Chapter 36 Quiz: The Psychology of Betting
Instructions: Answer all 25 questions. This quiz is worth 100 points. You have 60 minutes. A calculator is permitted; no notes or internet access. For multiple choice, select the single best answer. For short answer questions, be concise but thorough.
Section 1: Multiple Choice (10 questions, 3 points each = 30 points)
Question 1. A bettor consistently increases her stake size after two or more consecutive losses, believing the next bet is "more likely to win." Which cognitive bias is primarily at work?
(A) Anchoring bias
(B) Confirmation bias
(C) Gambler's fallacy
(D) Availability bias
Answer
**(C) Gambler's fallacy.** The gambler's fallacy is the mistaken belief that past independent outcomes affect future probabilities. If each bet is an independent event, the probability of winning the next bet is unchanged regardless of the previous streak of losses. The bettor is confusing the law of large numbers (which describes long-run convergence) with a nonexistent short-run "correction" mechanism. Increasing stake based on this belief compounds the error by exposing more capital during a period of no informational advantage.Question 2. After your model identifies a +EV bet on a soccer match, you search Google for recent news about the teams. You read three articles supporting your position and stop searching. Which bias does this behavior exemplify?
(A) Availability bias
(B) Confirmation bias
(C) Anchoring bias
(D) Hindsight bias
Answer
**(B) Confirmation bias.** Confirmation bias is the tendency to seek, interpret, and recall information that confirms one's pre-existing beliefs. The bettor selectively stopped searching after finding supporting evidence and did not actively look for disconfirming information. A debiased approach would involve deliberately searching for reasons why the bet might be wrong before making the final decision.Question 3. A sports commentator says, "The Patriots always play better after a loss --- they're a bounce-back team." This claim is most likely an example of:
(A) Anchoring bias applied to the spread
(B) Narrative bias combined with selective memory
(C) The Dunning-Kruger effect in broadcasting
(D) Loss aversion projected onto the team
Answer
**(B) Narrative bias combined with selective memory.** The "bounce-back team" narrative is a story that makes intuitive sense but is rarely supported by statistical evidence. The commentator is likely remembering instances that fit the narrative (availability bias contributing to selective memory) and weaving them into a compelling story (narrative bias). In reality, team performance after a loss typically reflects regression to the mean rather than a motivational response, and any "bounce-back" effect is usually statistically indistinguishable from chance.Question 4. A bettor originally estimated Team A's win probability at 60%. The sportsbook opens the line implying 52%. The bettor revises her estimate to 58%. This insufficient adjustment from her prior toward the market price is an example of:
(A) Gambler's fallacy
(B) Anchoring bias
(C) Overconfidence
(D) Sunk cost fallacy
Answer
**(B) Anchoring bias.** Anchoring bias occurs when a person relies too heavily on an initial piece of information (the "anchor") when making subsequent judgments. The bettor's original 60% estimate serves as the anchor, and her adjustment toward the market-implied 52% is insufficient. A Bayesian updater would weight the market information more heavily, especially if the market is known to be efficient. The bettor's final estimate of 58% is likely still overweighted toward her anchor.Question 5. Which of the following is the most reliable long-term indicator that a bettor is making good decisions, regardless of variance?
(A) Positive return on investment over the last 100 bets
(B) Consistently beating the closing line
(C) A winning streak of 15+ consecutive bets
(D) Outperforming a coin-flip model on moneyline bets
Answer
**(B) Consistently beating the closing line.** Closing Line Value (CLV) is the strongest known predictor of long-term profitability. The closing line represents the most efficient price because it incorporates the maximum amount of information. A bettor who consistently gets better odds than the closing line is demonstrating genuine pricing skill, even if short-term results are dominated by variance. A positive ROI over 100 bets (option A) could easily be due to luck, a winning streak (option C) is expected by chance, and outperforming a coin-flip (option D) is a low bar.Question 6. A bettor on tilt is most likely to exhibit which combination of behaviors?
