Games 3 Volatility and Randomness – common confusions

We have seen from the two previous posts (Games 1, Games 2) that games can be categorised as high/low volatility and high/low skill. We have also seen that higher volatility games are generally more fun to play and certainly make better social games and spectator sports.

Volatility can easily lead to confusion about what sort of distribution of outcome we are looking at. Let’s look at a few examples of this:

High volatility makes relative skill between players hard to see

With any game of high volatility, it can be hard to tell what the skill mismatch between players is.

Take the two charts below. Both games of high skill with players of the same skill differential. In the lower volatility version, the skill differential is obvious, but in the high volatility much less so. In reality, a better chess player will win a high proportion of games, even if the skill advantage is slight. Whereas with poker, we would see a lot more short-term variation in the winning player.

This can have consequences. At a poker table, some people will often play with a very aggressive style, ensuring high volatility in the outcomes of their games. After the game, they will complain about poor luck in not hitting their intended flush on the river, or being regularly outdrawn by another player. They may consider themselves skilful or perhaps, that poker is a gambling game where luck is the driver, without realising they are playing against the odds. They will consistently lose. This is one way that better poker players consistently take money off weaker players, where their own volatility of results blinds them to their lack of skill, so they continue to play.

Volatility acts to disguise any underlying skill differential. This is extremely helpful for the enjoyment of social games but can lead to important mistakes in other areas of life.

High volatility can be mistaken for randomness

If you only had the results of the first 10 games of a highly volatile game, it would be easy to decide that the outcomes are random with no discernible difference in skill. It is quite easy to see why these concepts get confused. Unless you have a lot of data and are paying close attention, it can be hard to spot the difference between a random outcome and an outcome where the volatility is high relative to the skill element. Repeatedly playing a game is often not possible either.

This mistake gets frequently made in economics and economic forecasting. Economies are volatile and this makes precise forecasting generally impossible. This often leads to logic flaw we can saying nothing useful about the future and that experts should be ignored.

A recent example of this is Brexit. Any forecast of growth and living standards over the next decade has a huge error band with or without Brexit. In other words, we are looking at something with inherently high volatility. Adding a large economic shock like Brexit is likely to add even more uncertainty/volatility to any forecast.

It is then commonly argued, in fact often assumed, that since predicting what will happen after Brexit is so difficult given the volatility, it means that economists have nothing useful to say. If “anything” can happen, we should think of the impact as simply random. This is a huge mistake.

In a previous post, “Is Climate Science True” ( I introduced the concept of conditional vs. unconditional forecasts.

To take an analogy, I am thinking of running the London marathon next year.
Please estimate how long it will take me to run it i) in running kit ii) wearing a gorilla costume.
I would strongly expect that your confidence in both of your answers is very low.
However, I bet you are very confident that ii) will take longer than i).

The addition of a gorilla suit adds volatility to the outcome. It does not mean that adding a gorilla suit has negligible impact and the effect is random.

Brexit adds volatility to the outlook for the UK economy. This does not mean the effect is random. It is clearly and strongly negative.

Similarly, average temperatures are volatile. This does not mean that climate change is untrue or that greenhouse gases are not causing it.

Volatility causes confusion on absolute skill of the game

We have seen that volatility can cause confusion on relative skill level.
It can also cause confusion on the overall skill level of the activity

1, High volatility does not mean low skill

It is a common error to assume that because a game has high volatility it means it has a low skill level. As an observer, you might see a relative novice beat an experienced player and conclude that this game is not very difficult to master (poker).
Or another example of an experienced player not consistently able to succeed (baseball home runs, a world number one player knocked out of Wimbledon early)
The nature of the game means that the volatility remains high (it is often designed that way) but the skill level may still be extremely high and difficult to master.

2, Low volatility with evenly matched players does not mean low skill
Think of a game where you only watch match-ups between players of very equal abilities. If you do not share the high levels of skill, then it is easy to think that the outcome is random and the participants’ skill level are not that high.

An example of this is in car racing. I see in Nascar that people drive flat out round and around in circles – not that hard. Even Formula 1 does not look too tricky. I know how to drive and what they are doing looks like my experience of driving. I didn’t really understand the level of skill involved until I went on a track day and witnessed how far even the best amateurs were from professional times, and how much further a decent amateur was from me.


