Sylver Coinage is a game played between two players. On each player’s turns they list a positive integer that can’t be made as a linear combination of the previously named numbers. The first player to pick the number 1, loses. An example game could work as follows:
Player 1 picks the number 4
Now no player can pick any multiple of 4
Player 2 picks the number 5
The only numbers left that players can now pick are: {1, 2, 3, 6, 7, 11}
9 for instance can be made using one 4 and one 5.
To show that any number greater than 4 also can be made using 4’s and 5’s we see the following:
12 can be made by three 4’s
13 can be made with two 4’s and a 5
14 can be made with two 5’s and a 4
15 can be made with three 5’s
Now every number can be made as 12 + 4k, 13 + 4k, 14 + 4k, or 15 + 4k for k >= 0
Player 1 picks 11
The only numbers left that players can pick from are: {1, 2, 3, 6, 7}
Player 2 picks 7
The only numbers left that players can pick from are: {1, 2, 3, 6}
Player 1 picks 6
The only numbers left that players can pick from are: {1, 2, 3}
Player 2 picks 3
The only numbers left that players can pick from are: {1, 2}
Player 1 picks 2
The only number left that players can pick from are: {1}
So player 2 must choose 1 and therefore lose.
Design a bot that plays the game best under all circumstances. This means that whatever the starting move, the bot still makes the best move from there. There are known states that result in winning and losing positions, but there are only complete strategies for a very small number of starting states.
• The program that tests the bots is written in Python3* and each bot has a function "nextMove" that gets called.
• The inputs for the function are 1) The moves played so far, 2) The remaining possible moves if there is a finite number of them, 3) The remaining time the bot has to make a move
• The function returns an integer which represents its move
• If the function returns an integer that is not a legal move, or returns something other than an integer, they lose. Please note, if you return a numpy int convert it to just int, otherwise the code will not accept it.
• The bot has a chess clock with 30 total seconds.
• During the competition, the largest move your bot can play is 1000000.
*Specifically, the bot has to work in the conda environment that can be loaded from sylverEnv.txt.
This package contains code for testing a new bot.
To make sure that your bot is compatible with the competition testing protocol, please download the sylverEnv.txt file and run conda create --name <env> --file sylverEnv.txt in the command line.
In order to test your bot, please download the following list of files from this folder into the same folder on your device:
testingSylver-version-1.3.pynumericalSemigroupLite.py
The following files are optional but will allow you to test your bot against my bots:
bestBot.pybetterBot.pymediumBot.pyrandomBot.pyworstBot.py
Once these files are downloaded into a folder, add a file called "myOwnBot.py" which has a class "myBot" with a function "nextMove" to the folder.
Then, simply run the code testingSylver-version-1.3.py to test your bot.