Calculate the odds of winning a battle in Andromeda's Edge.
In Andromeda's Edge, combat is resolved by rolling dice. Each participant has between one and six dice, and also has a "targeting" value ranging from one to five. The player with the single highest die result is the winner; in the case of a tie, the tied dice are discarded, and the next-highest die is used to determine the result. If all of the dice come up exactly the same, then everyone loses.
The table below shows the odds of the "active" player in a combat winning, given different targeting and number of dice. Click on the desired targeting values and then find the cell matching the number of dice being rolled by the two players. These tables were designed to be printed onto reference cards, but the current implementation is an online interactive page, below:
Click for interactive probability table
The background color of the cell indicates the likelyhood of the active player winning, in case you just want to "go by vibe".
Note that in Andromeda's Edge, combats can involve more than two players, and in 2-v-2 mode, there can be joint combats with up to twelve dice, with each ally having their own targeting value. This program does not yet account for these situations. Computationally, the odd for these variants are not difficult to calculate; however, the number of different combinations to consider goes up quickly, making it difficult to present tables in a form that could be printed. If this program were converted to Javascript, or perhaps embedded in a mobile app, then the parameters could be selected on a form, and the results could be calculated on the fly. This program is open source, and pull requests are welcome. Feel free to fork or adapt it to your own purposes.
This project started out as an experiment to determine if Chatgpt could be coerced into calculating the odds of winning a combat in Andromeda's Edge with targeting. Initial attempts were done via brute force, and resulted in the AI telling me I had used too much compute time, and locking me out of further experiments for 24 hours. After that, I was able to get it to write the binomial_probability function that is at the core of this program today. My theory was that, in using probability theory instead of brute force, Chatgpt would have enough available processing power to complete the assignment. While it was able to calculate the combinatorics involved with two players rolling six dice (resulting in the probability_table function), the recursion required to calculate outcomes was beyond it, and I was forced to finish the algorithm and add the targeting calculations myself.
- A simple Python script will print out a probability table in plain text, using the targeting values stipluated on the command line.
- The same program has an
--htmlflag that will print the same table wrapped in HTML table elements. - An external stylesheet is applied to add color and graphic elements to the HTML table.
- A build script calls the program repeatedly to produce all combinations of the different possible targeting values for two players.
- The resulting pages are committed directly to the
mainbranch and served via Github Pages.
This could, clearly, be more sophisticated than it is, but it suffices for the task at hand.
No rights are reserved over any of the code presented in this project; see the License for more information. The copyright to Andromeda's Edge is held by its publisher, Cardboard Alchemy.
Portions of the css styling used in this project are distributed under the MIT License.
Everyone in my gaming group is immensely grateful to Luke and Maximus Laurie for designing Andromda's Edge, which is, perhaps, the best board game ever made. The biggest controversy among our members is whether Andromeda's Edge or its predicessor, Dwellings of Eldervale, is the better game. We are, however, all agreed that both games are absolutely amazing, and will both continue to be brought to our table often.
Prior art for calculating combat odds in Dwellings of Eldervale was presented by Jonathan / @Arcanist Lupu, which was very useful for confirming that the results produced by the binomial_probability were accurate.
Thanks to Simon Whitaker for github-fork-ribbon-css.