## Rock, Paper, Scissors with Handicap

May 10, 2010 rps No comments

So I was playing Rock, Paper, Scissors with my daughter the other day. (It was her idea; I didn’t tell her about the game, my previous blog post about Rock, Paper, Scissors, nor about the new rpsmatch.com site). She won, and I lost a few rounds. Then I noticed: she wasn’t using “Paper”!

So I  thought of this variation on the game: one player is not allowed to use one of the weapons. All other rules stay the same.

To make it more interesting, the other player would not know which weapon is not allowed. How to do that? The handicapped player chooses one card from 3, each card showing a different weapon. The player is not allowed to use that weapon. Only after the winner is determined is the card shown to the other player for verification. If the handicapped player cheated by using the forbidden weapon, then they lost!

I doubt this change gives the non-handicapped player an advantage.  But you never know. The number of draws should decrease, though. Then again, maybe not. Would be nice to figure it out (mathematically)!

## Rock Paper Scissors for Three Players

April 5, 2010 generic, rps 3 comments

In the summer of 2009, if not to say, a long long time ago, Sharon Twiss asked on twitter: “can groups of more than two use Rock-Paper-Scissors?

In case you’re not familiar with the game,  Rock, paper, scissors (wikipedia link)  is played by two people. “Rock beats scissors, scissors beats paper, and paper beats rock”.

## A basic way to play the game with more than two people

It took me quite a while to find this article about Rock, Paper, Scissors at indopedia.org, which explains how the game can be played by more than two:

The game is easily adaptable to more than just two players. This variant works remarkably well, even for large groups. The rules are the same, with the following exceptions:

• If all three weapon types are played, or only one type of weapon is played, the round is considered to be a draw. A new round begins.
• If there are only two different weapon types showing between all of the players, then all of the players showing the losing weapon are eliminated.

## A different way for three players

Let us add another “weapon”, called Lizard, like this:

Weapons and winning sequence for 3 Player Rock Paper Scissors

(I based the illustration image on another one from wikipedia, http://en.wikipedia.org/wiki/File:Pierre_ciseaux_feuille_l%C3%A9zard_spock.svg by Nojhan )

The game for three players is played like the original version, with this order

• Lizard beats Scissors
• Scissors beats Paper
• Paper beats Rock
• Rock beats Lizard

Count to three, and on three, each player chooses one of the weapons with their hand.

## How to determine the winner with the extra weapon?

What you do is look at the sequence of weapons chosen. For example, here

Player Blue: Lizard, Player Yellow: Scissors, Player Purple: Paper

Player Blue chose Lizard, Player Yellow chose Scissors, and Player Purple chose Paper. Lizard beats Scissors, Scissors beats Paper. So you would say Player Blue, who chose Lizard, won, right?

What to do when two players choose the same weapon? Let’s say like this:

Player Blue and Player Yellow: Scissors, Player Purple: Paper

Both Player Blue and Player Yellow chose Scissors, Player Purple chose Paper. Scissors beats Paper. There are two winners, so now Player Blue and Player Yellow play a round of 2-player Rock-Paper-Scissors to determine the winner.

Let’s look at this case,

Player Blue and Player Purple: Paper, Player Yellow: Scissors

both Player Blue and Player Purple chose Paper, and Player Yellow chose Scissors. Scissors beats Paper, so Player Yellow won. No need for a 2-player round.

Obviously, if all players choose the same weapon, then it is a draw, and the game starts from the top.

## Two different versions of this game

Now we come to a case that has no equivalent in the 2-player version:

Player Blue and Player Yellow: Lizard, Player Purple: Paper

Two player chose the same weapon, and the other player chose a weapon that neither beats the other weapon directly, or is beaten by it. (They are opposite in the circle).

Here I see two options. Either this is declared a draw, or the player who chose the single weapon is declared the winner. I think time will tell which is the better choice.

I’ll try to explain the advantage of adding another weapon in a separate post. Stay tuned!

## Thanks

Thanks go to my friends Sara and Gerry who played this game with me yesterday. Sara won.