#### Introduction

Ranked system in Gwent: The Witcher Card Game is a modified ELO system, where peak scores rather than current ELO (or using Gwent terms – MMR) determine the position on ladder. Starting factional MMR (fMMR) for is equal to 2400 for each one of 6 factions.

While it is obvious that in temporary (rather than peak) MMR system a player with 50% winrate would achive no more than his starting rank on average, with Peak System the situation is less clear.

In the preceeding article Random Walk or Gwent Monkey Threshold we analyzed three vivid examples and recognised that to explore full monkey capabilities some optimization of play strategy is needed. The random walker needs to always choose the faction for which:

- Current fMMR is closest to peak (amongst Top4 factions)
- Current fMMR is closest to the lowest Top4 peak (amongst 5th and 6th faction)

#### Methodology

There is a consensus amongst pro players that ELO system with **K=15** resembles MMR system used in Gwent very well. Then **net fMMR gain/loss** for every game against player at the same fMMR is equal to **7.5**.

For the sake of simplicity we assume winrate does not depend on rating and every game is played against an opponent at the exact same fMMR level. Obviously the average peak MMR would depend on the number of games played with each faction.

Unlike official ranked system, we don’t set any placements threshold. Peaks obtained below 25 games on a faction are considered as full value. While placements threshold may be useful for some niche studies, it only leads to discontinuity and complicates the analysis of results for no reason.

To achieve best possible total MMR, random walker plays N matches using following algorithm:

1)How much below peak are Top4 factions? [a,b,c,d]

2)How much below lowest Top4 peak are current 5th and 6th faction? [e,f]

3)If one of factions from Top4 and 5th/6th factions have same values, then Top4 is chosen

4)Choose index with lowest value and play a game (generate a random number and compare with winning probability)

5) Update fmmr, reorder factions with respect to peaks

6) Repeat N times

#### Results

#### Conclusions

**Total MMR**

While each next 100 games are least efficient for the total MMR climbing, the impact of griding still remains significant. According to this very simplified model, **656 **games are needed to achieve 10.000 MMR on average in a random walk. In general, the higher factional MMRs, the worse the model reproduces reality (beacuse of MMR gain damping).

Still it seems clear that **Top500** position is more probable than not with just a pure grind. On the other hand, MMR regions needed to compete in Gwent Esports (Top64 and better) are absolutely beyond reach even when consequently applying the most efficient strategy queuing strategy.

**Peak Scores**

In the following three graphs, factions are ordered from the best to the worst in terms of peak score.

While I knew that very good scores are possible only thanks to good luck, the average performance of the best faction in a random walk is impressive. Apparently, having one faction at **2500** after **200** ladder games is a standard when using queing strategy as in the model.

One out of 6 factions is then supposed to clearly lead the field – at 200 games the **second** peak would be only **2457 fMMR **on average, which is 43 fMMR below the top, and the **3rd** would be at **2435 fMMR**.

Following the monke convention we can say that every ladder monkey has an **‘alpha’ ****faction**.

**Current Scores**

Same effect applies to current scores. On average, only Top1 and Top2 faction will have positive (>2400) fMMR value, while the remaining 4 would be negative. For the most though, these negative values will not drop below 2350, simply beacuse every faction doing badly becomes neglected by queing algorithm very soon.

It is also interesting to compare peak and current scores. For the terminal values (1000 games) we can see that the gap is roughly equal to **100 MMR **for Top3 factions.

**Number of Games**

The growth of no. of games is almost linear, which means a constant (on average!) playrate. Assuming that linearity holds in full range, roughly 36/23/17/13% of games would be played with Top4 factions. Faction with the lowest active peak would be played almost 3x less often than the best one!

**Closure**

Thanks for reading! Probably that’s the last chapter of ‘Monkey’ cycle. I believe most worthy estimates (like average placements scores) are already made at this point. Stay tuned! And always remember to search for your alpha faction!