If you know that coin coins tend to land heads around 50% of the time and one just landed tails, you might think more heads will follow–an error known as the gambler’s fallacy. However, that would be unreasonable and counter-intuitive.
Only when there is equal evidence supporting both scenarios should one commit the gambler’s fallacy or hot-hands fallacy.
Rules
A key to creating an effective coin gambling strategy is understanding and applying its rules correctly. The aim should be to generate a random sequence of Heads and Tails that produces either a positive expected payoff, or at least not one with negative implications. Humans tend to struggle in creating such sequences; therefore an automated computer program may be best utilized in creating them, giving gamblers the feeling they are making progress towards victory while continuing to gamble with renewed optimism.
Variations
A coin toss is an unpredictable event; however, many people assume the odds of heads-to-tails outcomes increasing after a string of tails increases (known as “gambler’s fallacy”). This effect may explain why certain individuals end up experiencing excessively long sequences of wins and losses; however, by understanding your odds for winning or losing with more than 50% accuracy you can predict your opponent’s next move with ease.
To explore this question, a series of experiments were carried out where participants played against either unexploitable opponents or those designed to exploit any item biases expressed by them. Reaction times were recorded for every trial and the differences in response times between win and loss trials were then examined; it was found that having an exploitable opponent caused more severe cycles of shift behavior regardless of credit manipulation used – suggesting that reinforcement learning biases may be more responsive to competitive threat than fixed outcomes.
Strategy
Experiment 1 was designed so as to not exploit any item biases shown by participants (i.e., unexploitable). For this and all subsequent experiments, credit manipulation was an within participant factor while oppositional factors (opponency = unexploitable; exploiting; exploiting), were between participant factors split across three experiments (1 = unexploitable; 2 = exploiting; 3 = Exploiting). If participants’ credit balance fell too low under either fixed or variable credit conditions a warning sign would appear on screen with participants no further play allowed during play if this occurred (i.e. they would no longer be permitted to play the game).
After selecting an RPS, opponent and participant displayed their selections for one hundred millisecond. Subsequently, trial outcomes (‘WIN’ + 1, “LOSS’ -1,” red font or a draw; yellow font) were presented; these differences in response time between trials where learning an opponent model could occur and those where it couldn’t. Significant positive correlations were discovered between self-imposed reductions in processing speed following losses with poorer quality decision-making (post error speeding), as well as shift behavior negatively correlations with win rate.
