posted 10-28-2000 02:46 AM               

A simple rock, paper, scissors (RPS) system of direct counters is a perfectly solid and legitimate basis for a strategy game provided that the rock, paper, and scissors offer unequal risk/rewards.

Consider a strictly equal game of RPS. We’ll play 10 rounds of the game, with a $1 bet on each round. Which move should you choose? It makes absolutely no difference whether you choose rock, paper, or scissors. You’ll be playing a pure guess. Since your move will be a pure guess, I can’t incorporate your expected move into my strategy, partly because I have no basis to expect you to play one move or another, and partly because I really can’t have any strategy to begin with.

Now consider the same game of RPS with unequal payoffs. If you win with rock, you win $10. If you win with scissors, you win $3. If you win with paper, you win $1. Which move do you play? You clearly want to play rock, since it has the highest payoff. I know you want to play rock. You know I know you know, and so on. Playing rock is such an obvious thing to do, you must realize I’ll counter it ever time. But I can’t counter it (with paper) EVERY time, since then you could play scissors at will for a free $3. In fact, playing scissors is pretty darn sneaky. It counters paper—the weakest move. Why would you expect me to do the weakest move? Are you expecting me to play paper just to counter your powerful rock? Why wouldn’t I just play rock myself and risk the tie? You’re expecting me to be sneaky by playing paper, and you’re being doubly sneaky by countering with scissors. What you don’t realize is that I was triply sneaky and I played the original obvious move of rock to beat you.

That may have all sounded like double-talk, but it’s game theory (in the mathematical sense) in action. And it had quite a curious property: playing rock was both the naïve, obvious choice AND the triply sneaky choice. For much more on that concept, read my article on Yomi Layer 3.

Fighting games rely heavily on RPS. They have both overall games of RPS going on as well as many rapid fire situations of RPS. Virtua Fighter 3 games can even have 5 sets of RPS take place in a period of 2 seconds! No joke!

Virtua Fighter’s overall system of RPS is as follows: attacking beats throwing, throwing beats blocking or reversing, and attacking beats blocking and reversing.

To be clear, let’s define terms.

An attack is a move that deals damage. An attack has an initial startup phase where it can’t yet do damage (a punch extending), a short phase where it actually can do damage (the sweet spot of the punch), and a recovery phase (the arm retracts). If the defender is blocking correctly, an attack will not damage him, but he can be thrown.

A throw is a special type of move that instantly grabs an opponent whether he’s blocking or not and does damage. The catch is, a throw will not grab an opponent who attacking (specifically, a throw will fail if the opponent’s move is in startup or hitting phase).

A reversal is a special type of move that grabs an incoming attack. Reversals usually look like throws, but they work at the exact opposite times. A reversal only works when the opponent’s move is in startup or hitting phase, which are, incidentally, the only times a throw would fail.

Even these explanations are simplified, but the RPS system is basically there. Attack the opponent. If they tried to throw you, you’ll hit them. If they block or reverse your attack, they nullified your attack. If you expect them to block, you can throw. If they expect you to throw, they can attack.

Dead or Alive 2 basically uses this same system, except that the risk/reward for doing a reversal is much different. Reversals are difficult and relatively rare in Virtua Fighter, but they’re incredibly easy and do a ridiculous amount of damage in DOA2. Reversals are so effective, in fact, that they can paralyze the enemy into not attacking for fear of being reversed. Of course, that’s when you throw them….

Real-time Strategy games are the other kings of the RPS system. Like fighting games there’s the concept of RPS on large scale and a small scale. On the small scale, particular units are designed to counter each other in a RPS way. A marine dies to a guardian. A guardian dies to a corsair. A corsair dies to a marine. Abstractly, there are 6 categories of unit. Ground units can either attack 1) other ground units, 2) air units, or 3) both. Air units can attack 4) other air units, 5) ground units, or 6) both. Pure ground-to-ground units usually beat both other types of ground units, yet lose to both types of air units that can attack ground. Similarly, pure air-to-air units usually beat both other types of air units, but loose to both types of ground units than can attack air.

RPS is not limited purely to units countering each other though. Real-time strategy games also have the concept of trading off powerful units now for a strong economy now, which leads to even more powerful units later. So on one extreme, a Zerg player in Starcraft might sacrifice his entire economy to get a quick attack force (“6 pool” is the term). This will likely beat a player who chose the other extreme of playing for pure economy and no immediate attack force (by building double oven triple hatcheries). A moderate build (pool on 9th peon, one sunken colony) will likely defend against the early attacker’s rush, though. Surviving the rush, the moderate build will have a much superior economy and win in the end. However, this moderate build will produce an inferior economy to the player who built 2 or 3 hatcheries and went for pure economy.

