Rock Paper Scissors Strategy

Pick a a number from 1 to 4.

In Rock Paper Scissors each game has a third chance of either player winning and a third chance of a draw right? Well not quite.

It is true that if you were playing against someone who plays their moves randomly then you are just going to draw long term, but humans are awful at being random. Was your number 3? About 75% of the time people pick 3, with around 10% each picking 2 or 4 and 5% picking 1. Something just feels more random about 3. Ask people to pick a random number between 1 and 100 and you will find a disproportionate number picking 37 or 73.  Knowing that you will be playing flawed players is the key to getting an advantage.

Firstly, let's look at the long term percentages of each choice:

Rock 35.4%

Paper 29.6%

Scissors 35.0%

If you played 1000 games and play Rock as your first move you will win 54 more games than if you just picked randomly. Similarly for Paper you would win 4 extra and for Scissors you will lose 58 more.

So we should always pick Rock right?

(Be aware that there seems to be a gender divide on the first move as well. Males tend to throw Rock more often and females prefer Paper. Every site I've been on seems to quote this, but I can't find a study which provides the data, so I'm going to approach this with some caution.)

The problem and fun comes from players adapting to what you have already done. If you always pick rock then people will quickly catch on. So while Rock looks a solid first move we need some strategies for playing the same person a few times in a row.

If you have just won a round, then a good strategy is to pick what would have lost you the game as your next move. For example, lets say your Scissors just beat their Paper. Your opponent is less inclined to play Paper again (illogically) because it feels like a losing move. So they switch to Rock hoping that you will repeat your move or Scissors because they have seen it just win a game. By switching to Rock you will either draw or win. This strategy is crazily effective.

If you see someone play the same thing twice in a row then assume they will switch next time. This is another flaw of what humans perceive as random. If you ask someone to list out a random sequence of Heads and Tails then you will get something like this: HTTHTHHTHHTTHTTHTTHH. However if you flip a coin to get the same results you will get something more like this: HHHTTHTTHTTTTTHHHTHT (computed by taking the first 20 decimal places of Pi and giving Hs for 0-4 and T for 5-9 by the way). The difference is that humans don't perceive long strings of the same value as "random", whereas if you take a random string of 3 Heads or Tails then a quarter of the time you will get a string of 3 of the same.

So in an effort to be more random and therefore less predictable, people rarely pick an option 3 times in a row which means you should probably assume they won't repeat.

When in doubt and you think you've become too predictable then just pick one at random. Using digits from somewhere in the middle of your favourite irrational number is a good way to get random numbers on the fly, if you don't trust your monkey brain with creating randomness. Which, of course, you shouldn't. This will allow you to be on a level pegging with the World Champion. Prizes at the World Championship are often 5 figures.

If you want to have a go at beating a computer which learns to play as it goes along by playing you (similar to a certain M&M creation) try this applet that the NY Times ran a couple of years ago. It learns what sort of patterns you do and will get better and better as it goes along.