Before “Make-A-Pick” came to be the ever-challenging game that it is today, it was a series of questions that required further research. When does a player/gambler stop risking their current score? How does the current winning streak and previous steps affect the next decision? If we introduce a binary selection dynamic to the game, does this change the way the player takes risks?

The keywords to introduce here are: the gambler’s fallacy, Penney’s game, counterintuitive statistics, winning streaks and binary selection.The gambler’s fallacy is based on the misconception that if a certain event occurs more frequently than average, that it will occur less frequently in the future in a balancing manner. What is overlooked here is the fact that if this event is statistically independent from the alternative outcome, there is no correlation between the frequency of occurrences between these two events. This misinterpretation is what leads gamblers to bet on red, in the game of roulette, if they see black come up consecutively in the previous several rounds. The fact that these two outcomes are statistically independent, that there’s no predefined sequence to what the next pick will be, contradicts with the intuitive response the players have when there is repetition.

The paper “Neural Representation of Reward Probability: Evidence from the Illusion of Control” by Kool, Getz & Botvinick from June 2013 in the Journal of Cognitive Neuroscience (http://www.mitpressjournals.org/doi/full/10.1162/jocn_a_00369) focus on reward based decision making and probability distortion.

In the paper, it is explained that the brain encodes potential outcomes based on the probability of occurrence and incentive value. This means in decision-making situations, we create representations of reward magnitude, but studies show that they are inconsistent in different parts of the brain. Other studies point out that the same is true for reward probability. These representations are distorted, meaning they are biased due to many different factors and do not reflect the true mathematical nature of probability or value. And although these distortions are expressed systematically in behavior, they are not always reflected on the neural level.

Their study introduces further findings on how neural representations of probability are immune to such distortions. The neural-behavioral dissociation they found in their results points out an inconsistency of internal representations on reward probability.

A decision maker has to evaluate potential outcomes using (i) value and (ii) probability. This comes from the classical theories of economic choice. More recent behavioral economic theories revealed that there are subjective representations of value and probability, and they may be subject to distortions. But still, value and probability remain as the 2 key elements in the decision-making process.

Numerous studies point out that in the case of reward magnitude, encodings have a variety based on: pertinent outcome, frame of reference, current plan of action or flexibility in the face of change. The illusion of control (IOC) is a tendency to overestimate the probability of favorable outcomes in chance situations, when those situations are chosen rather than imposed. The underlying factor may also be competition, familiarities, need for control and so on in IOC but in this case the researchers are using choice. First reported by Langer, participants were less willing to trade their lottery tickets when they chose it themselves vs when it was given to them in the case of IOC presence.

Reward prediction error (RPE) is a signal that originates in the midbrain when reward outcomes are revealed. It encodes the difference between observed and expected outcome. The more unexpected the outcome is, the larger the signal gets. With the experiment, the authors of this paper want to measure RPE in cases where IOC is present; since participants should report with less RPE in positive outcome scenarios and more RPE in negative outcome scenarios.

In order to observe this, they prepared 2 experiments: the first one is a behavioral test to confirm that the task yields the classic IOC effect. The second one has participants performing the same task while undergoing neuroimaging (fMRI). The data flatly contradicted their prediction, even though participants showed clear IOC on a behavioral level the RPE signals were immune to this effect. The way the participants perceived the outcome was not affected by the distortion that could be observed in their behavior. So in conclusion we could say that the part of our brain which controls our behavior is not affected in the same way as the part that perceives, calculates and expects outcomes.

All images by Onur Olgaç