#combinatorialgames — Public Fediverse posts

A nice discussion of different proofs of the Hex Theorem: https://www.pureabstracts.com/blog/hex-cannot-end-in-a-draw

#CombinatorialGames

A nice discussion of different proofs of the Hex Theorem: https://www.pureabstracts.com/blog/hex-cannot-end-in-a-draw

#CombinatorialGames

A nice discussion of different proofs of the Hex Theorem: https://www.pureabstracts.com/blog/hex-cannot-end-in-a-draw

#CombinatorialGames

One of my students coded up some Toads and Frogs games last year and this semester wanted to improve the Elephants and Rhinos positions so they were all generated with mean value of zero.

The issue is that if you generate really random E&R boards, they are often either extremely unbalanced or there are very few moves available.

They got it working! Now you can play Elephants and Rhinos games where it's complicated to find and make the best moves. Try it out here:

https://kyleburke.info/DB/combGames/elephantsAndRhinos.html

(I don't want to say it's "hard" because you can still find them in polynomial time.)

#CombinatorialGames #UndergradResearch

One of my students coded up some Toads and Frogs games last year and this semester wanted to improve the Elephants and Rhinos positions so they were all generated with mean value of zero.

The issue is that if you generate really random E&R boards, they are often either extremely unbalanced or there are very few moves available.

They got it working! Now you can play Elephants and Rhinos games where it's complicated to find and make the best moves. Try it out here:

https://kyleburke.info/DB/combGames/elephantsAndRhinos.html

(I don't want to say it's "hard" because you can still find them in polynomial time.)

#CombinatorialGames #UndergradResearch

One of my students coded up some Toads and Frogs games last year and this semester wanted to improve the Elephants and Rhinos positions so they were all generated with mean value of zero.

The issue is that if you generate really random E&R boards, they are often either extremely unbalanced or there are very few moves available.

They got it working! Now you can play Elephants and Rhinos games where it's complicated to find and make the best moves. Try it out here:

https://kyleburke.info/DB/combGames/elephantsAndRhinos.html

(I don't want to say it's "hard" because you can still find them in polynomial time.)

#CombinatorialGames #UndergradResearch

One of my students coded up some Toads and Frogs games last year and this semester wanted to improve the Elephants and Rhinos positions so they were all generated with mean value of zero.

The issue is that if you generate really random E&R boards, they are often either extremely unbalanced or there are very few moves available.

They got it working! Now you can play Elephants and Rhinos games where it's complicated to find and make the best moves. Try it out here:

https://kyleburke.info/DB/combGames/elephantsAndRhinos.html

(I don't want to say it's "hard" because you can still find them in polynomial time.)

#CombinatorialGames #UndergradResearch

One of my students coded up some Toads and Frogs games last year and this semester wanted to improve the Elephants and Rhinos positions so they were all generated with mean value of zero.

The issue is that if you generate really random E&R boards, they are often either extremely unbalanced or there are very few moves available.

They got it working! Now you can play Elephants and Rhinos games where it's complicated to find and make the best moves. Try it out here:

https://kyleburke.info/DB/combGames/elephantsAndRhinos.html

(I don't want to say it's "hard" because you can still find them in polynomial time.)

#CombinatorialGames #UndergradResearch

#Sprouts2026 was yesterday and it was great! Sprouts is our annual conference in abstract games (often #CombinatorialGames) where students present #UndergradResearch for the contributed talks.

Here are my summaries of the talks: https://combinatorialgametheory.blogspot.com/2026/04/sprouts-2026-summaries.html

Here are a bunch of my after-the-fact thoughts: https://combinatorialgametheory.blogspot.com/2026/04/sprouts-2026-afterthoughts.html

I need to make sure I figure a bunch of those things out in time for next year!

Thank you to everyone who attended and especially to all of our great speakers. Craig and I agreed that we're very lucky to get such amazing talks!

#Sprouts2026 was yesterday and it was great! Sprouts is our annual conference in abstract games (often #CombinatorialGames) where students present #UndergradResearch for the contributed talks.

