B/EATDOWN: Making RPS+ work for 3 or more players

If you know Rock Paper Scissors, draws are common. Play with more than two and it’s even rarer to get a winner in one throw.

Odds of win vs tie using RPS

Rock Paper Scissors Lizard Spock reduces the odds of a draw with two players from 1/3 to 1/5, simply because there are more hands to choose from.

But RPSLS doesn’t really help with more than two; draws still happen more often than not. And RPSLS degrades fast if there are more than three.

Odds of win vs tie using RPSLS

In part this is because, in both RPS and RPSLS, all interactions are the same type: Rock beats Scissors, Paper beats Rock, Rock beats Lizard, Paper beats Spock, etc.

But we can take a leaf out of classical five element theory and make a distinction between the inner interactions and the outer interactions: the destroying and producing cycles.

https://www.roddsanchez.com.au/2017/09/five-element-wu-xing/

The destructive cycle is the standard Rock beats Scissors; like Water douses Fire or Metal cuts Wood. The productive cycle is different; it’s like one element drawing energy from the other, like Fire grows stronger by eating Wood and Wood draws strength from Water.

This distinction between beating and eating only matters when playing with three or more players. When playing with two players, there’s only one interaction so it doesn’t matter if you’re beaten or eaten.

But for three or more, making this distinction means fewer draws.

B/EATDOWN

This is how you use it.

  1. Three or more players thrown down hands.
  2. Remove all elements eaten by other elements.
  3. If two elements are left, remove the element beaten by the other.

I like to think of this like one element gets a power-up then rampages. Most of the time you don’t even need step 3; everything’s resolved through one element eating the next until we hit the apex consumer.

You can still draw, of course, but it’s a lot less often for higher player numbers. In a three-player game, there’s one winner more than 2/3 the time. With four players, it’s similar odds to normal two-player RPS.

Odds of win vs tie using B/EATDOWN

For those who like maths, there are more numbers at the end to enjoy.

Examples

If the throws are Rock, Spock, and Lizard, then Lizard eats Spock and Rock eats Lizard, so Rock wins! Spock doesn’t beat Rock because it’s already knocked out by Lizard eating it first.

If it’s Rock, Scissors, and Spock then we first remove Scissors (eaten by Spock, then remove Rock (beaten by Spock), so Spock wins!

If it’s Lizard, Paper, Rock, and Spock: then Paper wins because it’s the only one not eaten.

Complexity

Of course, you still need to remember what does what. That’s more complicated than RPS, but it’s the same complexity as RPSLS.

In fact, there’s no change to the RPSLS pentagram; just how you resolve it. And a lot of the time you only need the arrows in the outer cycle.

Also, it doesn’t matter what the hands are: only the interactions matter. Just use whatever elements you find helpful to remember.

I like the five elements instead of lizards and spocks. Or my Five Hands variant: Crown, Sword, Peace, People, War.

Odds

Numbers, as promised.

RPSCombosWinsWin %TiesTie %
2-player3267%133%
3-player27622%2178%
4-player811215%6985%
5-player243156%22894%
RPSLSCombosWinsWin %TiesTie %
2-player252080%520%
3-player1256048%6552%
4-player62516026%46574%
5-player312540013%272587%
5ECombosWinsWin %TiesTie %
2-player252080%520%
3-player1259072%3528%
4-player62540064%22536%
5-player3125165053%147547%

presently

Merry 2019!

I’ve been enjoying my presents, a fine bottle of Scotch and a finer copy of Jason Lutes’s Berlin. I find both are best chewed with care and savoured slow.

Perfect for the quiet moments between family visits.