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Rock-Paper-Scissor system

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questccg
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Does anyone have a set of rules that can be followed to implement (or better understand) a Rock-Paper-Scissor system?

Firstly does it still work if we add a fourth (or more) element?

Odd-wise, aren't the odds of winning 1 in 3 (or 33.33%)? So how can you gamble, if the odds are the same on each turn? Aren't bets just blind betting???

Does anyone have an more complexe examples where an RPS system has been used (and how it works)?

Empires
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There are alot more combinations....

The most common is a 5 way Rock-Paper-Scissors-Lizard-Spock.
The chart works in that each element beats two other elements.

Rock beats Scissors and Lizard
Scissors beats Paper and Lizard
Paper beats Spock and Rock
Spock beats Scissors and Rock
Lizard beats Spock and Paper

You can make a chart as large as you like, but keep in mind that each chart must have an odd number of elements, or it results in a cycle instead of a RPS.

The current number of combinations I know of are-
RPS 7
RPS 9
RPS 11
RPS 15
RPS 25
and my personal favorite : Rock Paper Scissors 101. There are 101 elements, and 5,050 outcomes.
Here is a link: http://www.umop.com/rps101/rps101chart.html

Hope this helps!

topdeck
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Examples

Magic: the Gathering's color wheel is an example of a more complex R/P/S system.

Yomi is also a more complex R/P/S system.

You are correct that in it's base, unbiased form, there is zero reason to choose one selection over another, you always have a 33.33% chance of winning. The same can be said for any number of elements in the system that have an equal number of things that they win against and lose to.

The strategy in a R/P/S system is when you know that one side is skewed ever so slightly, now it's an interesting mind game. If the distribution of an opponent's throws are going to be 40% Rock, 30% Paper and 30% Scissors, now what do you throw?

Your answer should be 100% Paper, since you have a 70% chance of not losing. That's the first level of thinking. Now if you jump to the second level of thinking, where your opponent knows what they normally throw, but now they know that you should throw 100% paper based upon that fact, are they really going to throw rock?

whoshim
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Stratego

Stratego has a small instance of RPS. The spy can kill the 10, which can kill anything else, which can kill the spy.

Spy>10>Any>Spy

The game, when played, is very RPS in the sense that you bring X, so I move over Y, so you are prepared with Z.

I usually pair my spy with my 9, so that I can handle any threat, for instance.

questccg
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Very interesting...

topdeck wrote:
The strategy in a R/P/S system is when you know that one side is skewed ever so slightly, now it's an interesting mind game. If the distribution of an opponent's throws are going to be 40% Rock, 30% Paper and 30% Scissors, now what do you throw?

Interesting. I may have such a scenario. I have three (3) types of creatures: melee (basic attack), ranged (distance attack) and flight. Now in my scenario, creatures that fly (flight) beat melee, melee beat ranged and lastly ranged beat flight.

Now in my "standard" deck, there will be 20 creatures. That is not divisible by three (firstly). Secondly there are not too many creatures who can fly and there are not many creatures that have ranged attacks... What the exact distribution will be is yet undetermined. Perhaps it will be something like 5 creatures that fly, 10 creatures with melee and 5 creatures with ranged.

So 50% melee, 25% flight and 25% ranged. If my understanding is correct, you should always play creatures that fly because the odds are 75% to 25%. Obviously the 25% against other creatures that fly is not a "guaranteed" victory, just better odds.

questccg
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Great help here...

questccg wrote:
So 50% melee, 25% flight and 25% ranged. If my understanding is correct, you should always play creatures that fly because the odds are 75% to 25%.

This is really HELPING in designing a "better" game. Hmmm... I don't know if I want this sort of disproportion in the odds. From a card perspective, yeah it sounds cool to have 10 melee creatures... But from the odds perspective - it's nuts! ;)

I may have to choose something like 24 cards, 8 of each. This will make the odds 33.33% making it impossible to favour one type of card over another. Need to think about it some more...

questccg
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The opposite of what I wanted

topdeck wrote:
Now if you jump to the second level of thinking, where your opponent knows what they normally throw, but now they know that you should throw 100% paper based upon that fact, are they really going to throw rock?