Appreciating how volatility will mask the underlying features of a game is important, to the outsider it is easy to assume that an uncertain outcome implies randomness or low skill.

This is flawed logic.

Games 2 Why do we play games?

A simple answer that many people will come up with is that we play games to win. But I think this is much less true than people think and many other aspects of games are more important. Participating in a game and also being a spectator can often be hugely enjoyable irrespective of who wins. There is clearly a lot more to games than winning.

For a start, it’s important to consider what we mean by “winning”. Does it mean the same to all participants?

Some examples

Playing golf with friends, is the objective to have the fewest number of strokes over 18 holes? I know plenty of people whose play is not consistent with that. Other goals are often far more important. The desire to hit the longest drive of the day, the most outrageous recovery, get a birdie or simply to have the best story to tell in the bar later.

Do people really play poker to win money? I think we do it because it is fun and it is often the outrageous play that generates the best story. The worst poker players often have the best stories.

In these two examples, it is clear the enjoyment of the game is not purely coming from “winning”. The thrill of participating comes from the volatility of the outcome and is highly enjoyable, and this is a similar motivation for being a spectator as well.

In the previous post, I introduced the idea that we can categorise games according to both skill and volatility. These different categories have important consequences for why people play these games.

Spectating versus Participating
If we think about the quadrants for participants versus spectators, the experiences are similar but not the same.

Low Skill Games

Whereas low skill games can be fun to play if there is high volatility in the outcome (e.g. snakes and ladders or roulette), it is debatable how entertaining they will be to watch. Enjoyment would most likely come from the seeing the joy of your children playing or the drama of the emotions of the participants.

High Skill Games

What is perhaps less obvious is that adding volatility even to highly skilled games generally makes them more enjoyable both as a participant and spectator.

Social games – add volatility
If you want to play a game of skill socially with friends, it is helpful if there is a decent amount of volatility in the game. This will mean that even with a decent mismatch in ability, none of the players can be sure of the outcome and on any given day anyone might win. Therefore, pool is a much more fun game to play with a mixed group of friends than snooker.
Importantly these sorts of games will be highly enjoyable for spectators, the level of volatility creates an enjoyable amount of uncertainty in the results.

Serious Games – low volatility

Games with low volatility and high skill can be extremely engaging. A game of chess in a tournament between 2 players of similar standard with a long-time limit is an absorbing pursuit. Equal matched opponents make it difficult to call. These types of games can be fantastic as a participant, as you know how you play on the day is all that matters. Luck has a very minor part to play.

As a spectator, this game may not be much fun at all!
People who watch chess are keen players themselves in my experience. Even then, entertaining commentary by experts is usually required to interpret and explain what is going on.It is hard to persuade a casual player that watching the World Championships is fun, in fact they generally find it astonishing that I would do it.

Spectator sports & games – add lots of volatility!

Large, popular spectator sports are invariably high skill. But they also all have high volatility, and in many cases deliberately adjust the rules to make sure there is plenty of it.


Have you ever wondered why tennis has games and sets? It is to add volatility to the result. The better player will still win on average but the chances of an upset are increased.

An obvious alternative method of scoring would be that you play a specified number of points, with equal time serving, and the person with the higher number of points wins. But this sounds boring. The better player will tend to win and there is little drama during the game.

The rules of tennis cleverly make some points worth a lot more than others, to make things less predictable. If you win all your service games to love, but lose just one close one in a set you may lose the set even if you won more points during the set. If you win a set 7-6 and then lose one 0-6, you are level despite winnings far fewer points.


I just watched the Lions tie the series with the All Blacks. If the scoring system had been to play 3 80 minute sessions and the total number of points won then the All Blacks would have been comfortable, and highly predictable, winners.

Football (soccer)

Goals are hard to achieve and just one often decides a game. Even relatively poor teams can score against much better ones and good teams can struggle to score against far weaker ones. This means that the league will generally be won by a very good team but any individual match has a high level of uncertainty and thus is exciting to play and watch.


