Are we ever bound to lose the game?
I’m a returning reader, give me the latest updates.
I’m a first time reader, give me the spiel.
Is there a configuration of the cards that makes it impossible to win?
This question concerns the board game known as The Game. I was introduced to this game by my friend Albert, and since then it has become a favourite amongst all my friends. This is a cooperative card game, where the players win against the game when all the cards from a deck of 98 cards have been placed into piles, according to the rules of the game. One day after playing the game, I began wondering whether configurations of the deck of cards exist for which it is impossible, no matter how well or badly the players play, to win the game.
Still to this day, I have no idea how to solve this problem. However, I have realised that in consistently failing to solve this question, I run into other interesting questions, and find out about several different things along the way. Because of this I have decided to start documenting this adventure, which takes me to many places I would have otherwise possibly never met. As such, this is a work in progress.
What is presented here is a mental route that I’ve been following, which is often taking some tangents as I seem to come across interesting problems or ideas, and a section with other games. I have been mathematically trained, so at times such language is used. I have tried to make this accessible to people who haven’t come across aspects of this language, and when I find it necessary to use technical words I have set up links to their descriptions. Similarly, when there is a proof of some concept, I try to make it easily digestible. It is strongly emphasized here that if you are reading this and have any comments, thoughts, concerns, questions or corrections, I would be more than happy to hear them. If you have enjoyed what you’ve read, I’d love to hear that too, and if you feel like it you can also buy me a coffee.
If you are a first time visitor, I suggest following the enumerated route first, starting from 1. Rules, which will walk you through the basic preliminaries.
Tangents and definitions exist, around which you can roam freely.
Latest updates in reverse chronological order
- 24/11/2023: Other games deserve our love too. A detour from The Game with a brief study of the distribution of Cribbage scores.
- 09/11/2023: The latest update on the game is contained in A subsequence formulation and shows that the game is always definitely winnable with 16 ascending and 16 descending piles.