Green/White Tokens with Chandra
Raphaël Lévy, 1st place at GP Manchester
This deckbuilding choice sparked quite a debate online. Paulo Vitor weighed in last week with his recommendation to “not play this card in future GW decks.” Raphaël Lévy himself defended his choice by explaining that the extra power is “worth the risk of not being able to cast it a third or a quarter of the time.”
And Reid Duke had a request for me.
— Reid Duke (@ReidDuke) June 2, 2016
All right, I’ll run the numbers.
When deciding whether to include Chandra or not, you should compare it to the next-best alternative. It seems natural to me that if you don’t play Chandra, then you would run another late-game card instead, such as Secure the Wastes, Tragic Arrogance, Linvala, the Preserver, or Dragonlord Dromoka.
For concreteness, I’ll compare Chandra to Linvala in this article. I don’t know if Linvala is the optimal alternative—it probably isn’t, to be fair—but I like comparing off-color 6-drops to on-color 6-drops (where both are hittable by Oath of Nissa) because it focuses the question on the colored mana issue only.
So, should GW Tokens play Chandra or Linvala? I’ll go over three different probabilities that could help answer this, although I like the third one best.
Perspective 1: Probability of seeing at least 1 Oath of Nissa by turn 6
Using a simple hypergeometric distribution, the probability that you see at least 1 Oath of Nissa in your top 13 cards (which corresponds to turn 6 on the draw or turn 7 on the play and no mulligans) is 63.4%. This is the number I’ve seen the most in discussions surrounding Raph’s list, but there are at least four issues with its interpretation.
First, you don’t always have 6 lands on turn 6, and without the requisite amount of lands, it doesn’t matter whether you are holding Chandra or Linvala. Second, you will hold Chandra more frequently in games where you cast Oath of Nissa because the enchantment allows you to select Chandra from the top of your deck. Third, conversely, if you draw Oath of Nissa on turn 6, then it won’t help you cast Chandra on curve. Fourth, the hypergeometric probability doesn’t account for mulligans, which is an issue if you’re more likely to mulligan land-light opening hands with Chandra and without Oath.
I’m not the first to point out some of these issues, but they do indicate that the measure of interest is a bit more nuanced than the 63.4% number.
Perspective 2: Probability of seeing Oath before Chandra
Another perspective is to look at all the possible orderings of 4 Oath of Nissa and 2 Chandra in your deck. For example, the sequence in which you draw them could be Oath-Oath-Chandra-Oath-Chandra-Oath, which would be fine, or it could be Chandra-Chandra-Oath-Oath-Oath-Oath, which could leave you with an uncastable Chandra. Looking at all possible orderings, the probability of drawing an Oath before a Chandra is 66.7%.
But once again, this percentage does not adequately capture all relevant facets. One problem is that drawing 1 Chandra and 0 Oath of Nissa in your opening hand need not be a problem if you draw Oath of Nissa in time. Another problem is that in the favorable Oath-Oath-Chandra-Oath-Chandra-Oath ordering, you might not see Chandra before the game ends. It’s nice if you would be able to cast Chandra if you would draw her on turn 30, but that’s unlikely to matter against a real opponent.
Overall, these ordering arguments have several inherent problems, and the best way to understand them is to imagine a deck with 1 Chandra, 10 Oath of Nissa, and 10,000,000 other cards. In such a deck, an Oath will usually be ordered before a Chandra, but conditional on drawing Chandra in a reasonable-length game, which is what matters when you’re evaluating that specific inclusion, the likelihood of also drawing Oath is very slim—less than a thousandth of a percent. In other words, you need conditional probabilities.
Perspective 3: Conditional probability with land counts and card selection
The probability that I find most appealing, especially when comparing Chandra to Linvala, is the probability of being able to cast a drawn Chandra once you have at least 6 lands on the battlefield, taking into account card selection by Oath of Nissa, mulligans, and a game that ends by turn 10.
To determine this number, I coded a simulation that runs under the following assumptions:
- You are always on the play.
- You have a deck with 25 Savannah, 4 Oath of Nissa, 2 Chandra, and 29 irrelevant cards. So you simplify the mana base a little bit.
- You mulligan any hand if it contains 0, 1, 6, or 7 lands. Moreover, you mulligan any 7-card opening hand with 2 lands, at least 1 Chandra, and no Oath.
- You ignore the free scry after a mulligan for simplicity.
- You start every turn by playing a land if possible and subsequently check if you can cast Chandra. If not, you cast Oath of Nissa if you have one, play a land if possible, and finally check again if you can cast Chandra.
- When you play Oath of Nissa, you take Chandra, if possible. Otherwise, you take a land if a land is in your top 3.
- The game ends once you either have Chandra in hand and 6 lands on the battlefield or at the end of turn 10, whichever comes first. There are 3 possible outcomes: (a) you were able to cast Chandra via Oath on the first turn you had 6 mana available, (b) you were not able to cast Chandra due to a missing Oath on the first turn you had 6 mana available, or (c) you didn’t draw Chandra or 6 lands before the game ended.
- Ten million games are simulated, and the probability I’m interested in is the number of games with outcome (a) divided by the number of games with outcome (a) or (b).