Here are my summaries of the talks: https://combinatorialgametheory.blogspot.com/2026/04/sprouts-2026-summaries.html

Here are a bunch of my after-the-fact thoughts: https://combinatorialgametheory.blogspot.com/2026/04/sprouts-2026-afterthoughts.html

I need to make sure I figure a bunch of those things out in time for next year!

Thank you to everyone who attended and especially to all of our great speakers. Craig and I agreed that we're very lucky to get such amazing talks!

#Sprouts2026 was yesterday and it was great! Sprouts is our annual conference in abstract games (often #CombinatorialGames) where students present #UndergradResearch for the contributed talks.

Here are my summaries of the talks: https://combinatorialgametheory.blogspot.com/2026/04/sprouts-2026-summaries.html

Here are a bunch of my after-the-fact thoughts: https://combinatorialgametheory.blogspot.com/2026/04/sprouts-2026-afterthoughts.html

I need to make sure I figure a bunch of those things out in time for next year!

Thank you to everyone who attended and especially to all of our great speakers. Craig and I agreed that we're very lucky to get such amazing talks!

The #Sprouts2026 program is coming along! We have nine contributed talks all lined up (from undergrads) and our keynote info should be going up later this week. https://kyleburke.info/sprouts/sprouts2026/

#CombinatorialGames #UndergradResearch

The #Sprouts2026 program is coming along! We have nine contributed talks all lined up (from undergrads) and our keynote info should be going up later this week. https://kyleburke.info/sprouts/sprouts2026/

#CombinatorialGames #UndergradResearch

The #Sprouts2026 program is coming along! We have nine contributed talks all lined up (from undergrads) and our keynote info should be going up later this week. https://kyleburke.info/sprouts/sprouts2026/

#CombinatorialGames #UndergradResearch

The #Sprouts2026 program is coming along! We have nine contributed talks all lined up (from undergrads) and our keynote info should be going up later this week. https://kyleburke.info/sprouts/sprouts2026/

#CombinatorialGames #UndergradResearch

The #Sprouts2026 program is coming along! We have nine contributed talks all lined up (from undergrads) and our keynote info should be going up later this week. https://kyleburke.info/sprouts/sprouts2026/

#CombinatorialGames #UndergradResearch

A while ago, I wrote about Welter's game: a simple combinatorial game where two players take turns moving coins down a line until no moves are possible. It has some curious connections to coding theory, but for our purposes, it's just a little game to play over the holiday.

However, the game setup implicitly discriminates against people who don't have any coins, and we can't have that, so here's a web version: https://welter.fuglede.dk/

#maths #combinatorics #games #combinatorialgames

A while ago, I wrote about Welter's game: a simple combinatorial game where two players take turns moving coins down a line until no moves are possible. It has some curious connections to coding theory, but for our purposes, it's just a little game to play over the holiday.

However, the game setup implicitly discriminates against people who don't have any coins, and we can't have that, so here's a web version: https://welter.fuglede.dk/

#maths #combinatorics #games #combinatorialgames

A while ago, I wrote about Welter's game: a simple combinatorial game where two players take turns moving coins down a line until no moves are possible. It has some curious connections to coding theory, but for our purposes, it's just a little game to play over the holiday.

However, the game setup implicitly discriminates against people who don't have any coins, and we can't have that, so here's a web version: https://welter.fuglede.dk/

#maths #combinatorics #games #combinatorialgames

A while ago, I wrote about Welter's game: a simple combinatorial game where two players take turns moving coins down a line until no moves are possible. It has some curious connections to coding theory, but for our purposes, it's just a little game to play over the holiday.

However, the game setup implicitly discriminates against people who don't have any coins, and we can't have that, so here's a web version: https://welter.fuglede.dk/

#maths #combinatorics #games #combinatorialgames

A while ago, I wrote about Welter's game: a simple combinatorial game where two players take turns moving coins down a line until no moves are possible. It has some curious connections to coding theory, but for our purposes, it's just a little game to play over the holiday.

