Table 1
Possible sequences, choices and outcomes in the MHD.
| Sequence | Door A | Door B | Door C | Initial choice | Initial choice | Initial choice | |||
|---|---|---|---|---|---|---|---|---|---|
| Door A | Door B | Door C | |||||||
| Final choice | Final choice | Final choice | |||||||
| Stay | Switch | Stay | Switch | Stay | Switch | ||||
| 1 | Car | Goat | Goat | Win | Lose | Lose | Win | Lose | Win |
| 2 | Goat | Car | Goat | Lose | Win | Win | Lose | Lose | Win |
| 3 | Goat | Goat | Car | Lose | Win | Lose | Win | Win | Lose |
| Total number of wins: | 1 | 2 | 1 | 2 | 1 | 2 | |||
Table 2
Characteristics of included studies: participants, version, material, number of options, and number of trials.
| Alternatives | Prize (when specified) | ||||||
|---|---|---|---|---|---|---|---|
| Baratgin & Politzer, 2010 | 1 | 47 students | Physical | Tubes | Cotton ball | 3 | 1 |
| 2 | 100 students | Physical | Tubes | Cotton ball | 3 | 1 | |
| Burns & Wieth, 2003 | / | 124 students | Paper | Boxers/Doors | 3 | 1 | |
| Burns & Wieth, 2004 | 1 | 326 students | Paper | Boxers/Wrestlers/Doors | 3 | 1 | |
| 2 | 379 students | Paper | Tennis players/Boxes | 3/32/128 | 1 | ||
| 3 | 614 students | Paper | Boxers/Doors | 3 | 1 | ||
| 4 | 280 students | Paper | Doors | 3 | 1 | ||
| De Neys, 2005 | 1b | 41 students | Computerized | Doors | Car | 3 | 1 |
| De Neys & Verschueren, 2006 | 1 | 239 students | Computerized | Doors | Car | 3 | 1 |
| 2 | 129 students | Computerized | Cups | Marble | 3 | 1 | |
| 3 | 102 students | Computerized | Cups | Marble | 3 | 1 | |
| DiBattista, 2011 | / | 189 students | - Training: computerized - Post-test: paper | Doors | Car | - Training: 3/20 - Test item: 6 | - Training: unlimited - Test item: 1 |
| Efendic & Drace, 2015 | / | 36 students | Computerized | Doors | 3 | 60 | |
| Fox & Levav, 2004 | 1a | 104 students | Physical | Cards | Ace | 5 | 1 |
| 1b | 126 students | Physical | Cards | Ace | 5 | 1 | |
| Franco-Watkins et al., 2003 | 1 | 142 students | - Training: physical - Final MHD: ? | - Training: cards - Final MHD: doors | - Training: ace - Final MHD: car | - Training: 3/10 - Final MHD: 3/10 | - Training: 30 - Final MHD: 1 |
| 2 | 259 students | - Training: computerized - Final MHD: ? | - Training: cards - Final MHD: doors | - Training: ace - Final MHD: car | - Training: 3/10 - Final MHD: 3/10 | - Training: 30 - Final MHD: 1 | |
| 3 | 165 students | ? | Doors | TV/DVD player/desk | 3/4/5 | 3 | |
| Herbranson & Schroeder, 2010 | 3 | 12 students | Computerized | Squares | 3 | 200 | |
| Herbranson & Wang, 2014 | 2 | 12 students | Computerized | Squares | 3 | 100 | |
| Hirao et al., 2016 | / | 32 students | Computerized | Cards | Money | 3 | 120 (2 × 60) in each condition |
| Hirao et al., 2017 | / | 21 students | Computerized | Cards | Money | 3 | 360 (6 × 60) |
| Howard et al., 2007 | / | 108 students | Computerized | Boxes | Money | 3 → 25 | 23 |
| Idson et al., 2004 | / | 95 students | Combination of paper and computerized | Boxes | 3 | 1 MAO, 1 MM | |
| Klein et al., 2013 | / | 15 students | Computerized | Black squares | Green square | 3 | 500 or end of 60 minutes session (whichever came first) |
| Krauss & Wang, 2003 | 1 | 135 students | ? | Doors | Car | 3 | 1 |
| 2 | 137 students | ? | Doors | Car | 3 | 1 | |
| 3 | 110 students | ? | Doors/Prisoners | Car/Prisoner not executed | 4/3 | Each problem once | |
| Mazur & Kahlbaugh, 2012 | 2 | 36 students | Computerized | Boxes | 3 | 200 | |
| 3 | 16 preschoolers (ages 3–5 years) | Computerized | Doors | Fun picture | 3 | 50 | |
| Petrocelli, 2013 | / | 10 physicians | Computerized | Doors | Money | 3 | 60 |
| Petrocelli & Harris, 2011 | 1 | 47 students | Computerized | Doors | Money | 3 | 60 |
| 2 | 65 students | Computerized | Doors | Money | 3 | 60 | |
| Saenen et al., 2015a | / | 385 students | Physical | Cups | Toy | 3/10/50 | 10 |
| Saenen et al., 2015b | / | 68 students | Physical | Cards | Red card | 3 | 80 |
| Slembeck & Tyran, 2004 | / | 93 students | Computerized | Doors | 3 | 40 | |
| Stibel et al., 2009 | 1 | 32 students | ? | Boxes | Money | 3/100 | 1 |
| 2 | 152 students | ? | Boxes | Money | 5/6/7/8/9/10 | 1 | |
| 3 | 82 students | Computerized (online survey on internet) | Boxes | Money | 3 | 1 | |
