What's so great about Rock-paper-scissors?

Personally, I think it's the Simultaneous Action Selection that is interesting, not necessarily the RPS implementation itself. (...having just been writing an initial draft for the Wiki pages on this very subject!)

[note: having written this first part, I then realised that there are two different ways in which non-transitive combat has been invoked in various threads. I shall therefore add a second section below.]

Most commonly, combat is between two players, and it can be resolved in one of two ways. Either one player sets a target for the other, or the outcome is resolved simultaneously.*

All non-transitive systems are doing is to make the simultaneous action selection involve a little more consideration than just generating a random result - of course, that doesn't stop them from frequently degenerating into a random result, but that's not a problem with the system itself!

In essence, I think that's the appeal of the system. It creates the illusion of control which, when repeated over a long series, becomes more real.

(*obviously, this doesn't stop later modification of the result, which can also be conducted sequentially or simultaneously...)

[Part the second]
The other circumstance under which non-transitive combat has been invoked is when units need to have different combat results against different other types of unit.

This is the case of a system where Infantry beat Archers beat Cavalry beat Infantry. In this example, players need to know which parts of the cycle their particular units fit into, and therefore how best to deploy them, based on information about their opponent's resources.
Again, this will begin as much more of a random set of outcomes, but over a long series of encounters players will start to be able to try and discern patterns they can use.

In both case, the advantages of non-transitive systems over other random resolution systems only becomes apparent over a much longer period. Sometimes this can work oer a series of games against the same opponent (a fine example of this would be "Blue Moon" which only begins to shine when each player has learnt how their opponent is likely to react in various circumstances.)

What's wrong about it? RPS or all systems where you must do a guess, add a level of psychology. I can't agree on that a RPS and a dice system are equal.

As for RPS we have two variants: open or closed:
We can see an open variant in the game World in War (Speltjänst). Here we have 4+4 (ground and sea battle) types of units that can kill each other in a half complex order. When you move your units into an area, both sides roll a dice to se how many attacks they have. Then they start to remove enemy units (and try to eliminate the risk for your units).
A closed variant you have to guess what units the other player is using. A good example of this is Orcs (Fantasy Flight), where when you attack see half of what units the other player has but not the other half. You can make some acceptations but never be sure. (A more known variant of a closed RPS is Stratego).

Most battle systems have a RPS hidden inside (also those with dice). Some units are better then other against each other. A good example of this is DBA (DBM, DBR, Hott). There is a complex variant of how good units are against each other and then the outcome of the dice shall be interpreted.

// Johan

p.s. A RPS without any extra (twist) is just boring.

Scurra nails the main point for me: when I hear people suggest RPS combat systems, my first thought is that the RPS applies to the units not to player decisions. (The most recent example is OutsideLime's Hedge Wizardry.)

Thus, every unit is strong against some opponents, but weak against others, which provides easy balance and forces players to think about how best to manage these resources.

To be fair to the simultaneous action selection (SAS) versions of the mechanic, it only boils down to pure randomization if both players are aware of the optimal strategy. In the case of RPS itself, this optimum is patently obvious to most players, but this need not be the case.

Suppose I propose the following game (and no shouting out the answer if you already know this one...): we each secretly select a number from 1 to 5 inclusive. If the difference between our numbers is not exactly 1, we each score as many points as the number we chose. If one player chooses a number 1 lower than their opponent, they score the sum of both player's numbers, and their opponent scores nothing. The first player to reach an agreed-upon point total wins.

While this example is still rather transparent to a student of game theory (at least in terms of optimizing each round's score), it wouldn't be expected that the optimal strategy would be at all obvious to John/Jane Q. Citizen. For most published games with a simultaneous-selection element, the complexity of the problem grows beyond the reach of even computer search. Just as the easy solubility of Nim or TicTacToe doesn't reduce Chess to "the first player wins", RPS doesn't reduce Bartle's 'Waving Hands' to "flip a coin to determine the winner".

And even if you do know the optimal strategy, if it contains a random factor, it can still be challenging to implement it. Typically, humans are HORRIBLE at generating true randomness without using mechanical aids. If it's difficult for people to uniformly select among three equivalent alternatives, it's nigh impossible for them to accurately emulate much more complex probability distributions.

I think one of the biggest differences between using dice and simultaneous action selection is player's perceptions of agency. While dice simulate the impact of events outside the control of the players (and provide something to blame other than one's own decisions), SAS simulates a host of real-life situations where we must act without knowledge of how others have committed themselves to acting, even though their actions will have a larger effect on us than likely external interference. Despite the simplistic nature of the system described above, I'd tend to classify melee combat as being better and more immersively represented by SAS than opposed dice rolls.

That said, since the optimal strategies do contain random elements, it's best to exercise the same caution when adding them to your game that you would with dice or cards: don't have an otherwise heavy game have too much hinge on a small number of SAS decisions. While there is room for learned skill in SAS-based games, they usually aren't amenable to the same kinds of analysis as 'proper' combinatorial games, despite some dedicated players' arguments to the contrary... (http://www.worldrps.com/index.php?option=com_content&task=view&id=20&Itemid=33)

We are still playing this one at the game club. I even proposed to use this game for initiations of new members. What I did not like from this RPS system is that 1 combination made the player inflict 2 wound. Which mean that if you are playing the monster, you have no interest in playing this combination.

Anyways, another implementation of RPS that I found pretty anoying was in a PS video game made by Atlus that I can't remember the name. It's a tactical game where you move unit on a battle ground and each unit has a element corresponding to a RPS pattern. The weapons and many other stuff follow also a RPS pattern.

Now when you move your units, you try to attack with the right unit and make sure they don't expose yourself to their nemesis units. But you soon come out with a headache because you cannot deploy your unit to make sure you will be completely be protected from nemesis unit. So throwing them all in the melee is the best strategy, you just make sure you attack the right units in combat.