However, the game setup implicitly discriminates against people who don't have any coins, and we can't have that, so here's a web version: https://welter.fuglede.dk/

#maths #combinatorics #games #combinatorialgames

#ICCGTJ is already over! The last day of talks great! Here are my summaries: https://combinatorialgametheory.blogspot.com/2026/03/international-cgt-in-japan-day-four.html

Thanks to all the organizers and to everyone spreading #CombinatorialGames in Japan!

#ICCGTJ is already over! The last day of talks great! Here are my summaries: https://combinatorialgametheory.blogspot.com/2026/03/international-cgt-in-japan-day-four.html

Thanks to all the organizers and to everyone spreading #CombinatorialGames in Japan!

We had another great day of #ICCGTJ yesterday! Here are my quick talk summaries: https://combinatorialgametheory.blogspot.com/2026/03/international-cgt-in-japan-day-three.html

#CombinatorialGames

We had another great day of #ICCGTJ yesterday! Here are my quick talk summaries: https://combinatorialgametheory.blogspot.com/2026/03/international-cgt-in-japan-day-three.html

#CombinatorialGames

Day two of #ICCGTJ was excellent! We had multiple talks by teams of high schoolers, which is absolutely amazing. Here are my quick summaries: combinatorialgametheory.blogspot.com/2026/03/international-cgt-in-japan-day-two.html

#CombinatorialGames

Day two of #ICCGTJ was excellent! We had multiple talks by teams of high schoolers, which is absolutely amazing. Here are my quick summaries: combinatorialgametheory.blogspot.com/2026/03/international-cgt-in-japan-day-two.html

#CombinatorialGames

Here are my summaries of the first day of talks at the International Conference on CGT in Japan (#ICCGTJ): https://combinatorialgametheory.blogspot.com/2026/03/international-cgt-in-japan-day-one-talks.html

Conference site: https://deguchikikaku.sakura.ne.jp/

#CombinatorialGames

Here are my summaries of the first day of talks at the International Conference on CGT in Japan (#ICCGTJ): https://combinatorialgametheory.blogspot.com/2026/03/international-cgt-in-japan-day-one-talks.html

Conference site: https://deguchikikaku.sakura.ne.jp/

#CombinatorialGames

Added another game to my playable list of games. (I implemented this year ago, then somehow lost it.) You can now play #Slimetrail: https://kyleburke.info/DB/combGames/slimetrail.html

#CombinatorialGames

Added another game to my playable list of games. (I implemented this year ago, then somehow lost it.) You can now play #Slimetrail: https://kyleburke.info/DB/combGames/slimetrail.html

#CombinatorialGames

Added another game to my playable list of games. (I implemented this year ago, then somehow lost it.) You can now play #Slimetrail: https://kyleburke.info/DB/combGames/slimetrail.html

#CombinatorialGames

Added another game to my playable list of games. (I implemented this year ago, then somehow lost it.) You can now play #Slimetrail: https://kyleburke.info/DB/combGames/slimetrail.html

#CombinatorialGames

Added another game to my playable list of games. (I implemented this year ago, then somehow lost it.) You can now play #Slimetrail: https://kyleburke.info/DB/combGames/slimetrail.html

#CombinatorialGames

Hi folks -- I am pleased to announce the public release of Tetro Domain, a small #pico8 strategy game playable on desktop web and mobile: https://puleo.itch.io/tetrodomain

As I mentioned in a previous post, this game is built around the concept of the strategy-stealing argument: its rules have been designed so that there is a nonconstructive proof that the first player always has a winning strategy on any board the game can generate. As the proof is nonconstructive, it does not actually provide any indication of what the winning strategy *is* -- but I believe it ends up being an interesting little strategic challenge to work out the winning strategy that is guaranteed to exist.

The computer opponent you play against is not *especially* strong, but I've found it to be strong enough to sneak out the occasional win against me if I let my guard down. I'm biased, of course, but I've found playing it on mobile especially to be an entertaining way to get a quick strategy fix within a couple of minutes.

