Thread by @danil_tat

DO WE REALLY NEED SCISSORS IN ROCK-PAPER-SCISSORS?
or
What is the minimum number of elements in rock-paper-scissors like systems and why?
#gamedev #gamedesign #gamebalance #games
1/18

RPS is often used in video games. Such systems are perfectly balanced but don’t make options in a game equal in power.
2/18

What the RPS-like systems do instead, is they make each option’s power a relative concept, dependent on a situation. This adds a layer to players' decisions and a sequence of interesting decisions is what makes good games!
3/18

The balance of RPS-like systems comes from the equality of the count of elements that each element beats and is beaten by.
Such balance is possible for intransitive relationships (cyclic relation of elements). The minimum number of elements for such relationships is 3.
4/18

So, this is it? We can’t get rid of scissors?😭 Is It time to give up?
But Shia LaBeouf doesn't allow us.
Agh... alright, let’s analyze the game deeper.
5/18

So here is the matrix of all possible states in the RPS.
We can see that the game is balanced since there are an equal number of states where P1 or P2 wins.
Also, elements are balanced - each element beats and is beaten an equal number of times.
6/18

But is it necessary for each element to be balanced in order for the game to be balanced?
Let’s experiment and tinker with the rules a little bit. We can use some game states with the same elements to give a win to one of the players.
7/18

But wait! The game still seems balanced - the number of wins of both players in the matrix is equal.
8/18

Indeed, this is an interesting version of the game.
Now it is not possible to play by choosing a random element, otherwise, the opponent will always choose his\her overpowered element.
9/18

The player is forced to think from a different perspective. Not just iteratively - what should I pick next, but statistically:
How often should I pick my OP?
How often should I counter the opponent's OP?
How often should I counter the opponent’s OP counter?
🤔
10/18

That is cool, but what about getting rid of scissors?😫
Wait a second... If P1 rock and P2 rock are different elements, doesn’t it mean that there are actually 6 elements in the game? -_-
And for keeping the intransitive property we need only 3!
11/18

We should keep the number of wins equal for both players and we can use states with double elements.

Wow, we designed a ROCK-PAPER game! Finally, no fckn scissors!
12/18

Is it actually working? Yeah, it does. As we can see on the graph, the game keeps an intransitive relationship - each element can be beaten by another one and beats someone.
13/18

Yeah, we created the ODD EVEN game, but what’s the point?
14/18

The point is that we created a framework for designing and balancing intransitive relationships in games:

1) Choose any number of options more than 2. The options can be different or the same for each player, equal number or not.
15/18

2) Determine results for each game state - each combination of elements including doubles.

Each element should win and lose at least once.
16/18

3) The balance of the system is determined by the total number of wins for each player. It could be the same, in order for the system to be fair, or different if it's meant to be overpowered for one of the players.
17/18

This deep dive into RPS is inspired by this great GDS talk from @Carrillo_GD

Also, you can check out my other decompositions

https://twitter.com/danil_tat/status/1596433251807424512?s=20&t=a4p3lxLDXgtbvo71LleoWw

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