#### Abstract

In this article we would try to assess the probabilities of win of best-of-N matches in Gwent, as well as whole tournaments. Starting from some basic assumptions, we will finally arrive at probabilities of qualifying to Open via Top64 and Top16 Qualifiers.

## Introduction

If you have ever played in a Gwent tournament, probably you asked yourself some questions: “What are my chances in Bo3 or Bo5 matches against weaker/stronger opponents?”, “How much random the final outcome is?”, “What are my chances of claiming top spots?” and so on. Well, the answer to these question is not so simple. Ideally, you would need to take into account many factors: tournament preparation, matchups, skill difference… We will do it in the simplified, but mathematically strict way.

##### Assumptions and p_{W} variable

Instead of many factors, we will use just one variable, **p _{W}**, which means probability of winning in a single game. This probability will be the same for every game in every match. For the sake of having some fun assessing your chances, you could use your ladder winrate as

**p**. We will neglect completely possiblity of draw in matches and games.

_{W}##### Geralt and Dandelion

In order to keep our proceedings more interesting, we introduce two characters. **Geralt** is *The Professional* in Gwent. His **p _{W}** is equal to

**0.6**against everyone.

**Dandelion**is an average player, often practicing together with Geralt. His

**p**is equal to

_{W}**0.4**against Geralt and to

**0.5**against other players.

##### Best-of-N matches

A single **game** of Gwent is too random. Therefore in each Gwent tournament **matches** are played between two players. Best-of-N format, usually Bo3 or Bo5 is used. The number is odd, so that there is always a winner. The play is stopped at the moment when one of players won more than half of the total number of games (for example Bo5 match ends after 3:0 result)

## Winning in a Bo3/Bo5 match

I would not present here the details of probabilistic computation i did. If you are interested in these, hit me up in the comments or Discord. All you need to know is that the solutions here are analytical, and the proper equation works for every N number in BoN.

#### Bo3/Bo5 graphs

##### Remarks

One thing to note right at the start. If you play against an equally good player, you have identical chances of winning **2:0** as **2:1** in **Bo3**. It is very counterintuitive, as always a tight struggle should be expected. Similar situation could be seen for **3:1** and **3:2** in **Bo5**. Amazing! If you are going to place a bet on the outcome of a match, and see that one player is slightly favored, go for **3:1** rather than **3:2**, and **2:0** rather than **2:1**!

#### Bo3 vs Bo5 graph

##### Remarks

Playing one game against Dandelion, Geralt obviously has **60%** win chances. In a **Bo3** match his chances increases to **65%** and in a **Bo5** to **68%**. The Bo3 and Bo5 winning probabilities are quite close to each other. Geralt wins almost the same number of games against Dandelion in Bo3 and Bo5 practice. The difference is smaller than 5% in the region of p_{W} resembling competitive play. Do not blame the small number of matches in Bo3 then, blame RNG! ðŸ˜‰

## Qualifying for Gwent Open

If you are not familiar with Gwent Masters format, please have a look at the official video or take a deep dive into the rules.

### Top64 Qualifiers

Top64 Qualifiers consist of two stages.

- 6-rounds Bo3 Swiss (Day1)
- Double Elimination Bo5 for best 8 of Day1, with two qualifying spots (Day2)

It could be shown that (neglecting draws and drops, which always happen) the final results of Day1 are strictly predetermined. In other words, the number of players with specific score is exactly known. There will be **one player** with perfect **6-0** score, **six players** with **5-1** score, and **fifteen players** with **4-2**, out of whom the lucky one with the best Buchholz gets to Top8. For the sake of simplicity, we will assume that 6-0 or 5-1 score is needed to claim the spot for Day2.

#### Top64 Swiss graph

##### Remarks

The chances for *Dandelion* to qualify for Day2 are obviously equal to **1/8 = 12.5%**. *Geralt* is clearly supreme here with **30%**+ chances. Still, missing Day2 in **7/10** cases, while having 60% winrate against top players is not especially appealing. Luckily, most often Geralt would finish the season in Top16.

#### Top64 – Double Elimination stage

What is peculiar about Double Elimination system with cutoff is that dependent on the first rounds results, different number of games is needed to claim the spot. The effect is relatively mild for 8 players – losing in quarterfinals or semifinals **5 **games are needed, final loser needs **4**, and winner only **3**.

##### Remarks

QF/SF curve represents here one path only: it has to be multiplied by 2 if summing up to ‘Qualification’ curve. Both *Dandelion *and *Geralt *are happy if reached Day2 stage. *Dandelion *has **25%** chances for getting the spot. The ‘Qualification’ curve has steep slope, so that *Geralt *already gets **55%**+ chances.

### Top16 Qualifiers

The format of Top16 Qualifiers is Double Elimination. Losing in first rounds is even bigger issue here and number of matches to be played vary from **4** (straight) to **7** (losing in R1 or QF)

#### Top 16 Double Elimination graph

##### Remarks

Top 16 Double Elimination also seems very fair. *Dandelion *obviously has **12.5%** chances here. *Geralt*‘s skill gets rewarded with **40%** chances. The probabilities of claiming spot after R1/QF loss are very low for both *Geralt* and *Dandelion*, but give rise to steeper ‘skill vs reward’ curve.

### Top16 vs Top64 Comparison

Comparing the probabilities of qualifying via Top16 and Top64 answers the question of how much grinding is worth. Do you need to fight for Top16, or could just rely on tournament preparation for Top64? Well, let’s see…

#### Top16 vs Top64 graph

##### Remarks

*‘Top16 Total’* label means here the total chances of qualification for Top16 player, including both Qualifiers. The graph shows that fighting for Top16 is definitely worth it, for both *Geralt* and *Dandelion*. Let’s look into *Dandelion* case. He is an average player and could not count for any advantage in tournaments. As Top16 player, he has **15%** chances to get to Gwent Open, as Top64 only **2.7%** (roughly **3%** without 5-1/6-0 assumption). Average players have to grind really hard to claim the spot!

Getting in the *Geralt* shoes, Top16 gives **50%** and Top64 only **17.5%**. Being *The Professional* requires going for Top16! Then every **p _{W}** percent you gain in preparation gets rewarded due to steep ‘

*Top16 total*‘ curve.

## Winning Gwent Open

The format of official main Gwent tournaments is single elimination Bo5 with 8 players, which is fast and most exciting for viewers. The competition is very straightforward here and probabilities are simple products.

#### Gwent Open graph

##### Remarks

The *‘Winner’* curve is less steep than in the case of Double Elimination format. Geralt would be an outstanding player in the Gwent elite, winning **30%**+ of tournaments, and finishing as second in **15%**.

#### Patreon

Writing in-depth Gwent articles is fun, but time consuming. If you like ‘Alphabet’ cycle and other articles, and fancy to support my efforts – here is the way to go: https://www.patreon.com/lerio2

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