Social Cognition
Matching Pennies Game
Also called: matching pennies task, mixed-strategy game, competitive game against a computer, penny matching game
Measure how unpredictably people choose under competition: participants pick A or B against a simulated opponent that exploits patterns in their choices and outcomes, scored by the share of rounds won.
5-8 minUntimed
Free to start: 10 free participants per account, then $0.99 per participant for academic research, or any yearly plan. Preview any test free after you sign up.
- Papers, 2021 to 2025
- 50
- Evidence grade
- D
- Registered clinical studies
- 0
What it measures
Measures how unpredictably people choose against an opponent that exploits patterns. In each round the participant and a simulated opponent choose A or B at the same time, and the participant wins when the letters match; the opponent plays against any pattern in the participant's earlier choices and outcomes. The main score is the share of rounds won.
Constructs
- Strategic unpredictability
- Mixed-strategy decision making
- Learning from wins and losses
- Avoiding exploitation by an opponent
Research uses
- Decision neuroscience and neuroeconomics
- Reinforcement learning and choice history research
- Impulsivity and self-regulation research
- Group comparison within a study
How the paradigm works
The Matching Pennies Game measures how unpredictably people choose when an opponent exploits any pattern in their choices. In each round two players choose one of two options at the same time; one wins when the choices match and the other when they differ. The only way to avoid being exploited is to choose each option half the time, independently of the rounds before, so the game shows how far choices depart from that and how they follow wins and losses (Lee, Conroy, McGreevy and Barraclough, 2004). Here the participant and a simulated opponent choose A or B, and the participant wins the round, and its points, when the letters match.
More about the paradigm
The opponent follows the rule of Lee and colleagues (2004) and Barraclough, Conroy and Lee (2004), as Soltani, Lee and Wang (2006) and Wang and colleagues (2022) describe it. Before each round it looks over all the earlier rounds for a pattern: how often the participant chose A after the same last 0 to 4 choices and, in the standard rule, after the same last 1 to 4 choices with their outcomes, each tested against one half (binomial test, p < .05). With no pattern it chooses at random; otherwise it takes the pattern farthest from one half and chooses A with 1 minus the predicted chance of A. A setting uses the choices alone, which win-stay, lose-shift play escapes, or a random opponent, against which every strategy wins about half the rounds. The standard instructions say the other player is a computer program and state its rule, as human studies of this opponent did (Chang, Wiratman, Ugawa and Kobayashi, 2021; Parr, Calancie, Coe, Khalid-Khan and Munoz, 2022). The standard session has 100 rounds (40 to 200), each followed by both choices and the result for 1 second, and each round won earns 10 points (1 to 1,000). One check question with feedback comes first, and there is no time limit.
The main score is the share of rounds won. Against the standard opponent about half the rounds is the most a player can expect, and patterns lower it: in a ConductScience simulation of 100 rounds, a player choosing at random won 50% of rounds (standard deviation 5 percentage points), one choosing A on 7 rounds in 10 about 42%, and a strict win-stay, lose-shift player about 11%. The entropy of each run of three successive choices (0 to 3 bits; about 2.95 for a fair coin over 100 rounds), the share of rounds in which the opponent found a pattern, win-stay, lose-shift, their combination and the share of switches are also reported (Parr et al., 2022). Monkeys facing this opponent became less predictable but kept some dependence on the last outcome (Lee et al., 2004). Choices under 100 ms count as anticipations. The scores support research and do not diagnose.
Scores
- Win Rate%
- Share of rounds in which the participant's letter matched the opponent's.
- Higher means less exploitable choices; about 0.5 is the most to expect against the standard opponent
- Choice Entropyscore
- Entropy, in bits, of the participant's choices in each run of three successive rounds: 0 when fully predictable, 3 at most. Choosing at random gives about 2.95 over 100 rounds.
- Higher means less predictable choices
- Pattern Rounds%
- Share of rounds in which the opponent found a significant pattern in the participant's earlier rounds; empty with the random opponent.
- Lower means fewer patterns; chance alone gives about 0.08 over 100 rounds
- Win-Stay%
- Share of rounds after a win in which the participant chose the same letter again.
- 0.5 when choices do not depend on a win
- Lose-Shift%
- Share of rounds after a loss in which the participant chose the other letter.
- 0.5 when choices do not depend on a loss
- Win-Stay Lose-Shift%
- Share of rounds after the first that follow win-stay, lose-shift: the same letter after a win, the other after a loss.
- 0.5 means no dependence on the last outcome
- Switch Rate%
- Share of rounds after the first in which the participant chose the other letter than in the round before.
- 0.5 for a fair coin
- Points Wonpoints
- Points over all rounds.
- Informational
- Check Correctflag
- 1 when the check question on who wins a round was answered correctly, 0 when not.
- 1 supports interpretation
- Median Choice Timems
- Median time from a round's screen to the choice, over choices at or after 100 ms.
- Informational
- Choices Under 100 mscount
- Choices made less than 100 ms after the round's screen appeared.
- 0 expected
- Roundscount
- Rounds played.
