It’s Sydney summer, and a beautiful day, the day after new year. When people catch a train, or go to the beach or otherwise take some time out from work and social gatherings. For myself, I had been wondering for some time about an advanced game of Rock Paper Scissors, based on the same choice principle, but extending that choice to more than the usual, I should say tradtional three articles. i.e [Rock or Paper or Scissors].
To do this I had to go back to game theory and look at the possibility of increasing the number of possible choices, and still make it an apparently evenly matched game, regardless of the choice, in the face of probability.
The beauty of rock paper scissors is that you only have to remember what beats what, and each choice only has to beat one other choice. So that makes it easy to remember. Only 3 things to remember, you can play a fast game.
The trouble with extending this is that you have to remember that each choice has to beat only 2 things, and therefore must be beaten by only 2 other things. This means that the set of things has to be 5. It cannot be 4. It took me quite some time to get over the fact that it could not be 4 and therefore had to be 5 things to pick from.
So just for fun, this morning after lines on a page and some trial and error, I came up with 5 things that could form the basis of an extended rock paper scissors choice game.
My first 5 top of the head things are:-
- Fire – which can burn Cup, and melt Scissors
- Rubber – which can smother Fire, and Hold Water
- Cup – which can contain Rubber and hold Water
- Scissors – which can cut the Cup and Rubber
- Water – which can corrode Scissors and extinguish Fire
As you can see each choice can be beaten by only two other choices and can beat the remaining two choices.
This gives two players an even chance at winning, but also makes it might be a better game for three players.
For instance if there are 2 players.
- Each player has a 40% [2/5] chance to beat the other player.
- Each player has a 20% chance that the other player will make the same choice.
For example if there are 3 players.
- Each player has a 16% [4/25] chance to beat both other players.
- Each player has a 48% [12/25] chance to beat only one player.
- Each player has a 4% chance that the other players will make the same choice.
I am sure this game could be a lot tougher to play, and score, and there would be much more debate about cheating and who jumped in first and other possibilities. Which is why it probably won’t evolve and further than this simple blog post. But if you get bored for example, on the New Year Holidays…
This is #23 in the Innovation Series.
If you would like to comment on this, try it out, or suggest improvements to the choice items, feel free to do so.. Comments are moderated, but if what you say helps extend the concept, lets see !..