# Arena

As fighters grow stronger, the zombies may become less of a threat and more of a resource to be harvested for fighters to become even more powerful. At this point, humanity and your shelter is looking less at a daily struggle for survival, and more towards the long term goal of rebuilding a human society and dominating the area around it. To sort out who is the strongest and compare their skills, fighters from different shelters can engage in battles and tournaments to settle the age-old question of who can kick who's butt.

The Arena is where we find out who is truly strong, and who is just a poser.

## Ranking System

Each arena match is between two players and the fighters they choose to field for the match. One player is considered the challenger, and may seek to battle any other player. The winner will gain ranking points and the loser will lose points, based on their relative rankings prior to the start of the battle.

Changes in ranking are governed by the Elo system to ensure fairness and reward players for challenging powerful opponents, while not penalizing them too hard for losing against someone with a strong record.

A player's performance in a given arena match is expected to fall along a normal distribution, with relatively small standard deviations over the short term. This should allow the Elo system to effectively measure their expected performance, becoming more accurate the more players play. The formula is explained in detail below.

Ra：Player A's current rating

Rb：Player B's current rating

Ea：The change in A's rating based on the match's outcome is determined as follows：

Eb：The change in B's rating based on the match's outcome is determined as follows：

Ea+Eb is 1, and is the total of each side's expected probability of winning：

Sa：Value based on the actual outcome，defined as：Victory = 1， Draw = 0.5， Loss = 0

K：The limit for points that can be gained or lost in a single match, currently set at K=32.

R'a：The rating of player A after the arena match：

R'b：The rating of player B after the arena match：

Example：

Player A has a rating of 1500，Player B has a rating of 1600. Based on the formula above, Player A has an expected victory chance of Ea = 0.36，and Player be has an expected chance of Eb = 0.64

If Player A wins: The final change in ratings is R'a = 1500 + 32*(1-0.36) = 1500+20.5 = 1520，Player A gains 20 points and Player B loses 20 points。

If Player B wins: The final change in ratings is R'b = 1600 + 32*(1-0.64) = 1600 + 11.52 = 1612，Player B gains 12 points and Player A loses 12 points.

## Season Rewards

The Arena is divided into seasons, each lasting a month. Rankings are reset after each PvP season, with rewards distributed based on ranking and leaderboard position.

Valuable NFTs are among the rewards that can be won by highly ranked players!

Season rewards is affected by DBAS mechanism.

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