# Analysis: Rolling the climate dice

Photo credit: Michael Summers - flickr
Tuesday, 17 April, 2012
Ben Newell
Imagine a six-sided die with four red faces, one green face and one blue face.

I am going to roll the die, and before rolling I will ask you to predict which colour it will land on: red, green or blue?

If you predict correctly you will win a dollar.

Which colour would you predict?

Now imagine that I roll the die six times and you have to predict before each roll which colour will come up? To maximise your profits, what should you predict, on roll one, on roll two … on roll six?

Probability matching and maximising

The answer in both cases – the single roll and the 6 rolls – is always to predict red, the dominant colour. But I am prepared to bet that during the six-roll game, after saying red a few times, many of you would be tempted to predict a blue or a green.

If you did, then like many people you have fallen foul of a classic violation of rational choice theory known as “probability matching”. This is the well-documented tendency to “match” predictions to the probability of an event’s occurrence.

If you adopt this strategy then you can never do better than about 50% correct.

Why? Because if you “match” your predictions to the odds of each outcome then you have the probability of guessing right on the 4/6 times when you say RED (4/6 x 4/6) plus the probability of guessing right on the 1/6 times when you say BLUE (1/6 x 1/6) or GREEN (1/6 x 1/6). Giving us: (4/6 x 4/6) + (1/6 x 1/6) + (1/6 x 1/6) = approximately ½ or 50%.

In contrast, the better strategy of always saying “red”, known as “probability maximising”, will yield 66% correct predictions.

Why? Because, if you say red for every roll then you have 1 * 4/6 chance of being correct. This is roughly 66%. You have maximised your chances of getting the answer right.

The climate dice

Now imagine that sides of our die represent different climate outcomes. Specifically, the red sides are “hot” anomalies (seasonal mean temperature anomalies that exceed a given threshold), the green side is “average seasons”, and the blue side is “unusually cool” seasons.

I will roll the die; what will you bet on – “hot”, “average” or “cold”?

This “climate dice” analogy has been used in a recent paper by James Hansen and colleagues to demonstrate how over the past 30 years the dice have become “progressively loaded”. There is no longer equal chances of warm, cool, or average seasons. Hansen et al conclude that the “distribution of seasonal mean temperatures anomalies has shifted toward higher temperatures and the range of anomalies has increased” (p.1).

Their analysis shows that in June, July and August of 2010, approximately 66% of the world was covered by temperature anomalies defined as “hot”, in comparison to 20% or less for anomalies in the cold or average categories. These percentages translate – roughly – to our four red (hot) sides, one green (average) side and one blue (cold) side.

Gambling on the climate

The implication of their analysis is stark. The odds of hot seasonal anomalies now far outweigh the odds of average or unusually cool seasons.

Ignoring these odds is the same as ignoring the increased accuracy one can achieve by “maximising” instead of “matching” in the dice game.

Once the dice game is explained, most people can see the error of their ways. They understand that the die has no memory, it is not “self-correcting”, and thus every time it is rolled, “red” is the most likely outcome. Moreover, they realise that even though a “green” and a “blue” side will come up every now and then this should not deter them from maximising. Whatever outcome they see, they are still better off predicting red for each roll.

What about for the climate dice? Can an explanation of the “odds” lead to the same kind of “aha!” experience, and more importantly the required change in perception and behaviour?

The challenge for communicating the idea that the climate dice are already loaded is summed up succinctly by Hansen:

The greatest barrier to public recognition of human-made climate change is the natural variability of climate. How can a person discern long-term climate change, given the notorious variability of local weather and climate from day to day and year to year? (p.1)

The analysis offered by Hansen, along with a huge number of other sources (such as the IPCC) provides the means for helping us to discern these long term patterns.

More importantly, the loaded dice allow us to see why an occasional “unusually cold season” (rolling a “blue”) should not lead to a dismissal of the idea that the globe is warming. Four sides are still red.

Just as rolling a green or blue in the dice game should not stop you maximising on red, so the occurrence of a cold season should not stop you thinking the globe is warming.

If we want to maximise our future well-being we would do well to heed these warnings.

* Ben Newell is an Associate Investigator, ARC Centre of Excellence in Climate Systems Science.