE4Y/chicityshoguns-deck

Once the metaphysical cat was out of the proverbial bag, we were faced with two choices: Abandon our Glasshoppers in the wilderness once again, or play the deck in the face of intense opposition. Over the course of the next week, the SPG Hivemind played hundreds of Pledge games. Even Two-Trick TonyGeeeee played his share. We tried and tested everything we could think of, and when reports came in of other team’s tech we tried those too. We settled on two flex slots, and the list of things we tried in those slots is too long to list. Highlights were Flameblast and Purify, Lowlights were OG Diogo and a card I won’t name because I’m not out to hurt other people’s feelings. During this period a couple things became clear. First was that the deck was still putting up respectable numbers against the decks that were meant to hard counter it. Second that the mirror was a total horrorshow.

Eventually we settled on two lists. One that BassoonBuffoon (who committed to Pledge early and was my boon companion throughout these trials) and I thought was correct. This deck played Titan and a pair of Purify in the main, and was a very safe choice. BB used it to qualify for day two of Dark Frontier, and top 8 the ETS the next day. Eventually he was mowed down by the buzzsaw that was ManuS on Sunday. He will be very hard on himself, but we’re damn proud of him… even when he neglects to warp in Heart of the Vault.

https://eternalwarcry.com/decks/d/2n86Bkbk988/who-cares-how-good-it-is-the-games-dont-last-forever   

The second list was bit of a lark. Somewhere around the hundred game mark boredom set in. I started throwing weird stuff in the deck just to see what happened. My early experiments with OG Diogo showed me how powerful double damage was in the deck. So naturally I replaced Sandstorm Titan with Zuberi, Outlands Warlord. Zuberi is an old friend of SPG who played a key role in a pair of decks built by Sifudanny and SooNo back when Rizhan had Lifesteal and Icaria, The Liberator was a card. This experiment went far better than expected. Zuberi into Glasshopper meant double damage Cykalis as early as turn five, turn four if you had Initiate on one. It was also another card that could break boardstalls in the mirror, where you often end up waiting for some combination of Darya and Gunrunner to show up. The real problem was that it left a deck that was already weak to flyers even more susceptible. So on Thursday night before the ECQ, after facing some form of Hooru Flyers in six games out of seven I cut a Zuberi for a third Purify and replaced the Xenan Initiation in the market with a Sandstorm Scarf. This was the list that theovermaster used to not only qualify for the top 64, but finish top 4, losing only to SPG’s own TonyGeeeee.

https://eternalwarcry.com/decks/d/li1q2CxMzo8/theovermasters-deck-top-4

The strangest thing about Theo’s run is the way it came about. During all the testing and ladder grinding we did prepping this deck it never really worked for him. Theo is one of the best players I know, but he’s also a bit of a hipster when it comes to deck choices. An aggressive Praxis midrange deck that represents a large portion of the meta IS NOT where he wants to be, ever. He had a hard time getting above a 50% win rate with it, even while others of us were hitting 70%+ rather easily. Then one night he and Jarboe sat down with the Zuberi list after I had logged off and they went to work. Something clicked. The addition of Zuberi was fun enough that he wanted to play the best deck in the format. So if you want to know why you should play Zuberi over the much more practical Sandstorm Titan, that’s it. That’s the reason. Fun. It’s sometimes enough to win you $500 and a spot in the final qualifier for Worlds.


A couple last thoughts before my fire burns out and the cyclopean darkness engulfs my cave, slipping me back into the oblivion of anonymity and dreams. This game has given me a lot, not the least of which is the chance to interact and form friendships with an amazing group of players from all around our small pocket of existence. Having like minded individuals to wile away the idle hours is one of the few things that keeps me engaged with Eternal. We give each other a ton of grief, and are often unkind in the extreme to one another, but nothing in this game means more to me than the people I play it with. So to my teammates, thank you and I love you… except for SecondBlue. That guy is a tool.                                                                          

            -Toez


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