Rock, paper, scissors: Poker redux

The Maspro Denkoh electronics corporation was selling its $20 million collection of Picassos and Van Goghs, but the director could not decide whether Sotheby's or Christie's should have the privilege of auctioning them.

So he announced that the deal would go to the winner of a single round of scissors, paper, stone - the children's game that relies on quick fire hand gestures, where stone beats scissors, scissors beat paper, and paper beats stone.

Sotheby's reluctantly accepted this as a 50/50 game of chance, but Christie's asked the experts, Flora and Alice, 11-year-old daughters of the company's director of Impressionist and modern art, and aficionados of the game.

They explained their strategy:

1. Stone is the one that "feels" the strongest
2. Therefore a novice will expect their opponent to go for stone, and will go for paper to beat stone
3. Therefore go for scissors first

Sure enough, the novices at Sotheby's went for paper, and Christie's scissors got them an enormously lucrative cut.

This took place back in 2005. (The excellent BBC News article also offers winning tips for Monopoly, Connect Four, Draughts, Othello/Reversi and Scrabble)

Graham Walker, via Andrew Gelman, provides a comprehensive list of winning strategies. For example:

When playing with someone who is not experienced at [Rock, Paper, Scissors], look out for double runs or in other words, the same throw twice. When this happens you can safely eliminate that throw and guarantee yourself at worst a stalemate in the next game. So, when you see a two-Scissor run, you know their next move will be Rock or Paper, so Paper is your best move. Why does this work? People hate being predictable and the perceived hallmark of predictability is to come out with the same throw three times in row.

Walker also offers an explanation as to why these tricks actually work:

Humans, try as they might, are terrible at trying to be random, in fact often humans in trying to approximate randomness become quite predictable. So knowing that there is always something motivating your opponent's actions, there are a couple of tricks and techniques that you can use to tip the balance in your favour.

I also have my own contribution to the literature on the inability of humans to act randomly. Ask someone to hide their hand behind their back and pick a random number of fingers. You would think that you would then have a 16.7% chance (not 20% - zero is a number too) of guessing the number right. However, that's not quite true. Zero and five are practically never chosen, while four or one will only emerge if you are asking someone who has tried this numerous times in the past. So, in most cases, you are only left to choose between two and three - a 50% chance of getting it right. And you can do even better than that: Most people's first instinct is to go for two, while if you allow them a few more seconds of thinking time they will revert to three - as one of my victims once explained, 'three is more difficult to guess'.

Addendum: A loyal reader (usually a reliable source) informs me of another trick: ask someone to come up with a number between 1 and 10, and most people will go for seven. According to the same source, this almost always works with girls, with guys being a tad bit less predictable.

Also, it's not only humans that occasionally have trouble with generating random numbers. Tyler Cowen recently posted a piece on Benford's Law, the tendency of many data series (such as the length of rivers) to include a surprisingly high number of entries beginning with the number 1.


  1. Anonymous Says:

    If in doubt, apparently scissors only gets thrown 29.6% of the time, which in theory means that paper would be your best shot at winning.

    I also like the idea of telling your opponent what your next throw is going to be and then actually delivering that throw when they usually expect a bluff.