I spent a very enjoyable time watching the golf at the Open at Royal Birkdale last weekend Spieth on the final day played an amazingly exciting round and ended up going on to win.

At hole 13:

He didn’t just miss the fairway
He hit the ball over 100 yards right of the fairway
So far away he eventually declared the shot unplayable and took a penalty, walked another 50 yards away from the hole and eventually hit the ball between some TV trailers on the practice ground.
He managed to finish that hole only 1 over, a bogey, a remarkable achievement

The next four shots were even more remarkable:

14th Hole                            1 under, birdie

15th Hole                              2 under, eagle

16th Hole                              1 under, birdie

17th Hole                              1 under, birdie

And by hitting par at the 18th, he took the championship.

Rory McIlroy was 5 over after 6 holes on the first day but went on a charge on the last day and despite losing a ball on the 15th, made eagle on 17 while Speith was in serious trouble on 13 and his odds of winning were tumbling fast from 100-1 to 20-1.

I like golf. But the volatility is what made the event so much fun to watch.

Formula One

Watching Vettel take pole and then leading a procession to the chequered flag for over 2 hours, for a couple of seasons was pretty dull. This does not mean that the skill of the engineers, designers and driver was any less admirable. It is just dull to watch the best car win every time with complete certainty. Formula 1 keeps trying new rules and specifications all the time to make the winner less predictable which the drivers and the fans both prefer.


Even chess can be tweaked to add volatility to the result which spectators and participants both think makes it fun – reduce the time limit and play Blitz.


It’s clear from the explorations in these posts that the enjoyment of playing games and sports does not derive purely from the act of winning. When skill and volatility are combined in a game, it can be thrilling for participants and spectators alike. It may be not totally obvious that volatility is such important ingredient, but it should be now clear that it’s often added to games and sports to make them better for spectators.

Games 1 What is a Game?

Skill and chance

A common way to think about games is that they are either games of skill, like tennis, or games of chance, like roulette. But this basic categorisation can lead to some important misunderstandings. A far better way to categorise them is in two dimensions, skill and volatility.

Introducing Skill and Volatility

Games can instead be categorised as having:

  • High Skill – where the result is importantly impacted by the relative skill of participants.
  • Low Skill or Unskilled – the result will mostly likely be to chance (Random)

We can also categorise them by volatility of outcome:

  • High Volatility – The winner and margin of victory of any particular result will be variable and somewhat unpredictable
  • Low Volatility – The margin of victory will be similar each time the game is played.

By “game” I’m using a fairly general definition – any competitive activity where you can judge who is the winner and often how easily the win was achieved. Games such a chess and poker, competitive sports such as football and tennis would clearly fall under this definition but similarly so can trading and starting a business.

This approach yields a 2 by 2 grid:


Let look at some examples for each quadrant:

Low skill element combined with high volatility

e.g. Snakes and ladders, roulette

Snakes and Ladders is clearly a game of chance with no skill but is surprisingly fun to play with kids. Climbing ladders ahead of the competition or sliding down huge snakes and losing your lead produces a lot of drama and excitement.

Games of no or low skill and high volatility make excellent games for young children. They are also quite common for adults but generally when money is added to the equation as they make popular gambling or casino games.

If we consider the distribution of outcomes of 20 matches played between 2 players, it might look something like the scatterplot below:

  • X axis is each game played.
  • Y axis is the result.
    Above zero signifies player A wins, below player B wins. 1 would signify a tight match, 5 would signify a relatively easy victory. In this case, we do not have draws – zero scores.

Low skill element with low volatility
a very boring game!

Snakes and Ladders without any snakes or ladders would be an example of this. The winner is the person who on aggregate throws the higher score when rolling dice. This seems extremely dull and not something that people would do for a purpose or for enjoyment.

High skill element with low volatility of outcome
e.g. chess, Go


Here the skill element dominates relative to the volatility of the outcome. In this category, we find
chess and Go and sports such as tennis. A significantly better player is almost certain to win and, in that respect, these games often do not work well socially as weaker players have little chance of winning so will not enjoy very much. These are the games I work hard at to become expert and enjoy fierce competition with players of a similar standard.

