Combinatorial Game Theory

We held Sprouts 2026 yesterday!  We are so lucky to get such awesome talks!  Here are my summaries of each of them: Arjun Agrawal: "Collecting Coins on Trees" Arjun introduced an impartial scoring game on a list of cards.  Each turn a player selects a card at one of the two ends of the list and adds that value to their score.  Arjun gave a O(n) strategy for the first player to win on even-length …

Sprouts 2026 was yesterday!  It was a success!  I have lots of thoughts.  Now you can read them! Stats: We had 10 contributed talks in addition to our keynote.  (1 total less than last year, which is the record so far.) We had our largest number of recorded attendees.  Right now that number is at 60, though I think I saw some people that were not officially registered.  (Not a significant problem…

Yesterday, Sunday, was the last day of the first international CGT conference in Japan.  Here are my summaries of the talks: Kentaro Hoshi: "Evolution of ANI (Artificial Narrow Intelligence) in Shogi and Social Adaptation: A case study for Symbiosis in the era of ASI (Artificial Super Intelligence)" Kentaro talked about Shogi and play has evolved in the past thirty years.  Prior to the modern age…

The talks continued to be great on day three!  Here are my summaries: Shun-ichi Kimura: "Disjunctive Sums can be Non-Commutative or even Non-Associative" Shun-ichi talked about "exotic" ending conditions that can break commutativity and associativity.  One example is subtraction games with sets not containing 1 where the terminal positions award a winner depending on whether there are tokens or n…

On day two of talks, there were multiple presentations by teams of high schoolers.  I didn't get the names of everyone in each team, but if I get those names, I'll update and add them later.  (I will point out which talks were done by the teams.) Kikuno Ooyagi: "A Nim with two different rules" This was the first of a few presentations given by teams of high schoolers!  I apologize in advance for …

I'm in Japan for the first time ever for the first ever International Conference on Combinatorial Game Theory in Japan !  Today was the first day of talks and we had a whirlwind amount of them! Koki Suetsugu started things off with the opening ceremony introduction, complete with information about Waseda and a complete history of CGT in Japan.  He and Tomoaki Abuku have done an amazing job promot…

Today was the first day of Integers 2025 .  I haven't been to Integers since 2013, so this is a very exciting trip for me.  Alfie is here and I've already met two new gamesters! But I'm getting ahead of myself.  Quick explanation: Integers is a Number Theory and Combinatorics conference, with lots of number theorists and (as I've experienced in my previous visits) a small bunch of gamesters.  Thi…

Sprouts 2025 was a big one for us!  We broke a lot of records: Most talks: 13 Most student talks: 11 Most submitted computer players: 6  (The previous record was 2!) Most participants in the human tournament: 16 Other exciting things that happened: The computer player tournament was a real competition this year!  All six submitted players seemed better than the Gorgons players that came in last y…

Yesterday was Sprouts 2025 .  In the afternoon session, we had our keynote by Matt Ferland of Dickinson College and six student talks.  Here are my (likely lacking) summaries of those talks. Matt Ferland, Keynote: "Supernim is Much Harder than Nim" Matt covered the Nim basics, then talked about superstars: games where all options are to nimbers.  Supernim is, then, the ruleset of any sums of supe…

Sprouts 2025 was today!  In recent years, we have included early morning talks for presenters who are in so far away of a time zone that they should be asleep during our normal talks.  (At this point, this just means presenters from Asia... and one who couldn't attend later in the day.)  Even at the early hour we started, Japan is 13 hours ahead of us, so it was already quite late in the evening …

The final day of CGTC 5 has come and gone.  Today featured more great research talks, followed by a short group of talks about different CGT books that are available that people might not know about.  (Some other CGT-relevant announcements were also made.)  This was actually another great decision made by Alda and Carlos; those talks really sparked a mood of camaraderie that closed down the confe…

The day two talks of CGTC 5 were also excellent!  One note I didn't mention before is that right before we started on Friday, Carlos declared that there would not be time for questions directly after individual talks.  I was a bit devastated at the time, but it actually worked out super well and we were pretty-much always on time (or more delayed by the length of breaks than anything else). Here …

We are in Lisbon for the "Granddaddy of them all": CGTC.  Ten years ago we had the first one and today we had the first day of talks for CGTC 5 .  They were excellent!  Here are my summaries: We started with the opening ceremony, an excellent introduction to the meeting and to NovaMath from administrators of the school (NOVA School of Science and Technology), Cemapre, and UAberto, as well as Carl…

Technically, yesterday, January 30, CGTC 5 hadn't started yet.  This year we were co-located with Recreational Math, which happened right beforehand, and there was a sort of bridge event last night in the form of a talk by Robin Wilson: "Lewis Carroll in Numberland", so I'm counting that as this year's day zero. Dr. Wilson talked about Charles Dodgson (Lewis Carroll), who was a Math lecturer at O…

Col is one of three basic placement games on graphs along with Snort and Node Kayles .  In all three, players take turns painting vertices their color, with a restriction based on what colors are neighboring.  In Col, you can't paint a vertex adjacent to another vertex that already has your color.  In Snort, you can't paint adjacent to a vertex in your opponent's color.  In Node Kayles, you can't…

Sprouts 2024 was on Saturday, and it was excellent!  Here are my summaries of the talks: Pritika Raj, "Red-Blue Hackenbush and the Construction of Real Numbers" Pritika covered the basics of Hackenbush and showed how to create integers from mono-colored stalks: path graphs with one end on the ground.  Then she got to dyadic rationals, and showed that they can also all be created from finite stalk…

Games at Mumbai just ended.  In a few hours, I will arrive at the airport and fly home.  My first time in India has been wonderful!  I loved it!  Here are some quick notes about my time here that I think are interesting: The traffic outside the IIT Bombay campus is the wildest I have ever experienced. Learning to look right first when I try to walk across a road is harder than I thought it would …

The talks on the final day of Games At Mumbai continued the excellence of the week!  Here are my summaries: Dhruv Basin, "On ergodicity of a 1-dimensional PCA with parity dependent updation rules" Dhruv talked about the site percolation problem--whether there are open clusters on randomly-generated graphs.  In a game version of this, vertices (integer coordinates of the Cartesian plane, so the bo…

Day 3 of Games at Mumbai had more excellent talks!  (I hope you like Wythoff's Nim! :-P) Indrajit Saha, "Subtraction Games in more than one dimension" Indrajit described a two-pile subtraction game in terms of animals taking from different piles of nuts: either 3 walnuts and 1 peanut or 1 walnut and 2 peanuts.  This generalizes to multi-dimensional subtraction games on tuples.  Indrajit has prove…

Anjali Bhagat, "Fork positions and 2-dimensional Toppling Dominoes" Anjali described Toppling Domines, giving some good examples of positions, options, and values.  Her definition included green dominoes, which is not something I'd look at before.  The best part is that she brought in actual dominoes to demonstrate along the edge of the podium.  She then introduced a 2-dimensional variant where o…