I have a game¹ for children (age 3-7) which had some rules that seemed pretty unfair. You basically have to bet if team fish or team boat wins. And most of the time with the default rules the boat wins or maybe you get a draw. So I tweaked the rules a bit and it was more "even".
But now I want to re-build the game in Godot as some Game Programming practice and I wondered how exactly the default probabilities are for either team to win and what to do make it fair for my version of the game.
The board consists of 13 fields.
- 1 Ocean tile (the goal for Team Fish)
- 11 Water tiles (with the middle tile being the start point for the fish)
- 1 Boat tile
Each turn you roll a d6. Depending on it's color one of the 4 fished go 1 tile to the left or
the boat. The boat start with two colored fishermen so it has a 2/6 change to move a tile.
If the boat reaches a tile with a fish - the fish is catched (thrown into the boat) AND now the fishs color counts toward the boat! So the more fish it catches the likelier it'll move further.
If a fish reached the ocean tile it is safe. If you roll a color that is already safe you can chose what fish you want to move instead. That's basically the only "strategic" element. Otherwise its just dice rolling until the board is resolved and you see the outcome.
Intuitively we always moved the fish fartest to the right, to save it from the boat (at least one more turn) but how are the odds if e.g. you use a random fish or the fish closest to the ocean.
If you have a ruby installed just do ruby scores.rb HOW_MANY_GAMES_SHALL_BE_PLAYED
setting the environment_variable DEBUG=1 you can watch the game (best to use with a small number of
rounds)
Alternativly if you have no ruby you can also run it via docker like that
docker build . -t fish
docker run -e DEBUG=1 fish 1
docker run fish 1000000
Each of the following tests was done with 100_000 games to determine the probabilities:
This confirms my "feeling" when playing the original - that it was "heavily" favored towards the boat.
{:boat=>53464, :fish=>34000, :draw=>12536}This evens out the odds quite a bit BUT it won't work for the physical game as I do not have more tiles int the box (I could handcraft one with my children which would probably be some fun, but I would like to find a solution that works with the physical game as well)
{:boat=>42317, :fish=>44961, :draw=>12722}Not too bad either. Slightly higher draws but pretty close chances for fish and boat. I think this will for now be my setup for the physical game because it's super easy to setup.
{:boat=>40692, :fish=>45417, :draw=>13891}This is only listed here because that whas my original attempt to tweak the chances for the fishes when playing the game. But it's heavily in favor of one team too (this team the fishes).
{:boat=>30469, :fish=>57329, :draw=>12202}- ¹ The original game: https://www.ravensburger.de/produkte/spiele/mitbringspiele/tempo-kleine-fische-23334/index.html There you'll fine the rules in German, French and Italian