How the median cut keeps the tournament fair
Every round of a Snakoff day ends the same way: the field is cut at the median, and the better half goes through. Here is how it works, why we chose it, and what our simulations showed.
The rule
When a round closes, we sort every ranked run by score: food first, then time alive. We find the run in the middle of the field, and everyone who scored at least as much as that player goes through. In technical terms, the line is the score of the ⌈n/2⌉-th best run, and everyone at or above it advances.
Two things follow from that. At least half the field always survives a round. And if several players tie right at the line, they all go through, so on some days a little more than half advances. With an even field and no ties, it's exactly half.
Why not a fixed top N?
A fixed number, say the top 100 into Round 2, sounds simpler. The trouble is that the size of the field changes from day to day. A top 100 is brutal on a busy day and meaningless on a quiet one. Halving works at any size: the shape of the day stays the same whether 50 or 5,000 people play.
We do adjust the number of rounds to the size of the field. The day's schedule is picked from the previous day's first-round field: fewer than 40 players gives three rounds, from 40 up to 4,999 gives the usual four, and 5,000 or more gives five. That keeps the final to a size where winning it still means something, without changing the cut itself.
Why not a fixed score?
The other obvious option is a target: eat 12 food to go through. But every day is a different arena. When we measured boards with bots, the median score on a single day ranged from about 6 to 18 food. A fixed score would knock out most of the field on a hard day and wave nearly everyone through on an easy one.
The median moves with the day. In our 14-day simulation across the new modes, the first-round line on food modes stayed between 6 and 14 food, depending on the board.
Why "at least as much as the player in the middle"
We considered the statistical median, the average of the two middle scores when the field is even. It has one practical flaw: it can come out as 12.5 food, which nobody can score. We wanted a line you can read as a single number on the leaderboard and either reach or not. So the line is a real run's score, and matching it is enough.
That's also why ties at the line go through together. Two players who ate the same food and lasted the same time played equally well by the rules of the round, and splitting them by something arbitrary would be harder to defend than letting both through.
The final is different, because it has to produce a champion. There, two finalists level on food and time alive are split by who ate their last food first. When we added that tie-break, simulated days with co-champions dropped from 10 of 30 to 2 of 30, and the two left were exact matches on every measure.
Bots in small fields
A median cut needs a field. When the game is quiet, we top the first round up with bots, which we call fillers, so that there are 48 entrants: one real player gets 47 bots alongside them, and the bots' share shrinks to nothing once 48 real players have entered. Bots have human-style names, but they are always marked as bots in the app.
The bots are built to play like people, including people who make mistakes. They turn late, misjudge corners and crash, and they're tuned so that a typical one scores around the median we expect from a typical human. That number is our assumption until there's enough real data to replace it. Bots never use a second chance.
What the simulations showed
Before relying on the rule, we ran a simulated month: 200 bot players of mixed skill playing 30 days against the real server code. Each round roughly halved the field as designed, from about 145 players to 74, then 37, then 19 in the final. The first-round line sat between 7 and 15 food, around the human median we'd assumed.
The same simulation also found problems, and we fixed them. The round schedule had been counting bots as players, so the three-round day could never happen; it now counts real players only. And the top two bot players won a large share of the days, which is what a single-run final does when one player is clearly the best. We've left that alone: when one player is clearly the best, a fair final should let them win most days.
These are simulations with assumed behaviour, so we read the shapes, not the exact numbers. The median cut doesn't need us to guess right: whatever the arena and whoever turns up, half the field goes through.