The Bus Stop Effect

Most people have heard of the butterfly effect, the idea that an event can depend on something quite small and not obviously related. The name comes from the idea that a hurricane could be caused by the simple act of a distant butterfly flapping its wings. Another example of a small change having a significant result can be seen at bus stops, although in this case the connection is much more obvious.

Often I find myself waiting at a bus stop, where the schedule states that a bus will come every 7-10 minutes, and after 15 minutes of waiting two buses will arrive. The reason for this is that we can treat the buses as being in an unstable steady state, that is there are enough buses so that on average a bus will arrive every 7-10 minutes but the exact travel time is variable. In a perfect world each bus would take exactly the same amount of time to get from one stop to another and each would collect and drop off the same number of passengers which again would take exactly the same amount of time. We don't need to move very far from this ideal model for significant disruption in the timetable to occur.

For example bus A collects its first load of passengers, however, one of them is out of credit on their travel card and has to pay by cash, and to further delay things doesn't have exact change; A then moves on towards the next stop. 7 minutes later bus B starts its route and collects it's passengers at the first stop without incident. Because A was delayed leaving the first stop the number of passengers waiting at the second stop has been increased, so it will take slightly longer to collect them. B was not delayed and so will now arrive less than 7 minutes after A left, so there will be fewer passengers than average and B will get away quicker than usual. At the next stop the time between A and B arriving will again be decreased and this will continue until eventually B catches up to A giving us the two buses phenomenon.

The reason I'm writing about buses in a gaming blog is because I would very much like to make a game which uses a simple mechanic such as this to introduce a high level of complexity into a game. In this game seemingly minor actions could eventually result in a major effect in the late game. One of the problems I have often found with board games is that they often sacrifice gameplay for complexity. I believe that a simple mechanic that involves a basic upkeep action can be used to introduce complexity while still keeping the game simple to play.

For example, let's say we have a four player share market game. To indicate the effect that the players are having buying and selling shares we could use a large complicated formula or more simply have five decks of cards, and for each share draw from the 0, 1, 2, 3, or 4 deck depending on how many players own that type of share. To make things more interesting we could have special event cards seeding around the middle of each deck so that the mean number of invested players will trigger an event first. Obviously this is just a rough example and the full game would need other factors such as a headlines deck and the risk reward options of insider trading.

Remember, next time you run after a bus and the driver take pity on you just remember, as you are busy thanking them, that you could be causing the buses to run in pairs.