I think that *probably* the strategy-stealing argument could be pushed much further to a game with more complexity than this game has -- this design is fairly simple but I'm quite pleased with how it came together.

#gamedev #indiedev #combinatorialGames

Hi folks -- I am pleased to announce the public release of Tetro Domain, a small #pico8 strategy game playable on desktop web and mobile: https://puleo.itch.io/tetrodomain

As I mentioned in a previous post, this game is built around the concept of the strategy-stealing argument: its rules have been designed so that there is a nonconstructive proof that the first player always has a winning strategy on any board the game can generate. As the proof is nonconstructive, it does not actually provide any indication of what the winning strategy *is* -- but I believe it ends up being an interesting little strategic challenge to work out the winning strategy that is guaranteed to exist.

The computer opponent you play against is not *especially* strong, but I've found it to be strong enough to sneak out the occasional win against me if I let my guard down. I'm biased, of course, but I've found playing it on mobile especially to be an entertaining way to get a quick strategy fix within a couple of minutes.

I think that *probably* the strategy-stealing argument could be pushed much further to a game with more complexity than this game has -- this design is fairly simple but I'm quite pleased with how it came together.

#gamedev #indiedev #combinatorialGames

Hi folks -- I am pleased to announce the public release of Tetro Domain, a small #pico8 strategy game playable on desktop web and mobile: https://puleo.itch.io/tetrodomain

As I mentioned in a previous post, this game is built around the concept of the strategy-stealing argument: its rules have been designed so that there is a nonconstructive proof that the first player always has a winning strategy on any board the game can generate. As the proof is nonconstructive, it does not actually provide any indication of what the winning strategy *is* -- but I believe it ends up being an interesting little strategic challenge to work out the winning strategy that is guaranteed to exist.

The computer opponent you play against is not *especially* strong, but I've found it to be strong enough to sneak out the occasional win against me if I let my guard down. I'm biased, of course, but I've found playing it on mobile especially to be an entertaining way to get a quick strategy fix within a couple of minutes.

I think that *probably* the strategy-stealing argument could be pushed much further to a game with more complexity than this game has -- this design is fairly simple but I'm quite pleased with how it came together.

#gamedev #indiedev #combinatorialGames

Hi folks -- I am pleased to announce the public release of Tetro Domain, a small #pico8 strategy game playable on desktop web and mobile: https://puleo.itch.io/tetrodomain

As I mentioned in a previous post, this game is built around the concept of the strategy-stealing argument: its rules have been designed so that there is a nonconstructive proof that the first player always has a winning strategy on any board the game can generate. As the proof is nonconstructive, it does not actually provide any indication of what the winning strategy *is* -- but I believe it ends up being an interesting little strategic challenge to work out the winning strategy that is guaranteed to exist.

The computer opponent you play against is not *especially* strong, but I've found it to be strong enough to sneak out the occasional win against me if I let my guard down. I'm biased, of course, but I've found playing it on mobile especially to be an entertaining way to get a quick strategy fix within a couple of minutes.

I think that *probably* the strategy-stealing argument could be pushed much further to a game with more complexity than this game has -- this design is fairly simple but I'm quite pleased with how it came together.

#gamedev #indiedev #combinatorialGames

Hi folks -- I am pleased to announce the public release of Tetro Domain, a small #pico8 strategy game playable on desktop web and mobile: https://puleo.itch.io/tetrodomain

As I mentioned in a previous post, this game is built around the concept of the strategy-stealing argument: its rules have been designed so that there is a nonconstructive proof that the first player always has a winning strategy on any board the game can generate. As the proof is nonconstructive, it does not actually provide any indication of what the winning strategy *is* -- but I believe it ends up being an interesting little strategic challenge to work out the winning strategy that is guaranteed to exist.

The computer opponent you play against is not *especially* strong, but I've found it to be strong enough to sneak out the occasional win against me if I let my guard down. I'm biased, of course, but I've found playing it on mobile especially to be an entertaining way to get a quick strategy fix within a couple of minutes.

