Combinatorial Game Theory
by Kyle
2M ago
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 stalks.  After that, Pritika explained how to use infinite stalks to create non-dyadic-rational real numbers.  For example, she showed that 2/3 is equal to an alternating Blue/Red/Blue ..read more
Combinatorial Game Theory
by Kyle
5M ago
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 be. All of the food was awesome!  I discovered so much! Many bathrooms have a bidet spray nozzle instead of toilet paper.  I attempted to learn to use bidets without usin ..read more
Combinatorial Game Theory
by Kyle
5M ago
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 board is infinite) are randomly either a trap, a target, or open.  Players alternate moving a token along edges that are the same respectively for each vertex.  If you land on a ..read more
Combinatorial Game Theory
by Kyle
5M ago
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 proven many excellent properties in two dimensions when there are two elements in the subtraction set.  For example, if S = {s1, s2}, then a tuple t is a P-position exactly when t ..read more
Combinatorial Game Theory
by Kyle
5M ago
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 one domino is lined up directly next to two dominoes on the same side.  These "fork dominoes" are interesting because they root domino can knock over both other two, but neither of t ..read more
Combinatorial Game Theory
by Kyle
5M ago
Today we kicked off a big day of talks at the first "official" day of Games at Mumbai.  Urban taught a CGT course (for grad students) last semester, and I believe that many of the presenters created new combinatorial games in his course, which they spoke about.  There were many very creative games! Carlos Pereira dos Santos, "A quick journey into Combinatorial Game Theory" Carlos gave us an intro to all of CGT.  (These talks are very interesting to me because I have heard many different versions and I'm always looking to improve the "Crash Course" talk I give every year at Spro ..read more
Combinatorial Game Theory
by Kyle
5M ago
On the "unofficial" first day of Games at Mumbai, we had two talks and two tournaments!  This has been a great conference already, but you are here to hear about the talks, so here we go. Karan Rawat, "All about Go!" Karan, a member of the Maharashtra Go Association, gave us an overview of Go.  He talked about the history and origins.  He compared it to Chess, which is apparently far more popular in India.  Karan talked about six of the top international Go federations and some of the top tournaments.  He explained many cultural aspects, especially high level tournamen ..read more
Combinatorial Game Theory
by Kyle
1y ago
Sprouts 2023 went great today!  Here are my summaries of the talks. Shikhar Sehgal, "Playing with Money: Using Symmetry and Combinatorial Game Theory to Solve Simplified Versions of Poker" Shikhar started by explaining the basics of poker, including the betting and bluffing and versions like Five-Card Stud and Texas Hold 'Em.  He then covered the notion of expected values.  Shikhar broke down all steps of poker into different turns, using expecting values in a scoring-game-outcome fashion.  When the tree is collapsed, the result seems to be very similar to a partizan game ..read more
Combinatorial Game Theory
by Kyle
1y ago
The last round of talks just happened!  They were great again!  Here are my summaries. Dana Ernst: "Impartial Geodetic Convexity Achievement and Avoidance Games on Graphs" Joint work with: B. Benesh, M. Meyer, S. Salmon, and N. Sieben.  Dana, who also spent time teaching at Plymouth State University, talked about impartial games on graph subsets that contain all shortest paths between vertices in the subset.  The games deal with alternating adding vertices to a set and either avoiding a set that "generates" the entire graph if you include all shortest paths between those v ..read more
Combinatorial Game Theory
by Kyle
1y ago
There were great talks again on Day 2!  Miloš Stojaković: "Strong Avoiding Positional Games" Joint work with Jelena Stratijev.  Positional games are played on a finite set X where the Winning Sets are given subsets.  Players take turns claiming elements until all are taken.  Then the winner is determined based on different classes of the positional games (e.g. the Strong Maker-Maker condition for Tic-Tac-Toe).  Miloš talked about Strong Avoider-Avoider: the first player who claims an entire Winning Set (now the "losing set") loses.  If no one does, then the ..read more

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