# Runemage Or The Maths Of Create In Gwent

### Introduction

With the April’s 2022 Forgotten Treasures expansion a lot of interesting cards with unusual effects was introduced to Gwent: The Witcher Card Game. Amongst them a new high-end gold card: Runemage, led to renaissance of interest in Create mechanics and underlying mathematics. In this article we would look in depth both into create mechanic itself and the impact of Runemage 3=>5 picks effect.

### Create

Create mechanic means playing one of 3 randomly selected cards spawned from a given card pool. There is no duplicates.

There is a total of 30 cards with create mechanic in Gwent 10.4 (including Chapter of Wizards, which only spawns a card with create – Runeword).

The card pool from which a card is Created could depend on:

• the constructed deck (Braathens, Artorius Vigo, Hattori and more…)
• opponent’s deck (Bribery, Double Cross leader ability)
• both players decks (Triss:Telekinesis)
• opponent’s faction (Imperial Diplomacy, Lydia van Bredevoort)

or be completely fixed to a group of cards (Runeword, Uma’s Curse, Aguara: True Form and more …). The pool may also depend on some characteristics of the Create card (Gerhart of Aelle, Filavandrel).

Each faction, except for Syndicate, has one Runestone card, capable of creating a random bronze card from this faction. In Syndicate instead of a Runestone there is a 8 provision 4 power unit: Walter Veritas, with identical effect.

## Runemage

Runemage is a 10 provision, 4 power neutral unit with unique Deploy effect. Since Runemage is deployed, all create effects let you choose from 5 rather than normal 3 options. This affects also Create effect of Runemage himself, so that all 5 factional Runestones could be created instantly.

Standalone Runemage value is not outstanding, nor stable enough, and he has to rely on synergies with other cards and abilities. To prove this let’s have a look at this comprehensive spreadsheet made by the_saltycaptain, which breaks down and evaluates all Runestones possibilites.

Evaluating something like Runestone value would be a part of our later study, but we shouldn’t expect too much. Meta cards in this provision range should play for 12+ effective points, which means than Runestone value should be 8+ on average. Comparison with the sheet shows that such value is hardly achievable.

Therefore, specific decks and synergies are needed, for example:

• other Create cards/abilities benefiting from additional picks
• Assimilate engines (2+ procs on Deploy)
• Special card engines (1+ procs on Deploy)

First two points obviously make Runemage a perfect pick for an Assimilate deck, where it would both proc Assimilate engines and improve average value of Create picks.

### The Math Of Create

In the mathematical sense, Creating $$n$$ cards from a given pool $$N$$ is identical with drawing $$n$$ cards from the $$N$$-cards deck during mulligans.

The difference is in the outcome we investigate: we always want to find just one best card, because only one card could be played via Create effect. Unlike draws, the overall quality of picks doesn’t matter.

#### Finding A Single Card

The chances to find one particular card are simply equal to $$\frac{n}{N}$$.

#### Finding One Of K Best Picks From N-Cards Pool

The best way to strike this problem is through its negative. What is the chance to miss all $$K$$ best picks amongst $$N$$ cards, if $$n$$ choices are spawned?

• One-by-one method

1st card couldn’t be from K: $$(N-K)/N$$

2nd card couldn’t be from K: $$(N-1-K)/(N-1)$$

‘n’th  card couldn’t be from K: $$(N-(n-1)-K)/(N-(n-1))$$

, where for each subsequent card the number of cards outside $$K$$ and the total number of cards in the pool decreases by 1.

The chance to miss all cards from $$K$$ would be equal to product of these probabilities.

• Combinatorics

In a similar way the problem could be striked from combinatorics point of view. $$(N-K)$$ cards could be chosen for $$n$$ slots in $${N-K}\choose{n}$$ number of ways, which divided by the total number of possible combinations: $${N}\choose{n}$$ gives the probability to miss all cards from K.

Both approaches lead to same final expression, which in the case of combinatorics is achieved directly:

$P_K=1-\frac{{N-K}\choose{n}}{{N}\choose{n}}$

, where once again: $$P_K$$ is the probability to find a card from the packet, $$N$$ is the total number of cards in the pool, $$K$$ is the packet size, $$n$$ is the number of cards created.

Sometimes the point gap between good and bad Create picks is substantial. In such case it could be useful to evaluate the chance of a lowroll, where only bad spawns are created.

We notice here, that this exact problem was solved in the paragraph above, but the interpretation was different. (N-K) was the number of ‘bad’ cards, when (K) was the number of good ones. Let’s invert this notation now, so that L (for Lowroll) is the number of ‘bad’ ones and (N-K) => L in the expression. Also, we are interested in failure rather than success, so no more subtraction from 1. Finally:

$P_L=\frac{{L}\choose{n}}{{N}\choose{n}}$

#### Flexibility Value

Create mechanics let you adapt card choice to opponent faced. This gives some additional value which is hard to assess. Identifying possible bronze game changers played from create cards is an element of general Gwent skill and require good card knowledge and experience.

For the sake of strict considerations, flexibility should also be defined exactly here. It wouldn’t be the choice made by player, squeezing most values out of picks presented to him. Instead by flexibility we would understand the dynamics of effective value of cards in the pool.

As a demo, let’s imagine that a certain Create targets pool consists of 8 cards. There are 4 different gameplay scenarios in our imaginary meta, and each one is equally probable (25%). For each of those scenarios, there are 2 different cards playing for 12 points value, and 6 cards playing for 4 points value.

