# Think of Rock, Paper, or Scissors before you enter [no cheating kplzthxbai]

rock

Rock

Spock...

Do I win?

#### Ex-User (5841)

##### Banned
ROCK!

*Edit: SERIOUSLY!?!?!

Rock.

#### Proletar

##### Deus Sex Machina
Scissors.

I just lost against myself. But on the other hand, I just won against myself. Fascinating.

#### Ex-User (5841)

##### Banned
Scissors.

I just lost against myself. But on the other hand, I just won against myself. Fascinating.

I don't think your scissors actually did anything given that your rock also lost, as have the half dozen rocks in a row before it...

I would just say paper, but that'd be cheatin'.

#### Proletar

##### Deus Sex Machina
I don't think your scissors actually did anything given that your rock also lost, as have the half dozen rocks in a row before it...

I would just say paper, but that'd be cheatin'.

Such rules have never been defined in this thread.

#### Ex-User (5841)

##### Banned
Such rules have never been defined in this thread.

Oh. You're GOOD.

paper

#### Coolydudey

##### You could say that.
In a game n players long where:
1) One person participates only once
2) They randomly say Rock, Paper, or Scissors
3) They only compare with the person directly below them
4) If they draw with the next k players, and the player k places after them then wins, they win k+1 times. Otherwise, they lose.

e.g. if A says rock, B says rock, C says rock, D says scissors, E says rock, F says paper, G says rock then: A has 3 wins, B has 2 wins, C has 1 win, D loses, E loses, F has 1 win.

What is the expected maximum number of wins out of all players? What is the expected number of wins?

#### Coolydudey

##### You could say that.
You see, the case where you compare with people both above and below you is very easy. It just amounts to finding the expected length of the maximum streak of draws and the expected total streaks of draws.

#### rjioej23

##### Member
Scissors

How many players are there in this game? Is it A-G i.e. 7 players?

Also, it depends on the size of the rock/paper/scissors. If the rock is the size of an asteroid, and the scissors and paper are small (scissors are regular school size and the paper is A4), then rock always wins. So the size of the items also matters.

#### Coolydudey

##### You could say that.
N players (n is an integer). Standard Rock Paper Scissors rules apply.

#### rjioej23

##### Member
Interesting question. Just a quick mistake in point 4 before tackling it. You forgot to mention that they also gain a win if they beat the person below them. In the statement it says they win if they draw and every other combination apart from a draw is a loss.

#### Coolydudey

##### You could say that.
Interesting question. Just a quick mistake in point 4 before tackling it. You forgot to mention that they also gain a win if they beat the person below them. In the statement it says they win if they draw and every other combination apart from a draw is a loss.

ok. 5) If they beat the person directly below them, they get 1 win.

#### rjioej23

##### Member
Hey @Coolydudey. Maximum total wins in a given game is n(n+1)/2, where n is the number of players playing. Am I correct? Did I understand question properly?

#### Coolydudey

##### You could say that.
Indeed it is. Can you prove that?

#### rjioej23

##### Member
My usual Maths work: a few examples, thinking a bit about the results, relating the results to my current knowledge and trying to use knowledge I already have (not too much!).

I noticed the summation from 1 to n in the results here, used that formula, and then that's it.

Sorry for poor non-mathematical explanation. Hope I get a prize for my answer by the way.

#### Coolydudey

##### You could say that.
My usual Maths work: a few examples, thinking a bit about the results, relating the results to my current knowledge and trying to use knowledge I already have (not too much!).

I noticed the summation from 1 to n in the results here, used that formula, and then that's it.

Sorry for poor non-mathematical explanation. Hope I get a prize for my answer by the way.

Well, you've done the most so far. It's actually quite a hard problem. If you want, you could try and figure out the case when you compare to people above you as well (e.g if you beat the person above you and the person below you, above you there were k draws, below you l draws, then you win k+l+2 times). For the expected value questions this is actually easier, but for the maximum win question, not so much.

As far as a proof goes, here is the main idea: show you get more wins by creating some draws.

...paper.

#### Glaerhaidh

##### straightedgy
Onyx, i mean rock!

#### OrLevitate

##### Banned
saw blarraun was last poster, thought he would identify metaphorically with rock and paper much more so than scissors, so i chose rock.

Paper

#### OrLevitate

##### Banned
"the what is boring without the in the butt butt" - Grayman

Rook.
Wait, rock.
I lose.

#### Jennywocky

##### guud languager
paper

I WIN WIN WIN WIN

#### TMills27

##### beep
Paper.

If you are really playing Rock, paper, scissors, there is a good chance your opponent may start with "Rock". Theorize to yourself why this may be.

If you are going for the second round (where on the first, you chose paper and won), your opponent, in quick haste, willmore than likely choose anything but his first choice, and a slightly more possibility with paper. If the conditions of the first round went well, I would choose scissors on the second.

This works a lot better when you kind of catch the person who doesn't normally play this game a little off guard. For instance, just coming up and quickly stating "Best 2 out of 3 of Rock Paper Scissors. Ready?" Then commence.

#### Jennywocky

##### guud languager
Ah, but if your opponent is aware of all that, they will specifically pick the OTHER choice so as to confuse you.

Although if he is aware that you are aware that he is aware, then perhaps he will pick the choice that he should traditionally pick because you expect him not to pick it!

^^ dizzying intellect
\_/

#### Grayman

##### Team Ignorant
I thought of rock as I read it first, then of PAper and then of scissors. Then I realized it said "or" and so I though damn its to late I already thought of all three. Now what do I do?

#### TMills27

##### beep
Ah, but if your opponent is aware of all that, they will specifically pick the OTHER choice so as to confuse you.

Although if he is aware that you are aware that he is aware, then perhaps he will pick the choice that he should traditionally pick because you expect him not to pick it!

^^ dizzying intellect
\_/

rock...
damit.

Rock.

#### B00Bz

##### NTP Master Race
I put my paper over all I thought you knew that, knew that

#### Reluctantly

##### Resident disMember
Get out of my mind, Cheese! Or I'll show you things you can never unsee!

...wait, stay in my mind.

Scissors.

#### Reluctantly

##### Resident disMember
BOOBz is a cheater. It's written all over him. He MUST be banned!
And Redbaron is in cohorts!

paper.

#### cheese

##### Prolific Member
BOOBz is a cheater. It's written all over him. He MUST be banned!
And Redbaron is in cohorts!

Wait.... was that me?

I forgot to think of an item! Crap! Jelly! Crapjelly! (Make sure you use the pectin that doesn't need sugar to set!)

rock

scissors

shit

#### Jennywocky

##### guud languager

Paper beats shit, I think.

#### B00Bz

##### NTP Master Race
BOOBz is a cheater. It's written all over him. He MUST be banned!
And Redbaron is in cohorts!