- Informational
Use and evidence
50 papers from 2021 to 2025 name this task in their title or abstract, up 6% compared with 2016 to 2020. That ranks it 255 of 395 test families in our census. See the counts for every test.
Show the numbers
| Year | Papers |
|---|---|
| 2025 | 17 |
| 2024 | 5 |
| 2023 | 7 |
| 2022 | 11 |
| 2021 | 10 |
| 2020 | 7 |
| 2019 | 11 |
| 2018 | 11 |
| 2017 | 11 |
| 2016 | 7 |
| 2015 | 14 |
| 2014 | 11 |
| 2013 | 8 |
| 2012 | 3 |
| 2011 | 14 |
| 2010 | 8 |
| 2009 | 12 |
| 2008 | 10 |
| 2007 | 7 |
| 2006 | 8 |
| 2005 | 2 |
| 2004 | 1 |
| 2003 | 5 |
| 2002 | 1 |
| 2001 | 1 |
| 2000 | 4 |
Use grade D
30 to 99 papers from 2021 to 2025.
Evidence grade D
Little published measurement evidence found.
- Papers on test-retest reliability
- 0
- Papers on reliability or validity
- 4
- Registered clinical studies using it as an outcome
- 0
Note on the counts: includes game-theory papers that run no task.
How the grades work
Use: A is 1,000 or more papers from 2021 to 2025, B 300 to 999, C 100 to 299, D 30 to 99 and E fewer than 30. Evidence: A means at least 25 papers report its test-retest reliability and at least 25 registered clinical studies use it as an outcome; B, at least 8 test-retest papers, and either 5 registered clinical studies or 150 reliability or validity papers; C, at least 2 test-retest papers, 30 reliability or validity papers or 3 registered clinical studies; D, little published measurement evidence found. The counts measure use. They include every paper that names the task in its title or abstract. Grades describe the published research on this task, not ConductCognition's version of it.
Source: ConductCognition test census 0.14.0, counted 2 November 2026 from OpenAlex and ClinicalTrials.gov.
Task design
The trial sequence as the test runs in ConductCognition.
- Each round
- The participant and a simulated opponent choose A or B at the same time. The participant wins the round, and 10 points (standard; 1 to 1,000), when the letters match; the opponent wins every other round. Both choices and the result show for 1,000 ms.
- Opponent
- A computer program following the rule of Lee and colleagues (2004). Before each round it tests the participant's earlier rounds for a pattern after the same last 0 to 4 choices and the same last 1 to 4 choices with their outcomes (binomial test, p < .05), and plays against the choice it predicts; with no pattern it chooses at random. Its draws come from the session's seed and are saved.
- Opponent rule
- Exploits choices and outcomes (standard), exploits choices only, or random. The standard instructions say the other player is a computer program and state its rule; a neutral wording leaves that line out.
- Rounds
- 100 (standard; 40 to 200) against the same opponent.
- Check
- One question with feedback before the first round: the participant chooses A and the opponent B.
- Scores
- The share of rounds won, the entropy of three successive choices, the share of rounds in which the opponent found a pattern, win-stay, lose-shift and the share of switches.
Lee and colleagues (2004) rewarded monkeys for choosing the same target as the computer over thousands of trials. Chang and colleagues (2021) and Parr and colleagues (2022) ran people against the same opponent and told them how it worked, as the standard instructions here do. Points replace juice and money, and the study decides what they are worth. Against the standard opponent about half the rounds is the most a player can expect to win. In a ConductScience simulation of 100 rounds, a player choosing at random won 50% of rounds with a standard deviation of 5 percentage points, so compare groups rather than small differences between two people. The scores support research and do not diagnose.
Quality checks
Each session is marked valid, needs review or invalid, with the reason, before you see its scores.
Scored rows: the scored run's choices, one A or B per round. Winning depends on the opponent's choice, so accuracy is not judged against chance. The same letter on at least 90% of rounds, a run short of its planned rounds and a wrong check answer are flagged for review. Choices under 200 ms on at least half the rounds invalidate.
Why these rules
There is no correct option to compare with chance, so accuracy is not judged against chance. A round is won when the two letters match, so a win is an outcome of both players' choices, not a correct answer. Choosing one letter nearly every round lets the opponent win almost every round and usually means the participant stopped attending, but it is a choice, so it is flagged and never excludes. An answer under 200 ms is faster than a simple visual reaction, so it cannot reflect the item. Following response-time effort screening for untimed tests (Wise and Kong 2005), the session is invalid only when at least half the answers are that fast.
Running this test
Settings you can change
| Setting | Standard | Allowed |
|---|---|---|
| Rounds | 100 | 40 to 200 |
| Points per win | 10 | 1 to 1,000 |
| Opponent rule | Exploits choices and outcomes (standard) | Exploits choices and outcomes (standard), Exploits choices only, Random: A or B, each half the time |
| Opponent wording | A computer program, with its rule (standard) | A computer program, with its rule (standard), Neutral: the other player |
| Payment line | Hypothetical points (standard) | Hypothetical points (standard), The study pays for points |
Yearly plans can change settings within these limits. Free and pay-as-you-go studies use the standard settings.