(A) Smaller bets, fewer bets, more model reliance
(B) Larger bets, more bets, less model reliance
(C) Same-sized bets, fewer bets, more model reliance
(D) Larger bets, fewer bets, more careful analysis
Answer
**(B) Larger bets, more bets, less model reliance.** Tilt --- emotional deviation from optimal strategy --- typically manifests as increased bet sizing (chasing losses or capitalizing on perceived "momentum"), increased bet frequency (action-seeking behavior), and reduced adherence to quantitative models in favor of gut feelings or emotional reasoning. These three behaviors compound to dramatically increase variance and expected loss. The hallmark of tilt is the abandonment of process discipline.Question 7. The Dunning-Kruger effect in sports betting contexts predicts that:
(A) Expert bettors systematically overestimate their edge
(B) Novice bettors systematically underestimate their edge
(C) Novice bettors overestimate their ability while experts may slightly underestimate theirs
(D) All bettors accurately assess their skill level after sufficient experience
Answer
**(C) Novice bettors overestimate their ability while experts may slightly underestimate theirs.** The Dunning-Kruger effect describes a cognitive bias where people with low ability in a domain overestimate their competence (they "don't know what they don't know"), while highly skilled individuals may slightly underestimate theirs (they assume others share their level of understanding). In sports betting, this manifests as overconfident beginners who believe they have an edge based on limited analysis, and experienced bettors who may be too cautious about the edges they have identified.Question 8. After a game ends, you think "I knew that was going to happen" even though your pre-game notes show no such prediction. This is:
(A) Confirmation bias
(B) Hindsight bias
(C) Narrative bias
(D) Overconfidence
Answer
**(B) Hindsight bias.** Hindsight bias (also called the "knew-it-all-along" effect) is the tendency to perceive past events as having been more predictable than they actually were. The critical evidence here is the discrepancy between what you actually predicted (recorded in pre-game notes) and what you remember predicting (distorted by knowledge of the outcome). This is why written, timestamped prediction records are essential for debiasing --- they provide an objective check against hindsight distortion.Question 9. A bettor has a $50,000 bankroll and bets 2% per wager. After losing $5,000 (10% drawdown), she reduces her bet size to 1% "until things turn around." Assuming her edge has not changed, what is the primary cost of this behavior?
(A) No cost; conservative sizing is always prudent during drawdowns
(B) Reduced long-term growth rate due to under-betting when the bankroll has already adjusted
(C) Increased risk because she will need to bet longer to recover
(D) Violation of fixed-fraction sizing, which requires constant percentages
Answer
**(B) Reduced long-term growth rate due to under-betting when the bankroll has already adjusted.** If the bettor's edge has not changed (key assumption), then the optimal Kelly fraction has not changed either. A percentage-based staking system naturally reduces absolute bet size as the bankroll shrinks --- her 2% of $45,000 ($900) is already smaller than her previous 2% of $50,000 ($1,000). By additionally halving her fraction to 1%, she is now betting $450, which is well below her optimal Kelly fraction. This reduces her expected growth rate and extends the time needed to recover. The behavior is driven by loss aversion (the emotional impact of the drawdown), not by rational analysis.Question 10. Which technique is most effective at reducing the combined impact of multiple cognitive biases on betting decisions?
(A) Increasing the amount of time spent on each decision
(B) Following a pre-defined, written decision process with explicit criteria
(C) Discussing each bet with other bettors before placing it
(D) Reviewing outcomes of previous bets before making new decisions
Answer
**(B) Following a pre-defined, written decision process with explicit criteria.** A structured, pre-defined decision process (sometimes called a "decision checklist" or "pre-commitment protocol") is the single most effective debiasing tool because it externalizes the decision criteria before emotional or cognitive biases can distort them. It forces the bettor to evaluate each bet against objective criteria rather than subjective impressions. Spending more time (A) can actually increase some biases like overthinking. Group discussion (C) can help but introduces groupthink. Reviewing past outcomes (D) can trigger recency bias or hindsight bias.Section 2: True/False with Justification (5 questions, 4 points each = 20 points)
For each statement, indicate True or False and provide a 2-3 sentence justification.
Question 11. "A bettor who wins 60% of her bets over a 200-bet sample has definitively proven she has an edge."
Answer
**False.** At a 50% base rate (coin flip), the probability of winning 60% or more over 200 bets is approximately 0.23% --- unlikely but not impossible, especially when considering that most bettors place thousands of bets across their career and report only their best stretches (survivorship bias). To definitively establish an edge, we need to consider the specific odds at which bets were placed, test for statistical significance with appropriate corrections for multiple comparisons, and ideally validate through CLV analysis rather than raw win rate alone.Question 12. "The hot-hand effect has been conclusively disproven in sports, and any perceived streak of success is purely random."