I think that *probably* the strategy-stealing argument could be pushed much further to a game with more complexity than this game has -- this design is fairly simple but I'm quite pleased with how it came together.

#gamedev #indiedev #combinatorialGames

We got our first talk scheduled for #Sprouts2026! https://kyleburke.info/sprouts/sprouts2026/ I'm looking forward to receiving more proposals.

I've also been getting questions about writing #AIPlayers and updated the directions on that page. https://kyleburke.info/sprouts/sprouts2026/sprouts2026ComputerTournament.php (Some of the notes were about last year's game, whoops!)

#CombinatorialGames #UndergradResearch

We got our first talk scheduled for #Sprouts2026! https://kyleburke.info/sprouts/sprouts2026/ I'm looking forward to receiving more proposals.

I've also been getting questions about writing #AIPlayers and updated the directions on that page. https://kyleburke.info/sprouts/sprouts2026/sprouts2026ComputerTournament.php (Some of the notes were about last year's game, whoops!)

#CombinatorialGames #UndergradResearch

One of my students wrecked me in #FjordsGame today! #CombinatorialGames

One of my students wrecked me in #FjordsGame today! #CombinatorialGames

Hi folks -- I mentioned in a previous post that I've been working for the past month or so on a new #pico8 project. I don't think I am quite ready to release it with full fanfare yet but I *do* think it's at a state now where I've got something worth showing off a bit and I'd be interested to hear any preliminary feedback that people may have about it.

The project in question is a little turn-based strategy game called Tetro Domain. It's a small turn-based strategy game about claiming territories on a board divided into territories that are mostly tetrominoes (hence the name), together with some smaller territories that contain the points you are actually fighting over.

Mathematically, this game grew out of my interest in exploring the strategy-stealing argument that applies to games like Chomp and Hex. All my previous games have had the property that their positions were guaranteed winnable for the player, but -- one way or another -- those games were essentially based on my having an explicit description of the winning strategy in hand. That's a harsh limiter on how complex I can actually make the game. Tetro Domain, on the other hand, is guaranteed winnable by a version of the strategy-stealing argument -- which is nonconstructive. So I don't need to work out an explicit winning strategy to know that one exists!

There are some more bells and whistles I'd like to add before releasing it in full, but if you're interested in playing the current build of it, you should be able to get access through this URL: https://puleo.itch.io/tetrodomain?password=RAWe7Ru68dg7DvhEbGkj

(Feel free to share it out to anyone you think might be interested!)

#gamedev #indiedev #combinatorialGames

Hi folks -- I mentioned in a previous post that I've been working for the past month or so on a new #pico8 project. I don't think I am quite ready to release it with full fanfare yet but I *do* think it's at a state now where I've got something worth showing off a bit and I'd be interested to hear any preliminary feedback that people may have about it.

The project in question is a little turn-based strategy game called Tetro Domain. It's a small turn-based strategy game about claiming territories on a board divided into territories that are mostly tetrominoes (hence the name), together with some smaller territories that contain the points you are actually fighting over.

Mathematically, this game grew out of my interest in exploring the strategy-stealing argument that applies to games like Chomp and Hex. All my previous games have had the property that their positions were guaranteed winnable for the player, but -- one way or another -- those games were essentially based on my having an explicit description of the winning strategy in hand. That's a harsh limiter on how complex I can actually make the game. Tetro Domain, on the other hand, is guaranteed winnable by a version of the strategy-stealing argument -- which is nonconstructive. So I don't need to work out an explicit winning strategy to know that one exists!

There are some more bells and whistles I'd like to add before releasing it in full, but if you're interested in playing the current build of it, you should be able to get access through this URL: https://puleo.itch.io/tetrodomain?password=RAWe7Ru68dg7DvhEbGkj

(Feel free to share it out to anyone you think might be interested!)

#gamedev #indiedev #combinatorialGames

Hi folks -- I mentioned in a previous post that I've been working for the past month or so on a new #pico8 project. I don't think I am quite ready to release it with full fanfare yet but I *do* think it's at a state now where I've got something worth showing off a bit and I'd be interested to hear any preliminary feedback that people may have about it.