Again this is something to consider. I'm not sure 33.33% is the way to go... This makes it completly RANDOM. But from the odds perspective, it is fair and equal. With a disproportionate distribution, you get into that mindset of "Will he ALWAYS try to play a creature that flies?" And if so, "Should I therefore play a ranged creature?" But melee creatures are the bottom of the barrel... The opposite of what I was looking for! Meh...

questccg
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Mind game

questccg wrote:
With a disproportionate distribution, you get into that mindset of "Will he ALWAYS try to play a creature that flies?" And if so, "Should I therefore play a ranged creature?"

I guess then with the "mind game" comes next: "Well since he thinks I'm going to play a creature that flies, he will probably play a creature with ranged attack, therefore I should instead play a creature with a melee attack"...

Maaartin
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Balancing is not obligatory

questccg wrote:
I may have to choose something like 24 cards, 8 of each. This will make the odds 33.33% making it impossible to favour one type of card over another. Need to think about it some more...

This makes no sense to me. Sure, with 3*8 cards you can remove any imbalance... and maybe in doing so remove also a significant part of the strategy. As such, pure RPS is pure luck, well, maybe with some psychology involved. It's a mechanic used in many games, but there must be more than just this.

You don't need to balance it, see Stratego, which is extremely imbalanced and has no problem with it. What you wrote earlier (i.e., "5 creatures that fly, 10 creatures with melee and 5 creatures with ranged.") sounds good to me. Tell us more about what's going on in your game and we'll see if it works nicely.

questccg
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RPS has priority

questccg wrote:
Interesting. I may have such a scenario. I have three (3) types of creatures: melee (basic attack), ranged (distance attack) and flight. Now in my scenario, creatures that fly (flight) beat melee, melee beat ranged and lastly ranged beat flight.

More than the RPS, there is also a gambling conflict mechanism which consists of summoning ARMIES of Creatures (as opposed to one) to do battle.

BUT the RPS system takes PRECEDANCE in battles: never will an army of knights defeat a couple of dragons.

Yamahako
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This is why, you can use an

This is why, you can use an RPS balancing system - but tweak it with numbers.

For example:

Flight does 2x vs. Melee
Melee does 2x vs. Ranged
Ranged does 2x vs. Flight

So if you have a Dragon (4 power, Flight) Then he's worth 8 power against my Knight (2 power, Melee)

If you have 2 Dragons, I would need 6 Knights to win that exchange.

If you combine it with a possible blind bid scenario that you talked about in your previous thread - where I can bid a certain number of chips say Dragons cost 3, and Knights cost 2

Your 2 dragons would cost 6, and my Knights would cost 12. But this isn't too bad, since Dragons are supposed to win against Knights - so I have to outbid in order to win.

Take the similar scenario you have 2 dragons (6 chips) and I have 3 archers (2 power, Ranged, 2 cost - total of 6 chips). Then I have 12 power to your 8, and I win with an equal amount of chips.

Seems like it could be interesting and work. I don't know the rest of your game - but at least the combination of those two mechanics could work. Though I find 5 item RPS to be a bit more interactive.

questccg
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RPS 5 AND RPS 3!

Yamahako wrote:
Though I find 5 item RPS to be a bit more interactive.

I am trying to implement a BONUS system using RPS 5. Not sure about it (I'd like comments...):

Death beats Water and Earth
Light beats Death and Fire
Water beats Fire and Light
Fire beats Earth and Death
Earth beats Light and Water

I plan to use the RPS 3 (Flight, Melee, Ranged) for BONUS as well... Yes there will be a lot of bonuses. But what else do you have to do besides calculate a few values and add bonuses... Not much else! ;)

questccg
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Variant RPS 5

I also have this variant of the previous RPS 5:

Death beats Water and Fire
Light beats Death and Water
Water beats Fire and Earth
Fire beats Earth and Light
Earth beats Light and Death

I think this one is BETTER... But I'm not 100% certain.

questccg
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RPS 5 is random (40/60)

questccg wrote:
I am trying to implement a BONUS system using RPS 5.

RPS 5 has been implemented using a series of "classes". 40% of the time, one player will trigger an additional BONUS. The other 60% of the time - no bonus. These bonuses are special abilities.

For example: A demon (Death) when he fights against Water or Fire will trigger his special ability which is "Possession". Possession allows you to control your opponents ANTE on the NEXT TURN.

Some abilities add strength, other force you to skip turns, some steal gold pieces (money), etc. This RPS 5 works independantly of combat victory...

The RPS 3 (Melee, Flight, Ranged) is now a bonus of +10 ATK. This bonus is added LAST and is a major advantage. We felt a bonus of (2x) was too large.

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