| 4 | 61 students | ? | Boxes | Money | 3/100 (both with removal of initial choice) | 1 | |
| Tubau, 2008 | 1a | 44 students | ? | Cards | Ace | 3 | 1 |
| 1b | 40 students | ? | Cards | Ace | 3 | 1 | |
| 2 | 40 students | ? | Cards | Ace | 3 | 1 | |
| 3 | 32 students | ? | Cards | Ace | 3 | 1 | |
| Tubau & Alonso, 2003 | 1 | 57 students | Computerized | Windows | Red window | 3 | 45 |
| 2 | 61 students | Physical | Cards | Ace | 3 | 18 | |
| 3 | 60 students | Paper | Cards/Envelopes | Ace/Money | 3 | 1 |
[i] Note. Question marks (?) indicate that the information could not be retrieved from the article.
Table 3
Characteristics of included studies: design, independent and dependent variable.
| Article | Study number | Design | Independent variable(s) | Dependent variable(s) |
|---|---|---|---|---|
| Baratgin & Politzer, 2010 | 1 | 2 × between | Instructions | Probability judgment (winning when staying) |
| 2 | 2 × within | Instructions | Probability judgment (winning when staying) | |
| Burns & Wieth, 2003 | / | 2 × between | Problem context | - Behaviour: switching/staying - Probability judgment (winning when switching) in frequencies |
| Burns & Wieth, 2004 | 1 | 4 × between | Problem context | - Behaviour: switching/staying - Probability judgment (winning when switching) |
| 2 | 3 × 2 between | - Number of options - Problem context | - Behaviour: switching/staying | |
| 3 | 2 × between | Problem context | - Behaviour: switching/staying - Probability judgment (winning when switching and staying) in frequencies | |
| 4 | 2 × between | Training | - Behaviour: switching/staying - Probability judgment (winning when switching and staying) in frequencies | |
| De Neys, 2005 | 1b | 2 × between: results 1b compared to results 1a | Working memory load | Behaviour: switching/staying/equal |
| De Neys & Verschueren, 2006 | 1 | Correlational | Working memory capacity | Behaviour: switching/staying/equal |
| 2 | Correlational | Working memory capacity | Behaviour: switching/staying/equal | |
| 3 | 2 × between | Working memory load | Behaviour: switching/staying/equal | |
| DiBattista, 2011 | / | No systematic manipulation | - Behaviour: switching/staying - Correct explanation | |
| Efendic & Drace, 2015 | / | 2 × between | Instructions | - Behaviour: switching/staying |
| Fox & Levav, 2004 | 1a | 3 × between | Behaviour of host | - Behaviour: trading or not - Probability judgment |
| 1b | 2 × between | Behaviour of host | - Behaviour: trading or not - Probability judgment | |
| Franco-Watkins et al., 2003 | 1 | 2 × 2 × 2 between | - Choice restriction - Number of options during training - Number of options in final MHD | - Behaviour training: switching/staying - Behaviour final MHD: switching/staying - Probability judgment |
| 2 | 2 × 2 × 2 × 2 between | - Number of options during training - Number of options in final MHD - Probability reinforcement for switching - Hypothetical player’s decision | - Behaviour final MHD: switching/staying - Probability judgment | |
| 3 | - 3 × between - 3 × within | - Number of options - Prize | - Behaviour: switching/staying - Probability judgment (winning when switching and staying) | |
| Herbranson & Schroeder, 2010 | 3 | 2 × between | Probability reinforcement for switching | Behaviour: switching/staying |
| Herbranson & Wang, 2014 | 2 | 2 × between | Distribution of unequal base rates across the options | - Behaviour: initial choice - Behaviour: switching/staying |
| Hirao et al., 2016 | / | 3 × within | Probability reinforcement for switching | - Behaviour: switching/staying - Probability judgement (winning when switching and staying) - Physiology: stimulus-preceding negativity (SPN) |
| Hirao et al., 2017 | / | No systematic manipulation | - Behaviour: switching/staying - Probability judgement (winning when switching and staying) - Physiology: stimulus-preceding negativity (SPN) | |
| Howard et al., 2007 | / | 4 × between | - Representation of second stage information - Number of options | Behaviour: switching/staying |
| Idson et al., 2004 | / | 2 × between | Training type | Behaviour: switching/staying |
| Klein et al., 2013 | / | 2 × between: results humans compared to monkeys’ results | Species | Behaviour: switching/staying |