The project in question is a little turn-based strategy game called Tetro Domain. It's a small turn-based strategy game about claiming territories on a board divided into territories that are mostly tetrominoes (hence the name), together with some smaller territories that contain the points you are actually fighting over.

Mathematically, this game grew out of my interest in exploring the strategy-stealing argument that applies to games like Chomp and Hex. All my previous games have had the property that their positions were guaranteed winnable for the player, but -- one way or another -- those games were essentially based on my having an explicit description of the winning strategy in hand. That's a harsh limiter on how complex I can actually make the game. Tetro Domain, on the other hand, is guaranteed winnable by a version of the strategy-stealing argument -- which is nonconstructive. So I don't need to work out an explicit winning strategy to know that one exists!

There are some more bells and whistles I'd like to add before releasing it in full, but if you're interested in playing the current build of it, you should be able to get access through this URL: https://puleo.itch.io/tetrodomain?password=RAWe7Ru68dg7DvhEbGkj

(Feel free to share it out to anyone you think might be interested!)

#gamedev #indiedev #combinatorialGames

Hi folks -- I mentioned in a previous post that I've been working for the past month or so on a new #pico8 project. I don't think I am quite ready to release it with full fanfare yet but I *do* think it's at a state now where I've got something worth showing off a bit and I'd be interested to hear any preliminary feedback that people may have about it.

The project in question is a little turn-based strategy game called Tetro Domain. It's a small turn-based strategy game about claiming territories on a board divided into territories that are mostly tetrominoes (hence the name), together with some smaller territories that contain the points you are actually fighting over.

Mathematically, this game grew out of my interest in exploring the strategy-stealing argument that applies to games like Chomp and Hex. All my previous games have had the property that their positions were guaranteed winnable for the player, but -- one way or another -- those games were essentially based on my having an explicit description of the winning strategy in hand. That's a harsh limiter on how complex I can actually make the game. Tetro Domain, on the other hand, is guaranteed winnable by a version of the strategy-stealing argument -- which is nonconstructive. So I don't need to work out an explicit winning strategy to know that one exists!

There are some more bells and whistles I'd like to add before releasing it in full, but if you're interested in playing the current build of it, you should be able to get access through this URL: https://puleo.itch.io/tetrodomain?password=RAWe7Ru68dg7DvhEbGkj

(Feel free to share it out to anyone you think might be interested!)

#gamedev #indiedev #combinatorialGames

Hi folks -- I mentioned in a previous post that I've been working for the past month or so on a new #pico8 project. I don't think I am quite ready to release it with full fanfare yet but I *do* think it's at a state now where I've got something worth showing off a bit and I'd be interested to hear any preliminary feedback that people may have about it.

The project in question is a little turn-based strategy game called Tetro Domain. It's a small turn-based strategy game about claiming territories on a board divided into territories that are mostly tetrominoes (hence the name), together with some smaller territories that contain the points you are actually fighting over.

Mathematically, this game grew out of my interest in exploring the strategy-stealing argument that applies to games like Chomp and Hex. All my previous games have had the property that their positions were guaranteed winnable for the player, but -- one way or another -- those games were essentially based on my having an explicit description of the winning strategy in hand. That's a harsh limiter on how complex I can actually make the game. Tetro Domain, on the other hand, is guaranteed winnable by a version of the strategy-stealing argument -- which is nonconstructive. So I don't need to work out an explicit winning strategy to know that one exists!

There are some more bells and whistles I'd like to add before releasing it in full, but if you're interested in playing the current build of it, you should be able to get access through this URL: https://puleo.itch.io/tetrodomain?password=RAWe7Ru68dg7DvhEbGkj

(Feel free to share it out to anyone you think might be interested!)

#gamedev #indiedev #combinatorialGames

Now #BattleSheep against a student. #CombinatorialGames

Now #BattleSheep against a student. #CombinatorialGames