Inflation per player+2.0
Every player starts with +2 raw rating points for playing.
Rating system
How the Durak score works
A game is scored as a set of soft head-to-head results. Every player is compared with every other player at the table. You gain points when your finish beats what your rating predicted, and you lose points when your finish is worse than expected. The Durak result matters most, while the exact order among non-Duraks matters softly.
+2.0 inflation per playerPairwise K = 40.0Rating scale = 800.0Non-Durak order strength = 0.25Finish distance power = 1.15Durak result strength = 0.50
Settings
The exact constants
6numbers
These are the full scoring settings currently used by the rating calculation. None of the results use fixed rating brackets or hard-coded intervals.
Pairwise K40.0
The total movement scale before it is divided across opponents.
Rating scale400.0
The Elo-style scale used when comparing rating gaps.
Non-Durak order strength0.25
The maximum soft edge for finishing earlier than another non-Durak.
Finish distance power1.15
Makes adjacent non-Durak places close together and bigger gaps matter more.
Durak result strength0.50
Makes every non-Durak score 1.0 against the Durak, and the Durak score 0.0 back.
Step 1
Convert finishing order into pairwise actual scores
Aᵢⱼactual result
Let n be the number of players. Let i be the player being scored and j be one opponent. Finish positions are zero-based inside the formula: 0 means first out and n − 1 means Durak.
Against the Durak
If opponent j is Durak: Aᵢⱼ = 0.5 + 0.50 = 1.000
If player i is Durak: Aᵢⱼ = 0.5 − 0.50 = 0.000
Among non-Duraks
slots = max(n − 2, 1)
distance = |j − i| / slots
margin = 0.25 × distance^1.15
If player i got out sooner than opponent j
Aᵢⱼ = 0.5 + margin
If player i got out later than opponent j
Aᵢⱼ = 0.5 − margin
The Durak comparison is a full win or loss. Non-Durak comparisons are softer: beating the next non-Durak is a small result, while finishing much earlier than another non-Durak is a larger result. The actual in-game score shown later is the average of Aᵢⱼ across all opponents.
Four-player actual scores
What the soft results look like
1.000beats Durak
In a four-player game, there are three non-Durak positions. The soft non-Durak scores are calculated from the same formula above, not from a lookup table.
1
1st out
0.788average A
2
2nd out
0.667average A
3
3rd out
0.546average A
4
Durak
0.000average A
Step 2
Calculate the expected score from ratings
Eᵢⱼexpected result
The system then asks what result was expected before the game. A player rated higher than an opponent is expected to score above 0.500 against them. A player rated lower is expected to score below 0.500.
One pairwise expectation
Eᵢⱼ = 1 / (1 + 10^((Rⱼ − Rᵢ) / 800.0))
Average expectation for the game
Eᵢ = average(Eᵢⱼ for every opponent j)
Rᵢ = this player's rating before the gameRⱼ = opponent's rating before the gameEqual ratings give Eᵢⱼ = 0.500The rating gap scale is exactly 800.0
Step 3
Turn each pair into raw rating points
40/(n−1)pair weight
The K value is fixed at 40.0, then divided by the number of opponents so that larger tables do not become wildly more volatile. The pair weight is therefore 40.0 / (n − 1).
Pair weight
w = 40.0 / (n − 1)
Pairwise points
pointsᵢⱼ = w × (Aᵢⱼ − Eᵢⱼ)
In the debug breakdown, this same pairwise number is split into two visible parts: finish-order points w × (Aᵢⱼ − 0.5) and rating-expectation points w × (0.5 − Eᵢⱼ). Those two pieces always add back to w × (Aᵢⱼ − Eᵢⱼ).
Step 4
Add inflation and total the raw delta
+2.0per player
Every player receives +2.0 raw points for playing. This means total rating in the pool creeps upward by exactly 2.0 × n raw points before rounding.
Raw rating change
rawΔᵢ = 2.0 + Σⱼ [w × (Aᵢⱼ − Eᵢⱼ)]
Equivalent debug breakdown
rawΔᵢ = inflation + nonDurakOrder + durakResult + ratingExpectation
inflation is always +2.0nonDurakOrder comes from non-Durak vs non-Durak pairsdurakResult comes from any pair involving the DurakratingExpectation comes from rating gaps
Step 5
Round while preserving total inflation
2ntotal gain
Raw deltas are decimal numbers, but stored rating changes are whole numbers. The rounding method keeps the whole table honest: after rounding, the sum of all rating changes is exactly round(2.0 × n). Since 2.0 is already whole, that is exactly 2 × n.
Rounding target
targetTotal = round(2.0 × n)
New rating
Rᵢ,new = Rᵢ,old + roundedΔᵢ
The algorithm first floors every raw delta. It then gives the remaining points to the players with the largest decimal remainders until the rounded deltas sum to the target. There is no rating floor in this rating update formula.
Worked example
Input tuple: (1000, 1150, 900, 1200)
+8total change
The tuple is already in finishing order: first out, second out, third out, Durak. This is a four-player game, so n = 4, w = 40.0 / 3 = 13.333..., and the rounded deltas must sum to 2 × 4 = +8.
1
1st out · rating 1000
+181000 → 1018
2
2nd out · rating 1150
+31150 → 1153
3
3rd out · rating 900
+14900 → 914
4
Durak · rating 1200
−271200 → 1173
The high-rated Durak loses heavily because they were expected to do well and instead finished last. The 900-rated player still gains points despite coming third, because they avoided Durak against much stronger players. The raw deltas add to +8.00, and the rounded deltas add to +8.
Public leaderboard
Leaderboard score still includes an evidence penalty
−180/√gpenalty
Stored rating is the real rating. The public leaderboard uses a separate display score so a player with one lucky game does not immediately outrank players with more evidence.
Leaderboard score
LeaderboardScoreᵢ = round(Rᵢ − 180 / √(max(gamesᵢ, 1)))
1 game
Rating 1000
820score
4 games
Rating 1000
910score
9 games
Rating 1000
940score
25 games
Rating 1000
964score
100 games
Rating 1000
982score
Summary
What this system rewards
Everyone gets +2.0 for playingAvoiding Durak is the biggest resultNon-Durak order matters softlyBeating stronger players is rewardedLosing to weaker players is punishedRounded deltas always sum to +2 × playersLeaderboard score penalizes low sample size