The mean value of each card would be equal to (3/4)*4 + (1/4)*12 = 6 points. What is the value of Create card? We use recipe for ‘Finding one of K best picks amongst N cards pool’ and the number of choices would be parameter ‘n’:

As could be seen, mean value of Create card is substantially greater than average value of targets in the pool if only n>1. For in-game case of n=3, the value (=9.1) is already 3 points above average, and with n=5 (=11.1) 5 points.

Now imagine that instead of complementary gameplan scenarios, there would be just one 25% scenario in which all cards get 12p value (4p otherwise). In such case obviously, create card value is equal to average targets value (6 points)!

Flexibility value then comes from cards in the pool getting value in different scenarios possible during a game of Gwent! The more varied the value of cards with respect to different scenarios, the better Create card is!

Flexibility contribution is substantial (>3 points in the demo example!)  but hard to assess in the real meta. It would require evaluating the value of cards in a handful of typical scenarios and counting probability of each such scenario.

### Effective Create Card Value (!)

Average value is not a very good approximation of create card effective value, especially when the number of targets is relatively small with respect to ‘n’.

Let’s now assume that the picture is static and there is an effective value associated with each card from the pool. How to count the value of Create in such case?

It appears rather simple if we strike the problem in logical order. A player would always choose the best possible target. The chances to find this card amongst ‘n’-picks is simply equal to n/N (‘Finding a single card’)

If 1st best is not available, then we iteratively move to 2nd and so on up to N-n. That’s because n-1 worst targets would never be picked.

The probability that the 2nd best card would be the choice is equal to (probability that 1st wasn’t found)*(probability of finding 2nd amongst N-1 remaining cards). For 3rd:  (probability that 1st and 2nd wasn’t found)*(probability of finding 3rd amongst N-2 remaining cards). And so on…

This iterative approach is perfect for Excel spreadsheets, where N and card values could be varied.

### Create Power Evaluation Spreadsheet (!)

A copy of Google Sheet with a Template to use for your own calculations of ‘Effective Card Value’ as well as 3 examples:

• Bribery vs Dwarves
• Lydia vs Dwarves
• Diplomacy vs Dwarves

is accessible by clicking the button below:

1. Fill ‘Name’ column with names of all possible Create targets of a given card
2. Estimate ‘Value’ of each card
3. Sort ‘Name’ and ‘Value’ range by descending ‘Value’ (keep the rest of the sheet intact)
4. Replace ‘N’ parameter with the size of the card pool
5. Read effective Create card value from ‘Result’ table!

### Create & Runemage – Case Studies (Gwent 10.4)

We finish by evaluating three chosen create cards in an Assimilate deck. The context would be Dwarfs matchup (early patch Shinmiri Dwarves). All tables are accessible in attached spreadsheet (link). Direct Assimilate value of Create cards is ignored but for double procs (+3 in such case).

Evaluation of cards from the pool in the sheet is fast, rough and for the sake of demo (there are also mistakes for sure) – feel free to swap the numbers with your own!

#### BRIBERY vs Dwarves

Bribery: 12.7 points

Bribery w/Runemage: 14.4p

Δ = 1.7p

Bribery is a card with high variance, for which best picks usually could cheat provision system. It is not uncommon to find 15+ points target with 8 provision worth Bribery.

3 picks were rated as 15+ in the spreadsheet: Zoltan:Warrior, Munro Bruys and Zoltan:Scoundrel. Believe it or not, there is ~50% to find one of those cards with vanilla Bribery, and ~70% after Runemage use!

#### LYDIA vs Dwarves

Lydia: 13.7 points

Lydia w/Runemage: 15.2p

Δ = 1.5p

Lydia van Breedevort in an Assimilate deck always has at least 2 good bronze special targets (out of 8) when facing Scoia’tael: Orb of Insight and Bountiful Harvest. It is worth noting that the second one snowballs in power with Runemage. The main advantage of those 6 provision specials comes from double Assimilate proc.

When Assimilate engines are undisturbed, Lydia could reach very good value against Scoia’tael. The chances to roll one of two main targets is equal to 64% with vanilla create and 89%(!) after Runemage use.

#### IMPERIAL DIPLOMACY vs Dwarves

Diplomacy: 7.6 points

Diplomacy w/Runemage: 8.7p

Δ = 1.1p

In the context of Scoia’tael matchups, Diplomacy has some targets with good potential. In addition to best Lydia picks from the last paragraph: Orb of Insight and Bountiful Harvest, there are Sorceress of Dol Blathanna (very high value with Assimilate if not removed; possible 3x proc, snowballs with Runemage even more than vanilla Harvest), or Crushing Trap with 18 points ceiling against swarm decks. In the context of Dwarves matchup, Dwarven Chariot would also be amazing pick, and Cat Witcher Saboteur not bad (although rather overrated in the sheet) due to row stacking and random value against unaware opponents.

The Imperial Diplomacy is really good in this matchup, although the value would drop outside late use, where Crushing Trap would not achieve full value. The chances to roll one of Crushing Trap/Sorceress/Harvest/Orb of Insight are equal to 18% without

With big and not so much polarized with respect to value card pools, the net gain on Runemage is lower than in the case of Bribery and Lydia. Still, the added value is meaningful given that Diplomacy is a 4 provision bronze and 2 copies could be played.