This is all very textbook and a number of other factors come into play in practice, but the underlying RPS is there, and it most certainly has unequal payoffs. In Starcraft, the early rush is a very, very risky strategy. It’s all or nothing. You’ll either win right away off it, or your rush will fail and you’ll almost surely lose. Because of this, the early rush isn’t all that common (depending on the map), but the very threat that the opponent might play the early rush is enough to stop you from playing for pure economy every time.

RPS Gone Horribly Wrong: Killer Instinct 2

Killer Instinct 2 boasted a rock, paper, and scissors system of moves. Every character had 3 moves assigned RPS designations. It was all rather arbitrary and artificial. Jago’s “rock” move would beat any other character’s “scissors” move. Jago’s “scissors” move beat any other character’s “paper” move. The entire system was so homogeneous, that there was little basis from which to choose rock over scissors. The gameplay was based on blind guessing, and felt hollow and devoid of strategy. RPS needs to be a natural part of the game, and it absolutely has to have unequal risk/rewards for each move.

For those interested in reading about the lighter side of RPS strategy, I’ll leave you with this link: http://www.worldrps.com/index1.html

posted 07-30-2002 10:19 AM               

The one point I can think might deserve adding, is that along with varying costs/payoffs to each component in the RPS set, a game is further enhanced by being able to discern your opponent's direction before it occurs. I think that varying costs/payoffs in the RPS hand-game would make it more interesting then the game on it's own, but it's nowhere near as interesting as the interactions around VF or Starcraft, where you're probing your opponent for every bit of information you can, ie, watching their animations and movements closely in VF, or scouting your opponent in the early game in Starcraft.

posted 11-10-2005 10:25 AM               

This shows exactly why these RPS games stay alive so long after they come out. It's all about adaptation. If I know you're using a computer to do your odds thing, I can win by adapting and simply choosing paper. You may be using the general ideal, but if I know and expect it, I can still profit off of it.

Now if I was playing against a "real" human with this? I'd have to play a guessing game with him. Going rock too much would make him play a lot of paper... giving me the opportunity of playng scissors, though then I'd be at risk if he happened to choose rock on me... or if I continued to play paper I could sneak in rock every once in a while to take advantage of his counter. In 1000 games, assuming both players are relatively smart and adaptive, it is unlikely that more than 100 dollars will change hands. If I play 1000 games with your little simulator, I would probably have gained at LEAST 200 - I would have recognized your pattern and adapted, while your insistence on repetition would put you further and further in debt.

posted 11-13-2005 07:00 AM               

7*0=0
21*-10=-210
72*3=216

216-210=6

The point I was making still stands that your ratio will only miniize loss. If you look at it from a statistical standpoint, your ratio (assuming you take it farther and add decimals) to eliminate the inherent advantage of scissors I demonstrated) will end up going even with the opponent no matter what he chooses.

Think about it: rock wins 10 dollars ~7% of the time, and loses 1 dollar ~70% of the time. in the long run, its a wash.

paper wins 1 dollar ~21% of the time and loses 3 dollars ~7% of the time. Again, in the long run, we break even.

Scissors gains 3 dollars ~70% of the time and loses 10 dollars ~21% of the time. Assuming things are actually balanced wth decimals, scissors will break even against your algorithm too.

posted 11-16-2005 06:53 AM               

I generally pride myself on my ability to read and react to opponents in super smash brothers: melee. I am not a top level player by any means - my timing and execution are far lower than average... yet I am VERY rarely in the bottom 75% of entrants at any given tourney.

And yet, despite that, I have 3 preset strategies that I tend to use until I can get a bead on my opponent and start dealing with his strategy. Depending on the opponent and situation, I may never need to stop using any of these (and indeed, if I'm gaining I don't) . When I mix them up... especially since they tend to have completely different advantages and disadvantages... lets just say I've managed to drive several players who were far better than myself nuts with my style of play.

posted 04-01-2006 09:57 PM               

The optimal strategy in this game is 3/14 Rock, 5/7 (10/14) Paper, and 1/14 Scissors.

If your opponent uses all Rock, then he will get -1 10/14 of the time, and +10 1/14 of the time. -1*10+10*1=0. Even.

If your opponent uses all Scissors, then he will get -10 3/14 of the time, and +3 10/14 of the time. -10*3+3*10=0. Even.

If your opponent uses all Paper, then he will get +1 3/14 of the time, and -3 1/14 of the time. 1*3+-3*1=0. Even.

No matter what your opponent plays, he will never do better than 0. This should be obvious, since the game is symmetrical.

posted 07-11-2006 05:22 AM               

The %'s of RPS aren't suddenly thrown at eachother - it happens over the span of games.

No matter what strategy you use (even in normal rock paper scissors), patterns emerge. Sure, you might try and randomly mix it up - but even random number generators are just working on algorhythms. A human simply cannot become 'random'.

Unless I've misunderstood something, the potential for payoff against these '% of the time' strats is variable depending on A) How good you are at mixing your patterns B) How good I am at anticipating.