Computer analysis of Starve the Fox reveals fox dominance in asymmetric board game
A programmer uses Monte Carlo tree search to analyze the ancient Norse game, finding foxes win ~85% against equal opponents.
What to know
- Computer analysis using Monte Carlo tree search shows foxes win ~85% of games between equal players, despite family lore suggesting sheep can win with perfect play.
- The asymmetric rules—two foxes versus 20 sheep with different movement and capture mechanics—create a heavily fox-favored game that appears solvable through brute force analysis.
- Community interest focuses on playing the game interactively online; the author commits to building a web interface for testing the analysis.
- Readers report playing variants of the game in childhood with different names and rule variants, some claiming sheep can guarantee victory—claims not yet reconciled with the computer analysis.
The dispute Whether the computer analysis's finding that foxes win 85% reflects the true nature of the game or is an artifact of simplified rules compared to family variants where sheep allegedly win with perfect play. · positions read across 15 posts and comments
The article's analysis is solid and the finding is credible; commenters want to test it by playing online.
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“Excellent read nonetheless. I like how the asymmetry makes it a good game to play with kids.”
splitbrain · Lobsters ↗
Family tradition and alternative rule variants suggest sheep can win with perfect play, contradicting the computer finding.
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“My mom used to say that the sheep are guaranteed to win if they play perfectly though I don't know where she got this from…”
priner · Lobsters ↗
Some puzzle implementations in the article contain bugs or are poorly explained.
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“I think some of the puzzles are buggy? In the sense that you are told to eat a sheep, but the check is for a specific fox to eat a sheep…”
k749gtnc9l3w · Lobsters ↗
kqr Programmer and article authorkqr's wife's late grandfather Game enthusiast
How it unfolded 6 developments, newest first · click a bar or a number to jump postscomments
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6
Readers identify advanced AI methods in the analysis
A commenter notes the analysis goes beyond simple random rollouts into machine learning techniques, indicating the depth of the computational approach taken.
“I was almost nerd sniped into doing my own bot until I saw that you had gone beyond random rollouts into ML!”
— trenchant -
Ah! Well it is a great looking and reading draft! I was almost nerd sniped into doing my own bot until I saw that you had gone beyond random rollouts into ML!
2 more of the top 3 · 6 posts in this stretch
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> b68b91c4 Sb2-c3, how would you eat anything there? > bc3debbe What do you mean? There are two moves. Fd6-e7, this fox gets trapped by Sd5-d6. Fa3-b3, success: sheep cannot move backwards to a3, and any sheep moving to e7 yields its place to the nearby fox. So after the sheep's move, each fox still has a possible move.
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Is the "loopy game" terminology indicative of the fact that you've read about combinatorial game theory? It's been ages since I thought about that stuff, but I always thought it was really neat.
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5
Readers share childhood memories and alternative rule variants
Community members report playing the game as children under different names (wolves instead of foxes) and with differing rules, particularly regarding handling infinite loops. One reader mentions their mother's claim that sheep can guarantee victory with perfect play, contradicting the computer analysis.
“I played this as a kid! except we called them wolves instead of foxes. My mom used to say that the sheep are guaranteed to win if they play perfectly though I don't know where she got this from…”
— priner -
I played this as a kid! except we called them wolves instead of foxes. My mom used to say that the sheep are guaranteed to win if they play perfectly though I don't know where she got this from (in our rules if game got stuck in a loop, the wolf had to break it iirc, which might have influenced this). Allegedly her grandma always won with sheep…
2 more of the top 3 · 3 posts in this stretch
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But it is a draft! It hasn't passed through final editing and I'm not happy with all parts of it yet so I'm having the community preview it.
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you may want to remove the 'draft' tag 😄
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Author commits to building web interface
The programmer responds that building a web version would be straightforward and commits to creating one, noting they did not anticipate community interest in playing the game online.
“Unfortunately I only have a debugging interface for playing against the computer in the terminal. It wouldn't be too hard to get something on the web, though, I just didn't expect there to be any interest. I'll see if I can take the time.”
— kqr -
Unfortunately I only have a debugging interface for playing against the computer in the terminal. It wouldn't be too hard to get something on the web, though, I just didn't expect there to be any interest. I'll see if I can take the time.
2 more of the top 3 · 4 posts in this stretch
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It is true that the wrong solution in 798be409 allows sheep to trap one fox in one move, but then the planning horizon is not clear from the text on the page… Maybe reword it as «eat a sheep within X moves without losing a fox or leaving a one-move win to sheep»? ETA: 8048ba2b has one solution that does not instantly lose, and it says that tree…
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The puzzles certainly have been buggy in the past, but I haven't found any actual bugs in a good while. Any time I run across something I think is a bug now, it's just because I didn't read the situation out fully. The check is never for a specific fox to eat a sheep. If the puzzle doesn't accept a solution using one of the foxes, it is because…
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Article posted to Hacker News
The same analysis appears on Hacker News under the title "What the Fox Say?" with minimal initial engagement.
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I think some of the puzzles are buggy? In the sense that you are told to eat a sheep, but the check is for a specific fox to eat a sheep…
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Readers request playable web version of the game
Lobsters readers express interest in testing the analysis by playing against the computer, noting the only available interactive version is a puzzle tool presenting pre-arranged positions rather than full gameplay.
“Hmm I was hoping there was a link to play the game against the computer.”
— splitbrain -
Hmm I was hoping there was a link to play the game against the computer. But the only link to a playable version seems to be https://xkqr.org/fox-game-puzzles/ which presents pre-arranged game states as puzzles to solve. Excellent read nonetheless. I like how the asymmetry makes it a good game to play with kids.
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Programmer analyzes Starve the Fox with Monte Carlo tree search
A technical article examines the ancient Norse board game using computer analysis. The author implements Monte Carlo tree search in Python with OpenSpiel, testing the game's win rates between two equal players and finding the fox wins approximately 85% of the time.
“I have an unhealthy relationship with strategy games like these. I simply must put them through computer analysis to figure them out.”
— kqr
What people are saying 4 voices from 1 site · best of 15 · verbatim
- Does the author's implementation match all traditional rule variants, particularly regarding how infinite loops are handled?
- Are the puzzle implementations correct, or do some contain bugs that mislead players?
- Where did the claim originate that sheep can guarantee victory with perfect play?
- Nov 1
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In case anyone wants to follow the discussion with puzzle IDs: ``` loadPuzzle = function(id){ id = id || location.hash.replace("#",""); var tgt=null; PUZZLES.forEach(x=>{ if (x.i == id){tgt = x;} }); if(tgt){start(tgt);}; }; installLoadPuzzle = function() { var c = document.querySelector("#next").parentElement; var i =…
- Oct 30
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Hm, no hits for "fox" in the notes. No idea where I read it then, maybe I hallucinated it?
- Oct 29
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Great read. I swear I read about this game somewhere, I think it was in a reader for the game theory course at TU Delft, about 9 years ago. And I think it also mentioned that while it seems easier for foxes, sheep will always win with perfect play. Anyway, I have a similar urge to "computer analyze" games, and like someone mentioned it feels like…
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bc3debbe seems wrong to me? And puzzle b68b91c4. You can move the fox to e3 to guarantee catching two sheep. Maybe the other fox then is guaranteed trapped or something.