Answer
**False.** The original Gilovich, Vallone, and Tversky (1985) study concluded the hot hand was a fallacy, but more recent research (Miller and Sanjurjo, 2018) identified a statistical bias in the original analysis. When corrected, there is evidence for a small but real hot-hand effect in basketball shooting and other sports. However, the magnitude of the true effect is much smaller than what people perceive, and in sports betting, the market generally prices in any observable streak effects, making them difficult to exploit.Question 13. "Loss aversion --- the tendency to feel losses more intensely than equivalent gains --- has no practical impact on a bettor who uses a fixed-fraction staking system."
Answer
**False.** While a fixed-fraction staking system mechanically adjusts bet sizes appropriately, loss aversion still affects the bettor through multiple channels: it can cause the bettor to abandon the system during drawdowns (switching to smaller fractions or stopping entirely), to avoid high-variance positive-EV bets that "feel" risky, and to cash out futures or hedge positions prematurely to "lock in" gains rather than maintaining optimal positions. The staking system is a tool; loss aversion affects whether the bettor actually follows the tool's recommendations.Question 14. "Meditation and mindfulness practices have no empirically supported benefits for sports betting decision-making."
Answer
**False.** Research in cognitive psychology and neuroscience has demonstrated that mindfulness practice improves executive function, reduces emotional reactivity, and enhances decision-making under uncertainty --- all directly relevant to sports betting. Specifically, mindfulness has been shown to reduce the impact of sunk cost bias, improve delay discounting (the ability to wait for larger future rewards), and increase metacognitive awareness (the ability to notice your own thinking patterns). These benefits are supported by randomized controlled trials, though the magnitude varies.Question 15. "A bettor who keeps detailed written records of her reasoning before each bet is primarily practicing good record-keeping, not bias reduction."
Answer
**False.** Pre-decision recording serves a dual function: it is a record-keeping practice and a powerful debiasing tool. The act of writing down reasoning before the outcome is known creates an objective baseline against which hindsight bias can be measured. It forces the bettor to articulate (and therefore examine) their reasoning, which can surface confirmation bias, narrative bias, and unjustified overconfidence. The written record also prevents post-hoc rationalization of bad decisions that happened to produce good outcomes.Section 3: Short Answer (5 questions, 6 points each = 30 points)
Question 16. Define tilt in the context of sports betting and list four specific behavioral indicators that a bettor is experiencing tilt.
Answer
**Tilt** is an emotional state in which a bettor deviates from their optimal, pre-defined decision-making process due to psychological arousal, typically triggered by losses, bad beats, or frustration. It is borrowed from poker terminology but applies equally to sports betting. Four specific behavioral indicators: 1. **Increased bet frequency** --- placing bets outside normal patterns, including bets on unfamiliar sports or markets to "get action." 2. **Increased stake sizes** --- betting larger amounts than the model or staking plan recommends, often to recover recent losses quickly. 3. **Ignoring model output** --- overriding quantitative recommendations with gut feelings or emotional reasoning, often accompanied by rationalizations. 4. **Reduced pre-bet analysis** --- spending less time on each decision, skipping elements of the pre-bet checklist, or placing bets impulsively without running the full decision process. Additional valid indicators include: irritability or frustration disproportionate to the stakes involved, inability to stop betting at predetermined session limits, and seeking "revenge" bets against specific teams or markets.Question 17. Explain the difference between process-oriented thinking and outcome-oriented thinking in sports betting. Give a concrete example of how each would evaluate the same bet that lost.
