Advanced RPS Strategy Guide and Analysis

What is RPS? It's the game of Rock Paper Scissors, sometimes called Roshambo. A game with which we are all likely very familiar with but probably haven't tried to fully understand, much less play competitively. The reasons for this lack of intimacy are clear: the world of a Rock Paper Scissors player at first seems to be constantly at the mercy of chance. This is a by-product of the very nature of the game, where each attack launched may be parried by an equalizing defense. The mighty Rock is covered by Paper, Paper is cut by Scissors and Scissors are smashed by Rock. Therefore on any given single RPS throw the chances of a win, lose or draw outcome are divided equally amongst themselves. With this type of balancing dynamic, it had proven quite difficult for the Rock Paper Scissors enthusiast to construct a viable strategy for the game.

However, some of the more resourceful RPS players developed an interesting approach. The idea was to utilize pre-chosen "runs" of three throws each (a throw is a declaration of rock, paper or scissors) that would be played regardless of whatever their opponent may choose at random. Certain runs were even given names to further classify them. For example, if you wanted to come out representing strength you might choose the "Avalanche" run, which consists of throwing three consecutive Rocks. The idea behind playing runs was that, instead of selecting weapons on a throw-by-throw basis, you could form a sharpened throwing strategy to combat an opponent who was choosing their throws randomly at the moment of impact. With players implementing a more focused playing structure to their games, it seemed time to construct a format in which this form of play could be accentuated. Players usually played in a best-of-three format for either three or five short rounds. An upgraded system was needed to hone the more competitive nature involved.

Professional Rock Paper Scissors

There has been developed a method of play that we feel can present the game in a structured manner and also preserve the emotional involvement put into it by the players. The result is a format called "Professional RPS". It is arranged as follows:

Professional RPS Match Play...

1. A Match will consist of 9 sets of three-throw runs. There are 27 different three-throw runs which are presented in the chart to the left. Points are scored by winning individual sets of three-throw runs with a plus score against the opponent.

2. Players shall pre-choose a run at their own discretion. They shall face one another and in a clear and deliberate manner execute their chosen run simultaneously with their opponent in the standard one-two-three-shoot procedure, stopping after each throw only briefly to declare who has the advantage, if any, after the throws are completed.

3. If one player has achieved a plus score against their opponent once they have completed their first set (three throws each), that player wins the set and receives "one" point. If no player has achieved a plus score against the other, the set is considered drawn. No one receives a set point in this case.

4. The players then begin the second set in the same manner as above, followed by the third and so on until all nine sets have been completed (or one player achieves an unbeatable point total, see below). At that point, whichever player has accumulated more set points than their opponent shall be declared the Match winner.

5. In the event of a tie score after all 9 sets have been completed, a sudden-death overtime round will occur. A pre-chosen or randomly-chosen throw may be used. As above, the players shall face one another and execute their throw simultaneously. If one player defeats the other with this throw, that player shall be declared the Match winner on tiebreaks. In the event of another tie, players shall continue on with additional throws until one player defeats the other and is immediately declared the Match winner on tiebreaks.

6. Due to the nature of the scoring, a Match shall also be declared over if one player can accumulate a total of 5 Set Points at any time during the match. This lead is mathematically impossible to overcome in the 9 set format and therefore further play is unnecessary.

Our Contribution to the Game

The Professional RPS 9 Set Match format places more emphasis on knowing your opponent than has ever been necessary before. This is highlighted by the statistics of the new format. You have to be as prepared as possible on what your opponents initial throwing preferences are and must anticipate them if you can. Here's why.

In this format, gaining the initiative is a must. If a player can take the advantage with a winning declaration on the first throw of a three-throw set, then statistically they have a HUGE advantage for the remainder of the set (as explained below). They will win the set about 67% of the time, draw the set around 22% of the time and lose the set only 11% of the time. These stats show that a player who wins the first throw of the set should either win or draw the set a whopping 89% of the time. The player that loses the opening throw of the set will be primarily hoping for a drawn set, with a win being somewhat of a longshot at only 1 out of 9 chances.

