There has been some controversy and common misconceptions surrounding the way thinning cards like Roach are evaluated. This article will provide a clear description on how thinning cards reach more value than their initial value and proposes a method of calculating the true value using a mathematical formula. This method also provides further insight for veterans and newcomers alike. It needs to be said that this method still doesn’t paint the full picture but approximates it decently.
Thinning cards, thinning tools, and tutors are cards in Gwent that reduce the size of your deck during gameplay. They serve up to three purposes: (1) provide extra points over one or multiple rounds; (2) allow flexibility and access to key cards of your strategy; (3) improve future draws. A thinning card can serve one or all of these purposes. This article will use examples of thinning cards to explain how these purposes affect their true value. The examples used are Wild Hunt Riders, Royal Decree, Roach, Knickers and Oneiromency. It is useful to be familiar with these cards before reading the rest of this article.
Thinning in practice
Let’s start with Wild Hunt Riders. Wild Hunt Riders plays for 8 points for 5 provisions. It does not allow access to key cards or to be flexible, since it always summons the other copy from your deck, unless it is in your hand. Having the second copy in your hand is a downside, because Rider when played is only 4 points since its ability is blocked when in hand. It also limits your hand by 1 useful card. Besides giving points without playing it from hand, it also reduces your deck by 1 card. If a normal deck has 25 cards with 165 provisions total, the average provision of a card in the deck is 6.6. Since you draw 10 cards at the start of the game, one of which is 5 provisions, the average provisions left in deck is 100.6. Distributed over 15 cards, that makes 6.7 provisions per card in your deck on average. This average is in practice much lower, since you can have up to 2 or 3 mulligans to improve your hand at the beginning of a round. When the Riders enter the battlefield, only 14 cards are left in the deck, consisting of 95.6 provisions. The new provision average of a card in deck is around 6.8 provisions. Your future draws have improved by 0.1 provision per card. Since you have 3 draws and 2 mulligans per round, and still 2 rounds to go, it is estimated that the extra value gained by thinning your deck is 1 point. 1 point does not seem a lot, but this value is considered carry over and is amplified when combined with other thinning cards. Furthermore, if your deck is polarized in its provisions, which to an extent all decks are, thinning your deck is actually more beneficial.
Let’s consider the worst case scenario: your opening hand contains only 4 provision cards and one 5 provision Rider, and all your good gold cards are left in your deck. 124 of the 165 provisions are unavailable for the first round. However, you do have a Wild Hunt Rider in hand. When Wild Hunt Rider summons its other copy from the deck, only 14 cards remain accumulating 119 provisions. The deck provision average has been increased from 8,3 to 8,5 provisions per card. Applying the same method as earlier, Wild Hunt Riders now estimates 2 points of carry over.
These scenarios show that thinning your deck is beneficial. They show that Wild Hunt Riders’ ‘thinning value’ is somewhere between 0 and 2 points. The 0 points is arrived when wild hunt riders are played in the last round, when the thinning value cannot be utilized. To drive the point home, let’s consider Wild hunt Riders one last time, but now with the inclusion of Royal Decree.
In this scenario you play Royal Decree to thin out both Riders in the first round. Royal decree is 10 provisions and riders are both 5, meaning the rest of the cards are worth 6.6 provision on average. Both Riders are in your deck and Royal Decree is in your hand. Therefore, around 96 provisions remain in the deck. After this, you play Royal Decree into the Riders. The provisions have dropped to 86 and the card total to 13. The average provision value per card has increased from 6.4 to 6.6, meaning that the thinning value equals 2 points in this scenario. The real value of this play is not 8 points solely from the riders, but actually 10 points, which is in par with the provision cost of royal decree. This shows that using multiple thinning cards is beneficial (to a certain extent).
Another benefit of Royal Decree, which has been overlooked thus far, is its flexibility described in purpose 2. Holding on to Royal Decree will guarantee access to one of your critical golds if you do not draw them, or enable you to answer a threat of your opponent’s with one of your ‘tech cards’. This benefit cannot be evaluated quantitatively, but is too large to be neglected in this article. Consistency is key to building a competitive deck, which is why these thinning cards score higher than thinning cards that do not share this quality.
How to calculate the thinning value
The calculations in the examples show the thought process of the method, but do not explain step by step how the numbers are derived. In this section, the calculation is dissected into a systemic method and ultimately combined in a single formula.
First, the relevant thinning cards are isolated from the deck, and the sum of their provisions is subtracted from the total provisions of your starting deck. The new value is the total provisions of the rest of the cards, which will be divided by the number of those cards to obtain the average provision value of the remaining cards. Thus:
P stands for provisions and N stands for number of cards.
