Introduction
Dragonwood is a game about fighting fantasy creatures using cards and dice. I bought it for my son's sixth birthday and describe it in detail here.
Patterns of cards
The game uses a deck of adventurer cards, each of which is one of five suits and has a number 1 - 12. To fight creatures you have to discard a set of cards which have one of three patterns:
- Strike: cards are consecutive numbers (e.g. 7, 8, 9)
- Stomp: cards are all the same number
- Scream: cards are all the same colour
The first question I was curious about was, which action is easiest to get?
Empirical approach
I wanted to start with something that my son would be able to understand, so he could better understand the game. So I decided to start with a simple experimental approach.
We generated twelve random hands of five cards by shuffling the whole deck and splitting it into 12. This did mean that the hands weren't independent, but I think it's good enough. We then went through each hand and counted the patterns we saw and how big they were. There was more than one pattern, and sometime more than one pattern of the same type (e.g. two screams of different colours). In these cases, we counted both, which is why there are 13 scream patterns in 12 hands.
This is a pretty small sample size. I did want to try another set of 12 hands, but my son wasn't interested. But is agrees with my suspicions and experience in playing the game: screams are easiest to get, stomps are hardest.
Avoiding patterns
With the empirical approach we found at least one scream pattern per hand. In retrospect this is not surprising - if we'd had hands of size six, it would have been impossible to not have a scream, since there are only five different suits (this is an example of the pigeonhole principle). In contrast, you'd need to have a hand size of 13 before you couldn't avoid a stomp pattern. You can avoid a strike pattern with hand size of six, because you can have all even or all odd numbers. But you can't avoid it with a hand size of seven, because then you have to fill in one of the gaps. This again suggests that screams are most likely and stomps are least likely.