This factor is also very important for the player leading the match, since winning the first throw puts them in an excellent position to either retain or increase their Match lead with a won or drawn set. So knowing what runs your opponent is expected to throw can give you a serious advantage to bringing home the set point.

A Set Example

John and Tommy are prepared to start a match. They have each mentally selected a run and prepare to make their initial throw of the set. John has chosen the classic RPS run, while Tommy went with SPP. The players both "prime" (make the one-two-three motion) and then deliver their throws simultaneously. John's first throw, Rock, smashes Tommy's scissors and he leads the set +1 (and also now has excellent chances to win the set point). The second throw of the set has John's Paper drawing with Tommy's identical Paper. John still leads with +1, and now he cannot lose the set but only win or draw. The final throw has John's Scissors defeating Tommy's Paper, which wins John the Set Point with a +2 result. He now leads the match 1-0 (one set to none). The two players would then continue with the second set and so on until someone has either collected 5 Set Points (an insurmountable lead) or ends up with the most Set Points at the end of the nine set Match.

Rock Paper Scissors Statistics

there has been calculated a comprehensive collection of statistics for the Professional RPS format. These statistics also hold true for the Classical RPS format that uses a best-of-three-of-three sequence.

RPS is Definitive: As many players had known, if only instinctively, RPS has been shown to be a definitive outcome type of game (on average). When you take any given three-throw run against all of the other possible 27 runs (including itself), you will find that each run will win 10 times, lose 10 times and draw only 7 times. The number of times that a player will win is the same as the number of times that they will lose, but both are greater than the number of times players will draw. When considering a definitive outcome, a won or lost set will occur almost three-quarters (74%) of the time. Now let's see how some of the statistics we were quoting in the 'Contribution' section were arrived at.

RPS Initiative is Key: Considering the fact that if you take the advantage after the first throw of the set, you will be playing against nine possible runs that started with the opponents initial losing throw. See the chart below for an example using the classic RPS run against all the possible Scissor-lead runs (in which you would have won the first throw of the set):

When you have the initial advantage there will always be an exact number of final set outcomes distributed in the above manner. There will be precisely six set-point winning outcomes (one +3 result, two +2 results and three +1 results). There will also always be exactly two drawing results and only one losing result. This holds true for any run in which you win the first throw of the set. So if you are using any Scissor-lead run versus any Paper-lead run for example, you will win the first throw and then have 6 outcomes that win the set (67%), two outcomes that draw the set (22%) and only one outcome that loses the set (11%). Try it out for yourself!

Of course, the players can also tie with their first throws. If this should occur, the dynamic of the set changes again. With a tied first throw, the player who can win the second throw will have a 100% chance of either winning or drawing the set. And what if the second throw is tied as well? The players will throw one more time in an attempt to determine a point winner. How can you get an advantage here? Knowing your opponent will again help you salvage the point. We'll talk more below about the strategy of how you might predict these situations below.

Rock Paper Scissors Strategy

So how do you go about determining what your opponent will lead their run with? There are two contributing factors in predicting what the initial throw of their chosen run may be: Past Performance (Pattern) and Human Psychology (Mental). The first of these two factors is a product of analysis. If over time a player is shown to throw Rock-lead runs when trailing, for example, perhaps a Paper-lead run will be ventured to counteract this. If your opponent consistently chooses Scissors as their preferred opener for his first run (how smug are they?), then a crushing Rock-lead run will settle the score. However, how can you choose a strategy when a cagey opponent realizes the need to mask their preferences? Perhaps human psychology may come into play. In this case, the following chart may be of assistance when the opponents mind becomes the target of our strategy.

Initial Throw Prediction Chart

Rock-Lead: Full-aggression throw. The hard, weapon-like character of Rock can make it a subconscious choice when wanting to crush the opponent. It may also be chosen when the player feels backed against the wall or otherwise in imminent danger of losing. This is a fighting-back throw that tries to demonstrate brute force over tactical choices.