Note 1: The turn-10 cutoff is somewhat arbitrary, but I believe some cutoff is necessary to obtain a number applicable to real games of Magic, and it seems to represent a reasonable length for a game of Standard. I checked a recent set of GW Tokens videos by Josh Mcclain where games ended on turn 8 on average, but I’ve also watched outlier games that take forever. The impact of this assumption is not large: If I would take turn 8 (12) as a cutoff instead, then the castable-Chandra probability would decrease (increase) by 1 percentage point only.
Note 2: Outcome (a) includes games where you play Oath of Nissa on turn 1, hit all your land drops, and then draw Chandra on turn 10. Outcome (b) encompasses games where you are hitting all your land drops, were unable to cast Chandra on turn 6, and draw Oath of Nissa on turn 7. That may not be a complete failure, but it still represents at least a partial failure in my mind as you missed your curve when it mattered most. Either way, it’s a relatively unlikely scenario in the grand scheme of things, but you have to keep it in mind when interpreting the outcomes. You could determine separate numbers for more fine-grained outcomes like a turn-6 Chandra, a turn-7 Chandra, and so on, but I like to keep models as simple as possible.
The castable-Chandra probability of interest is 68.8%. So it’s in the same range as the previous two perspectives, but still a little higher.
Weighing the Risks and Rewards
So you now have a 68.8% probability. It doesn’t describe a very high level of consistency, but that number doesn’t tell the entire story. To figure out whether Chandra is better than Linvala, you need to weigh the risks and rewards by estimating the likelihood of winning the game in various scenarios.
Using the outcomes I described earlier, where outcome (c) is irrelevant for your purposes, you need to weigh outcome (a) and (b) and compare them to the corresponding scenario with Linvala. For that, you need to estimate 3 numbers:
- Wa: The expected probability of winning a game where you cast Chandra via Oath of Nissa on the first turn you had 6 mana available.
- Wb: The expected probability of winning a game where you were unable to cast Chandra due to a missing Oath on the first turn you had 6 mana available.
- WL: The expected probability of winning a game where you cast Linvala on the first turn you had 6 mana available.
Estimating these win percentages is a matter of experience, expertise, and guesswork. You need to aggregate numbers for a lot of different games in various matchups, and your metagame expectation can also play a role: Chandra may be better against 4-Color Rites, for instance, as it can devastate their board.
Wa ∙ 68.8% + Wb ∙ 31.2% ≥ WL
Let’s plug in some numbers. Suppose that Wa=60%, Wb=45%, and WL=55%, which means that Linvala’s absolute increase in win percentage is 2/3rds that of Chandra’s when they are cast. With those numbers, it would be correct to include Chandra over Linvala. Indeed, the left side of the equation would become 55.32%, which is slightly higher than the right side of 55%. These win percentage estimates are probably in line with Raph’s mindset, and they indicate that if you believe Chandra is much better than Linvala when you can cast her, then it can be correct to run Chandra.
But you need to be really sure that Chandra is much better. Personally, I would peg the numbers at something like Wa=55%, Wb=45%, and WL=52%, especially in a metagame filled with G/W Tokens and Bant Humans where Chandra is not that insane. With those numbers, Linvala is better than Chandra. But a lot comes down to your estimates on how likely you are to win when you cast Chandra, when you have a dead Chandra in hand, and when you cast Linvala.
My experience has typically favored consistency over power, which is also why I don’t like to splash Abbot of Keral Keep via 8 red sources in White Weenie. But at least the GW Tokens deck doesn’t have to weaken its mana base with red tapped duals, it’s about a 6-drop rather than a 2-drop, and I respect Raph’s claim that Chandra’s power is much higher than the next-best alternative. I still think I’d prefer a sure-fire Linvala over 2/3 of a Chandra, but it’s a lot closer than many other splashes I’ve seen.
The Dromoka’s Command Problem
Dromoka’s Command is one of the most-played cards in Standard, with 28 copies in the Top 8 of Grand Prix Costa Rica. So if opponents know that you have Chandra in your deck, then they can use their Commands aggressively to destroy your Oath of Nissa to deny you access to red mana.
How big of an issue is this? According to Lévy, it’s not that relevant: “Even though players at Grand Prix Costa Rica knew my deck list, no one targeted my Oath of Nissa.” Opponents may still do it if you reveal Chandra to Oath of Nissa, but in case your hand is unknown, the +1/+1 counter may be more valuable to your opponent than a forced sacrifice of an Oath of Nissa that won’t even do anything in over half of the games.
In other words, the presence of Dromoka’s Command can be a tiebreaker, but I wouldn’t view it as a deal-breaker.
Under a number of assumptions, a deck with 4 Oath of Nissa and 2 Chandra is 68.8% to cast Chandra when it matters. Hence, if you believe that the best on-color 6-drop is only 2/3 as powerful as Chandra, then it can be correct to include Chandra in your main deck. If you feel that Chandra only reaches that power level in certain matchups, which is a position I would be comfortable with, then she could be a reasonable sideboard inclusion. If you feel that Chandra never reaches that power level, then you shouldn’t play her.
Ultimately, when it comes to his red splash, Raphaël Lévy may be greedy, and I probably wouldn’t play main-deck Chandra myself—but he’s not crazy.