Need a setting this test does not have?
Devices and languages
- Untimed test: runs on desktops, laptops, tablets and phones. Participant devices
- Languages: English, Spanish, French, German, Italian, Portuguese (Brazil), Chinese (Simplified) and Japanese.
- Available on: Every plan, including the free plan.
- Recruiting online? See the setup guides for Prolific, Sona Systems, CloudResearch Connect and Qualtrics.
Cite and describe
Participants completed the Matching Pennies Game in a web browser (ConductCognition task version 1.0.0, scoring version 1.0.0; Lee D, Conroy ML, McGreevy BP, Barraclough DJ, 2004), with the standard settings (rounds: 100; points per win: 10; opponent rule: Exploits choices and outcomes; opponent wording: A computer program, with its rule; payment line: Hypothetical points). The main score was win rate (share of rounds in which the participant's letter matched the opponent's).
ConductCognition versions: task version 1.0.0, scoring version 1.0.0. Every export records the versions each session used, for a methods section.
- Lee, D., Conroy, M. L., McGreevy, B. P., & Barraclough, D. J. (2004). Reinforcement learning and decision making in monkeys during a competitive game. Cognitive Brain Research, 22(1), 45-58. https://doi.org/10.1016/j.cogbrainres.2004.07.007Matching pennies against computer opponents that exploit choice and reward history.
- Barraclough, D. J., Conroy, M. L., & Lee, D. (2004). Prefrontal cortex and decision making in a mixed-strategy game. Nature Neuroscience, 7(4), 404-410. https://doi.org/10.1038/nn1209The same game and opponents.
- Soltani, A., Lee, D., & Wang, X.-J. (2006). Neural mechanism for stochastic behaviour during a competitive game. Neural Networks, 19(8), 1075-1090. https://doi.org/10.1016/j.neunet.2006.05.044The opponent's tests of choice and outcome history, as this test runs them.
- Parr, A. C., Calancie, O. G., Coe, B. C., Khalid-Khan, S., & Munoz, D. P. (2022). Impulsivity and emotional dysregulation predict choice behavior during a mixed-strategy game in adolescents with borderline personality disorder. Frontiers in Neuroscience, 15, 667399. https://doi.org/10.3389/fnins.2021.667399People against this opponent; win-stay, lose-shift and choice entropy.
- Chang, F.-Y., Wiratman, W., Ugawa, Y., & Kobayashi, S. (2021). Event-related potentials during decision-making in a mixed-strategy game. Frontiers in Neuroscience, 15, 552750. https://doi.org/10.3389/fnins.2021.552750Telling participants that the computer analyses their past choices.
Source papers
- Lee et al. (2004): monkeys facing these opponents chose each target close to half the time but kept some win-stay, lose-shift dependence. ConductScience simulation (300 sessions of 100 rounds per player): choosing at random wins 50% of rounds against the standard opponent (standard deviation 5 percentage points); strict win-stay, lose-shift wins about 11%.Paradigm source, Adults
Questions
How long does the Matching Pennies Game take?
About 5 to 8 minutes, as listed in the test library.
What device does a participant need?
Untimed test: runs on desktops, laptops, tablets and phones. The browser must be Chrome, Edge, Firefox or Safari.
What scores does it produce?
Win Rate, Choice Entropy, Pattern Rounds, Win-Stay, Lose-Shift, Win-Stay Lose-Shift, Switch Rate, Points Won, Check Correct, Median Choice Time, Choices Under 100 ms and Rounds. Each session is also marked valid, needs review or invalid, with the reason.
How widely is the Matching Pennies Game used in research?
50 papers from 2021 to 2025 name it in their title or abstract, up 6% compared with 2016 to 2020. That ranks it 255 of 395 test families in the ConductCognition test census (use grade D). Source: ConductCognition test census 0.14.0, counted 2 November 2026 from OpenAlex and ClinicalTrials.gov.
How much reliability evidence does the Matching Pennies Game have?
In the published research, 0 papers report its test-retest reliability and 0 registered clinical studies use it as an outcome (evidence grade D in the ConductCognition test census).
Which settings can a researcher change?
Rounds (40 to 200), points per win (1 to 1,000), opponent rule (Exploits choices and outcomes (standard), Exploits choices only, Random: A or B, each half the time), opponent wording (A computer program, with its rule (standard), Neutral: the other player) and payment line (Hypothetical points (standard), The study pays for points). Settings can be changed on yearly plans; free and pay-as-you-go studies use the standard settings.
Which languages can participants use?
Participants can take this test in English, Spanish, French, German, Italian, Portuguese (Brazil), Chinese (Simplified) and Japanese. English is on every plan, and the other languages come with yearly plans. Have a native speaker read the machine-translated text before launch.
Is this a clinical test?
No. ConductCognition is for research use only. It runs, scores and exports the test; clinical interpretation is outside the platform.
Every test: the full test list.
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