| Krauss & Wang, 2003 | 1 | 3 × between | Inclusion of four psychological elements (i.e., perspective change, one-door scenario, mental models, frequency simulation) | Behaviour: switching/staying (Classification of switchers in ‘correct explanations’, ‘correct intuition’, ‘random switchers’) |
| 2 | 4 × between | Inclusion of four psychological elements (i.e., perspective change, one-door scenario, mental models, frequency simulation) | Behaviour: switching/staying (Classification of switchers in ‘correct explanations’, ‘correct intuition’, ‘random switchers’) | |
| 3 | 4 × between | Training type | Correct solution with mathematically correct justifications | |
| Mazur & Kahlbaugh, 2012 | 2 | 3 × between | Probability reinforcement for switching | Behaviour: switching/staying |
| 3 | Only assigned to 67% condition: results compared to students’ results | Age group | Behaviour: switching/staying | |
| Petrocelli, 2013 | / | No systematic manipulation | Behaviour: switching/staying | |
| Petrocelli & Harris, 2011 | 1 | No systematic manipulation | - Behaviour: switching/staying - Counterfactual thoughts following losses - Memory for decision/outcome frequencies | |
| 2 | 2 × between | Counterfactual salience | - Behaviour: switching/staying - Memory for decision/outcome frequencies | |
| Saenen et al., 2015a | / | 3 × 3 between Correlational | - Age - Number of options Inhibition capacity | - Behaviour: switching/staying - Probability judgment (winning when switching or staying) |
| Saenen et al., 2015b | / | 2 × between | - Numerical feedback format - Conditional feedback format | - Behaviour: switching/staying - Probability judgment (winning when switching or staying) |
| Slembeck & Tyran, 2004 | / | 2 × 2 between | - Communication - Competition | Behaviour: switching/staying |
| Stibel et al., 2009 | 1 | 2 × between | Number of options | - Behaviour: switching/staying - Probability judgment |
| 2 | 6 × between | Number of options | - Behaviour: switching/staying | |
| 3 | 2 × between | Memory task | - Behaviour: switching/staying - Probability judgment | |
| 4 | 2 × between | Number of options | - Behaviour: switching/staying - Probability judgment | |
| Tubau, 2008 | 1 (a + b) | 2 × 2 between | - Numerical format - Inclusion of a graphical representation | - Behaviour: switching/staying/equal - Probability judgment (winning when switching and staying) |
| 2 | Correlational | Mathematical skills | - Behaviour: switching/staying/equal - Probability judgment (winning when switching and staying) | |
| 3 | Correlational | - Mathematical skills - Anagram solving skills | - Behaviour: switching/staying/equal - Probability judgment (winning when switching and staying) | |
| Tubau & Alonso, 2003 | 1 | No systematic manipulation | - Behaviour: switching/staying/equal - Probability judgment (winning when switching and staying) in frequencies | |
| 2 | 3 × between | - Participant’s role - Perspective effect | Behaviour: switching/staying | |
| 3 | 3 × between | - Perspective effect - Explicit representation | - Behaviour: switching/staying/equal - Probability judgment (winning when switching and staying) | |
Table 4
Overview of the different phases in the MHD, its related causes explaining humans’ systematic failure on the MHD, and its related interventions to improve humans’ MHD performance.
| Phase 1: Before elimination | Phase 2: After elimination | Phase 3: After one completed trial | Phase 4: After multiple trials | |
|---|---|---|---|---|
| Research question 1: Causes explaining humans’ suboptimal MHD performance | - Difficulties with initial probability understanding - Illusion of control | - Failure to take into account the host’s dependent behaviour - Partitioning-editing-counting - Updating - Anticipated regret/General reliance on affect - Conservative response tendency (stimulus-preceding negativity) | - Counterfactual thinking - Experienced regret | - Probability matching - Distorted memory for decision/outcome frequencies |
| Research question 2: Improving humans’ MHD performance | - Numerical representation - Number of options | - Emphasis on the underlying structure - Representation of conditional information | - Experience due to multiple trials - Conditional frequency feedback - Probability reinforcement - Competition (and communication) |