Non-random with high volatility
e.g. pool, poker

This is the category that holds the most socially fun games. The skill element is undeniable but the outcome is uncertain enough that the lesser skilled player still has a chance to win. The uncertainty may even be sufficient that the weaker player may consider themselves the stronger one.

Volatility the key ingredient

People tend to be somewhat aware of the skill level of games. They tend to be less aware of the volatility of the game and why it matters so much.

Pool is a lot more fun to play socially than snooker. Both involve almost the same skills, but pool has much higher volatility. A better snooker player will take virtually every frame; but with a similar difference in skill the weaker player would still win some games of pool.

Golf is another game with high volatility and high skill. Even top professional golfers can have a range of 20 shots between their best and worst rounds. On any given occasion, players of slightly different standards can play together uncertain of the outcome, although they know on average who will come out on top.


People play games of many different types. It is easy to view them simply as either random or skilled but this misses important distinctions. Adding volatility into the framework brings into focus the differences between say chess and poker, fundamentally different games and enjoyable in their own ways.

The Backfire Effect

Recently in the news

  • You may find it puzzling that Republican voters are still backing Trump.
  • You may be amazed that the same voters do not believe that Russia interfered with the election, or that there is any connection to the Trump campaign.
  • In that case you must be shocked that the recent Donald Junior revelations have make their belief in ‘no collusion’ even stronger.[1]

But then again, is it that surprising? I previously discussed confirmation bias and desirability bias ( and but in this case feels like there is a different driver at work.

“Backfire effect”

This recent paper [2] found that “direct factual contradictions can actually strengthen ideologically grounded factual beliefs”. This is the “backfire effect”.

In contrast to what we saw previously:

Here we have:

The more evidence and the clearer the evidence against Trump, the more strongly his supporters believe him innocent. Trump supporters are not backing him because of facts or policies, this is about ideology and culture and it is a battle. Facts are irrelevant.

There are plenty of examples which demonstrate this. Tim Harford talks about how the tobacco industry managed to delay regulation for decades despite overwhelming evidence showing the link between smoking and cancer. [3] Another favourite example is what happens to cult members who believe that the world will end on a specific day. They give away their possessions and prepare for their ascension to heaven/alien spaceship. When the day arrives and nothing actually happens, they do not lose their faith; their faith in the end of the world actually increases. Perhaps the “backfire effect” also explains why Tony Blair’s support for the Iraq War became more fervent despite mounting evidence against the entire premise.

Back to Trump-gate

Given this, I fear that this ever-larger number of smoking guns will not help the Democrats much, even with increasing suggestions of criminal activity not just from the Trump campaign but from the Trump family itself. The way to defeat the Backfire effect is not to counter with ever more evidence. There was no possible evidence based argument that would have changed Blair’s mind about war.

The best approach is to build a compelling alternative narrative. Corbyn did this very successfully in the last election, making no attempt to defend himself against May’s attacks, focusing only on what he wanted to talk about. He did not change people’s minds about Trident, he stopped them thinking about it. What we focus on is far more important than the content of the debate.

Like all cognitive biases, spotting them in others is far easier than in oneself. We can all fall foul of the “backfire effect” when it comes to our most central values and beliefs. For business and investment, it has perhaps led to the most catastrophic of errors. The disasters of RBS, Lehman and Enron can be traced to core beliefs that proved successful at first, but then warning signs were ignored as the management became ever more evangelical in their confidence that their path was the right one.

When we are looking for investment analysis or advice, then we should be very wary of those with high and unchanging conviction. Some of the ones I regularly come across: the EU will break up/stick together or China will implode/ take over global dominance or the bond market will crash/inflation will never return. They argue passionately and eloquently (they are well practised) but are the ones most likely to be victims of the “backfire effect”. The element that makes them so popular as guru strategists and TV pundits makes them highly unreliable sources of investment advice.

Perhaps we should simply recognise that we may easily fall for this as individuals, but by building diverse enough teams and open enough culture, we may not fall for the same cognitive flaws.


As with confirmation bias and desirability bias, the “backfire effect” is important and can warp your interpretation of the world. Your political enemies and people you do not respect will not be the only victims of this. We can all fall prey to it and should be most sceptical of our views which are most closely linked to our core values and beliefs.