STATISTICAL MODELING OF GAME PLAY

By David L. Peterson,

Inventor/President,

Parpen Solutions

As game designers, we need to convince ourselves that our games play as intended: Too easy? Too difficult? Is there a catch-up feature? Is the duration right? Is it fun?

Many games involve an element of chance or randomness. This is intentional, of course, as unpredictability is fun and luck can beat skill on occasion. However, games with a heavy dependence on chance, such as dice and card games, present a challenge to gaining a full understanding of the game play. Building a statistical model of the game allows the designer to develop rules that result in a playable game for live game testing.

As an example, I’ve used the card game Phase 10™, which is based on the classic game of rummy. In this game there is a sequence of melds, or ‘Phases’, that must be completed in order. The ‘box and whisker’ plot below shows a Monte Carlo analysis of the number of draws required to complete each of the ten phases.

In general, the difficulty of completing each phase gradually increases as a player proceeds through the sequence. This difficulty gradient provides balance in that trailing players have opportunity to gain on the leader. The exceptions to this trend occur at Phase 7 and, in particular, Phase 8, which is much easier than the preceding and following phases. This has the effect of practically insuring that trailing players will ‘catch up’, leading to a showdown in the latter part of the game.

Now, as game designers, we can argue about whether and how this game can be improved. But we would not be able to have that discussion without this type of statistical analysis.