Category Archives: games

AlphaGo

Posted on May 27, 2017 by Brent

Many of my readers may have already heard about AlphaGo, a computer program developed by Google DeepMind which plays the ancient board game of Go. Developing a program to play Go is not that big of a deal—the first such … Continue reading →

Posted in games | Tagged AI, AlphaGo, board, game, go, Google, learning, machine | Comments Off

Computing optimal play for the greedy coins game, part 4

Posted on May 12, 2017 by Brent

Last time I explained a method for computing best play for instances of the greedy coins game, which is feasible even for large games. This general approach is known as dynamic programming and is applicable whenever we have some recursively … Continue reading →

Posted in computation, games, recursion | Tagged coins, dynamic, game, optimal, play, programming, proof, recurrence, strategy, tree, two-player, zero-sum | Comments Off

Computing optimal play for the greedy coins game, part 3

Posted on May 10, 2017 by Brent

In a previous post we saw how we can organize play sequences in the greedy coins game into a tree. Then in the last post, we saw how to work our way from the bottom of the tree upward and … Continue reading →

Posted in computation, games, recursion | Tagged coins, game, optimal, play, proof, recurrence, strategy, tree, two-player, zero-sum | 2 Comments

Computing optimal play for the greedy coins game, part 2

Posted on May 4, 2017 by Brent

I want to explain in more detail how we can think about computing the best possible score for Alice in the greedy coins game, assuming best play on the part of both players. I glossed over this too quickly in … Continue reading →

Posted in computation, games, recursion | Tagged coins, game, optimal, play, proof, recurrence, strategy, tree, two-player, zero-sum | 1 Comment

Computing optimal play for the greedy coins game

Posted on May 2, 2017 by Brent

Recall the greedy coins game, in which two players alternate removing one of the coins from either end of a row, and the player with the highest total at the end is the winner. What if we wanted to play … Continue reading →

Posted in computation, games, recursion | Tagged coins, dynamic programming, game, optimal, play, proof, recurrence, strategy, two-player, zero-sum | 2 Comments

Another greedy coins game update

Posted on April 29, 2017 by Brent

Another update on the analysis of the greedy coins game (previous posts here, here, and here). I will make another post very soon explaining how to compute optimal play. In my previous post I reported that Thibault Vroonhove had conjectured … Continue reading →

Posted in games, proof | Tagged coins, conjecture, game, proof, strategy, two-player, zero-sum | Comments Off

Greedy coins game update

Posted on April 22, 2017 by Brent

I plan to write a longer post soon, but for the moment I just wanted to provide a quick update about the greedy coins game (previous posts here and here). It turns out that the game is a lot more … Continue reading →

Posted in games, proof | Tagged coins, conjecture, game, proof, strategy, two-player, zero-sum | 18 Comments

Ties in the greedy coins game

Posted on April 20, 2017 by Brent

In my previous post I described the “greedy coins game” and conjectured that the first player always has a strategy to win or at least tie. I had been unable to prove it, but suspected there must be some nice … Continue reading →

Posted in games | Tagged coins, game, strategy, two-player, zero-sum | 24 Comments

The greedy coins game

Posted on April 17, 2017 by Brent

Here’s an interesting game I’ve been thinking about.1 There is a row of coins on the table; each coin can have any positive integer value. Two players alternate turns. On a player’s turn she must take one of the two … Continue reading →

Posted in games | Tagged coins, game, strategy, two-player, zero-sum | 19 Comments

Games with factorization diagram cards

Posted on February 17, 2017 by Brent

Since I published a deck of factorization diagram cards last September, a few teachers have picked up copies of the cards and started using them with their students. I’ve started collecting ideas for games you can play using the cards, … Continue reading →

Posted in arithmetic, counting, games, pattern, pictures, primes, teaching | Tagged cards, diagrams, factorization, games, SET, war | 4 Comments