I’m a bit struggling with working out the strategy of defining the initial rules, so I felt the need to do some further research. Previously I defined combination theory as a possible area of research, so I took that path. First of all I must mention that is a pretty hard area of maths, especially for me, who has always had problems with it.
Nevertheless, Berlekamp’s et al (2001) extensive work in 2 volumes “Winning ways for your marhematical plays” might help me to get on track. They work out methematical strategies to win in some types of games with the use of combinatorial game theory. Thus they provide a pretty complicated methods of calculating these strategies, but there is some information I can extract to help me with my game.
In chapter 1 they define several conditions (p. 16) that a game should satisfy in order to calculate combination strategies described in the main body of the chapter. Since my game is similar to the games they’ve been analyzing (Ski-jumps, Toads-and-frogs), these might be helpful to clarify the objectives my game should focus on as well.
- There are just 2 players – I thought about my game to be for 2-4 players, but as I was making the prototype, I realized that current amount of positions might be not enough for more than 2 players. So I will go with the 2 player option.
- There are several, usually finitely many positions, and often a particular starting position – Positions are the core idea of my game, but I might think about a starting position. The initial idea is that players can take any position (and amount of positions) on the branches of level 1. If I introduce a starting position, random appearance of colour in the app might work as player may get advantage in the situation if there is no current colour nearby. What will second player do in case there’s no available colour near starting potition? There might be an option to use this time to make birds and the next one to take up colour positions.
- There are clearly defined rules that specify the moves that either player can make from a given position to its options – This is the main question to resolve now – the rules.
- Left and Right [e.g. players] move alternately in the game as a whole – already considered.
- In the normal play convention a player unable to move loses – This is the thing highly possible to be implemented as closer to the end of the game there might be a situation, when one of the players overtakes most of positions (as their number reduces over time), the second one will not have opportunity to move any more. To resolve this issue, this ending condition might help.
- Ending condition. The rules are such that play will always come to an end because some player will be unable to move – see above
- Both players know what’s going on, i.e. there’s complete information – In my game players act simultaniously and openly choose positions
- No chance moves – This condition will not be satisfied as there is an element of random from the colour app
So, these conditions gave me several good ideas: starting positon and idea to restrict movement to nearby positions of current colour, ending condition if no positions left for a player. And I worked out 2 movement strategies to test:
- option 1: players can take any position of a highlighted colour within one level
- option2: players can take a position of a highlighted colour only if there are such positions nearby from their already placed birds
Case study: Snakes and Ladders
As a quick case study I want to look at Snakes and Ladders, as my game turns out to be very similar to it. Particularly I’m interested in the “up and down” mechanics. They have a chance to get the “lift” to target goal, but at the same time threat to go down by the same chance.
As the game is very old, I began looking at variants (which there are quite many) in hope that some of them may have gameplay alterations. I even found a 3D version
But this search didn’t bring much outcomes as there were no substantial changes to gameplay.
So I came back to theoretical research where I found an interesting paper by K. M. Badruddin et. al. (2009), who were focusing on altering Snakes and Ladders, and analyzed the effectiveness of 4 types of possible strategies. They offer the following alteration: “If the roll of die leads to square i which has bottom of ladder on it, the agent is allowed either to seize opportunity or to avoid the jump and remain at the square i for some strategic reasons” (p.2) So that they add an element of strategic skill to an originally game of luck. They analyze 4 strategies: Greedy (Always jump), Avoid snakes, Optimist (avoid jump if there is a more beneficial ladder ahead), and No-jump. They have concluded that Optimist “outperforms all the other startegies” (p.4), which fully correlates with one of my initial ideas to make players decide to skip an opportunity to get a bigger benefit later. Since I’m supported by mathematical evidence now, that the strategy works, I’ll take that path of development route and work out a mechanics that will encourage players for this strategy.
But my game differs in the aspect of there are no “snakes”, which means players can’t go down. So the strategy can conscern taking up the time opportunity to take positions. Players can choose to use the whole amount of time to make birds and the next set to place them on positions of next colour. So that they will think ahead on which position otions of that paerticular colour they have. Or make less or even just one bird to quickly claim a desired position, which may block or somehow interrupt the opponent.
This arises the question of randomness of colours in the app. Randomness can bring more risk taking to this strategy, but may discourage players from taking it too often as they won’t be sure about what colour will be next. So I think order is preferable here, but I’ll try both options.
Having taken additional time for research now gives me much more understanding and some particular ideas try try out in play test. So now I’m polishing the rules and strategies to take out to test.
Sources:
Berlekamp, E.R., Elwyn, R., Conway, J. H., Guy, R. K. (1982) Winning Ways for your Mathematical Plays, Academic Press.
K. M. Badruddin, T. Yamada and T. Terano (2009) “Comparison of different decision making strategies by simulation on variant of “Snakes and Ladders Board Game”, ICCAS-SICE, pp. 5370-5375.