With the average provisions of the remaining cards, the distribution of provisions between hand and deck can be calculated. In this case, we must distinguish between the ‘thinned card(s)’ and the ‘thinner card’, i.e. the card that is played from hand which thins the thinned card(s), because these cards are not always identical. Some thinned cards have multiple options of thinner cards in a deck. Roach, for example, can be pulled by any gold card. In that case, it is advised to choose the most frequently used thinner card in the calculation.
There is one card which has no thinner card: Knickers. The calculation of the value of Knickers is disconnected from this method, and needs a different approach. In the example with Royal Decree and Wild Hunt Riders, Royal Decree is the thinner card while the Riders are the thinned cards. With this distinction, the amount of provisions left in your deck before thinning equals the provision of the thinned cards plus the number of other cards times the average provisions of a remaining card. Thus:
The Provisions left in deck after thinning is obtained by subtracting the provisions of the thinned cards from the equation:
Now that the provisions before and after thinning are determined, the next step is to calculate the change in average provisions per card in your deck. Divide the provisions before and after thinning by the number of cards left in deck respectively and subtract the fractions from each other:
The total thinning value is the provision change times the number of new cards drawn during the rest of the game. Which is estimated to be 10 after the first round. It is possible to draw the same card again after the mulligan phase, which decreases the thinning value. This, however, is based on chance. The final step is this:
By adding the thinning value to the thinner card’s initial value, you get a better representation of their combined power. It is possible that the thinning value is negative. In that case thinning your deck takes away value of your future draws. This downside of some cards can be minimized when the number of new cards drawn equals zero. Understanding when thinning is beneficial is a tool gwent players can use to play more optimally and ultimately win more games.
As mentioned earlier, this method still doesn’t describe every interaction: for instance, some thinning cards can be summoned multiple times over multiple rounds. For example, Flying Redanian can be summoned from the graveyard as well as from the deck. This multiple-level carryover can be included in the calculation as just 6 extra points but that is just a simplification of a complex system. Another card that falls outside this approach is Knickers. Knickers thins itself and at a random time. It does not have a so-called thinner card. However, this approach can still be used to calculate its thinning value, since the thinner card’s provision is not used in the formula. There are some other things not which are not taken into account. For instance, the extra value of knickers can take opponents by surprise and its armor can potentially be 1 more point of damage mitigation.
Furthermore, purpose 2 cannot be evaluated because of its qualitative nature. The overall value of cards which serve this purpose must be assumed higher than the approximate value obtained by this method. Likewise, the value of thinning cards is best described as a range of probable values. Within this range not all values are equally likely. The true value depends on the scenario in which the thinning cards are played. This method excels in calculating the value in specific scenarios but is weaker at finding the average thinning value of thinning cards. After all, this is only one method on how to calculate thinning values. Perhaps I will discuss the other method(s) one day.
As a bonus, we look towards the unique ability of Oneiromancy to be played twice thanks to its Echo ability. We once again consider a deck with 165 provisions and 25 cards. This time, Oneiromancy is in the starting hand and there are two 10 provision cards in the deck which we intend to play with Oneiromancy. That leaves 132 provisions among the rest of the 22 cards which is on average 6 provisions per card. Thus the hand contains on average 67 provisions and the deck 98 provisions. The average provision of a card in deck is 98/15 = 6.53 provisions.
After Oneiromancy takes one 10-provision card out of the deck, the deck only has 88 provisions over 14 cards which is 6.29 provisions per card on average. Taking a 10 provision card out of your deck in round 1 has negative thinning value. However, since Oneiromancy is placed on top of the deck after a round ends, it reduces the downside of the negative thinning value substantially.
To understand why, let’s think of it as Oneiromancy is already in hand (it is guaranteed to end there) before you draw cards in round 2, but you only draw 2 cards instead. This shift in perspective allows us to see that the number of new cards drawn has decreased from the rule of thumb of 10 cards to 9 cards. Thus, when calculating the thinning value of Oneiromancy in this example, we take the difference in average provisions which is -0.248 and multiply it by 9. The result is -2.2 points of thinning value on average instead of -2.5 points when Oneiromancy does not end up back in your hand, for example when the opponent plays Squirrel to banish it.
This seems like it is still a downside to the card, but in this example a 10 provision card was played with it and also it was played in round 1 where there are still 10 approximately future draws left. Understandably, players tend to play the first Oneiromancy in round 2 for optimally a low provision card. This removes the downside completely. And, last but not least, don’t forget the flexibility of the card described by purpose 2 in the introduction. Having 2 flexible cards to play is a major upside which cannot be calculated here. So it is safe to say that Oneiromancy is a banger card when played optimally.