Paper-Lead: Low-aggression throw. Paper is a subtle throw that can turn an opponents aggression against them. However, it is the least attacking throw to the human mind, which sometimes may judge it to be a weak defensive maneuver. This view can cause it to be discarded if facing defeat or when the player feels a need to counter-attack more decisively.

Scissors-Lead: Half-aggression throw. The sleek and cutting nature of the Scissors throw utilizes a refined aggression. In comparison to the heavy-handed force of the Rock, this throw may be subconsciously viewed as a subtle finesse which is still aggressive but somewhat tempered by modern tact. A surgical strike that can accent an existing lead.

RPS Advanced Strategy: Forcing Before You Start Throwing

RPS Runs | Advanced Strategy: While the statistics above about the advantage gained by the player winning the first throw of the set will always hold true, a player will find that there are additional undercurrents of patterns that occur during gameplay. By breaking the throw chart down into separate categories, a player may discover that by carefully studying what types of runs their opponent is choosing (particularly if they are consistently throwing certain types more than others) they can gain a surprising depth of knowledge about how the game will play out concerning forced draws or forced results. Let's learn how.

There are three types of RPS run types, which has been classified as Heavy, Mixed and Straight Runs. We'll start with the most common, the Heavy category, which contains 18 of the total 27 runs.

A Heavy Run is one that utilizes two of any given throws in its run. They are further categorized down by the type of throw making the run Heavy. Using the the RPS Run Chart again you can see that the runs from the topmost entry in the chart, RRP, all the way down eighteen spots to the SPS run, are the Heavy type runs highlighted in blue. They all consist of two throws that are the same and then one other throw to complete the run (in any combination). For example, the RPR run is "Rock" Heavy because it contains two Rocks and one Paper Throw. A "Paper" Heavy example would be an RPP or PSP run, because they contain two Papers, and so on. This category does not include the RRR, PPP or SSS runs.

Mixed Runs are the next largest category with 6 entries. They are the next six runs on the chart (RPS, RSP,PRS,PSR,SRP,SPR) after the eighteen Heavy Runs and are highlighted in red. The Mixed runs are classified as such because they use all three of the throws once without duplicating any one of them. They can be in any combination as long as no throw is used more than once.

The Straight Runs are the final category. This grouping only contains three entries (RRR,PPP,SSS) and is highlighted in green. The Straight Runs are titled as such because they only contain one throw repeated three times in a row. Now that we know what the different types of runs are, let's explore how they interact with one another in a Professional RPS match.

How the RPS Run Types Will Interact

Mixed Versus Heavy: Whenever a player chooses a Mixed Run and faces any Heavy Run from the opponent, one thing is certain: There will be a definitive outcome! Mixed Runs that clash with any of the Heavy runs will either win or lose, but will not draw. However, the chances for a win or loss are split exactly at 50% each (until the first throw that is). So while we may know that no draw will occur, it's still a toss-up as to who will win. However, if this match-up occurs late in a match, especially in a tie situation, it will decide the action in one players favor. Pick a Mixed Run and have a friend use any of the Heavy Runs against it. One will win, but neither will ever draw.

Mixed Versus Straight: On the extreme flipside, when a Mixed Run goes up against a Straight Run a draw will ALWAYS occur. In this situation, neither the Mixed Run nor the Straight Run can claim set victory over the other. These two runs balance each other and must always end up a stalemate. Late in a match pitting a Mixed versus a Straight Run can cement a victory for the player in the lead as the drawn set is inevitable. Try it out for yourself.

Straight Versus Heavy: As in the Mixed Versus Heavy section above, no draws will occur when these two Runs are pitted against one another. The only rub is that the percentage chance for who will win the point are split at 50% each, before the first throw at least. The previous statistics concerning winning the initial throw will most likely decide the outcome.

Any Run Versus Any Run from the Same Group As Itself: This final interaction scenario results in one thing, some exciting RPS action! There are no certainties in this occurance, and you will want to rely on the previous statistics again to help determine a players winning chances (considering who wins the initial throw of the set). In some instances a win or loss may be more likely (as discussed), but all outcomes are still possible.