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# Category Archives: games

## AlphaGo

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

## Computing optimal play for the greedy coins game, part 4

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 on Computing optimal play for the greedy coins game, part 4

## Computing optimal play for the greedy coins game, part 3

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

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

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

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 on Another greedy coins game update

## Greedy coins game update

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

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

## The greedy coins game

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

## Games with factorization diagram cards

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