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Rock,
Paper, and Scissors in Strategy Games
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 blocking and reversing beats attacking.
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).
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|
Wolf performs his
Twirl and Hurl (one of the biggest throws in Virtua Fighter
3) on Shun. |
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….
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| Dead Or Alive 2's
system of attacks, throws, and reversals is not pictured
here. |
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 way too much
about RPS strategy, I’ll leave you with this
link.
Talk
back! Discuss this article in the forums.
|
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| "I
won $40 of Sirlin. Got him with scissors 3 times in a row." |
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| "This
is too complicated. Just skip all this." |
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| "Can
you
believe that the same company who made me made this sorry game?" |
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