Answer
**Process-oriented thinking** evaluates the quality of a betting decision based on the information available and the reasoning applied at the time the decision was made, independent of the outcome. **Outcome-oriented thinking** evaluates decisions primarily based on whether they won or lost. **Example:** A bettor identifies a +3.2% expected value bet on a tennis match at decimal odds of 2.10 (implied probability 47.6%) when her model estimates the true probability at 50.8%. She bets 2.5% of her bankroll per her Kelly-based sizing. The bet loses. **Process evaluation:** The bettor identified a legitimate edge (+3.2% EV), verified it against her model, sized the bet appropriately, and followed her pre-bet checklist. The bet was well-made regardless of outcome. Process score: high. **Outcome evaluation:** The bet lost money. The bettor "should have" either not bet or bet the other side. Outcome score: low. The critical insight is that a 50.8% probability means this bet will lose 49.2% of the time. Over thousands of repetitions, this exact type of bet will generate profit, but any individual instance is nearly a coin flip. Process-oriented bettors survive variance because they maintain discipline through losing streaks; outcome-oriented bettors change their strategy after every loss.Question 18. What is the "narrative bias" and why is it particularly dangerous in sports betting compared to other forms of analytical decision-making?
Answer
**Narrative bias** is the human tendency to construct and prefer coherent stories (narratives) over raw statistical information when making sense of events. People naturally seek causal explanations for what are often random or multivariate outcomes. Narrative bias is particularly dangerous in sports betting for several reasons: 1. **Sports are inherently narrative-rich.** The media, broadcasters, and fan culture produce constant narrative content --- "revenge games," "must-win situations," "playoff experience," "momentum" --- that attaches causal meaning to outcomes that may be largely random. 2. **Narratives are memorable; statistics are not.** A dramatic comeback win is remembered vividly; the 538 undramatic games where the favorite covered are forgotten. This interaction between narrative bias and availability bias amplifies mispricing. 3. **Narratives resist disconfirmation.** When a narrative-driven bet loses, the narrative can be adjusted rather than abandoned ("they were due, but the refs intervened"). This makes narrative-based reasoning self-reinforcing in a way that formal statistical models are not. 4. **Sports betting markets partly reflect narrative pricing.** Public money often flows toward compelling narratives, potentially creating value on the less narratively appealing side. The quantitative bettor who can resist narratives can exploit the mispricing they create.Question 19. A bettor rates herself as a 90th-percentile handicapper after six months of betting and a 58% win rate on 150 bets at standard -110 odds. Compute the p-value for the hypothesis that her true win rate is 50%, and discuss what this means for her self-assessment in the context of the Dunning-Kruger effect.
Answer
**Computation:** Under H0: p = 0.50, with n = 150: - Expected wins: 75 - Standard deviation: sqrt(150 * 0.50 * 0.50) = sqrt(37.5) = 6.12 - Observed wins: 0.58 * 150 = 87 - z-statistic: (87 - 75) / 6.12 = 12 / 6.12 = 1.96 - One-tailed p-value: approximately 0.025 **Interpretation:** The p-value of 0.025 means there is a 2.5% probability of observing a 58% or higher win rate over 150 bets if the true rate is exactly 50%. This is statistically significant at the 5% level but not at the 1% level. **Dunning-Kruger analysis:** While the result is suggestive of genuine skill, rating herself at the 90th percentile based on 150 bets shows signs of overconfidence consistent with the Dunning-Kruger effect. Reasons for caution include: (a) 150 bets is a small sample that could reflect a lucky streak within the confidence interval; (b) the true edge implied (about 3.5% yield) would need thousands of bets to confirm reliably; (c) a 90th-percentile ranking would imply outperforming the vast majority of sharp bettors, which is extraordinary and requires extraordinary evidence; and (d) the bettor may be exhibiting "peak of Mount Stupid" overconfidence, where initial success leads to inflated self-assessment before the complexities and challenges of sustained profitability become apparent.Question 20. Describe two specific ways in which overconfidence bias affects bet sizing decisions, and explain why each leads to worse long-term outcomes compared to properly calibrated confidence.
Answer
**Way 1: Overestimating edge magnitude leads to over-sizing.** When a bettor is overconfident in their probability estimate, they believe their edge is larger than it actually is. Since Kelly criterion stake sizing is proportional to edge (f* = edge / odds), an overestimated edge produces an oversized bet. Betting above the true Kelly fraction reduces the long-term geometric growth rate and increases variance. In the extreme (betting 2x Kelly), the expected growth rate drops to zero. This means overconfidence does not just reduce profits --- it can convert a profitable strategy into a break-even or losing one. **Way 2: Overconfidence in model accuracy leads to insufficient diversification.** An overconfident bettor may concentrate their bankroll on a small number of "high-conviction" bets rather than diversifying across many smaller opportunities. This concentration increases variance without increasing expected return. If the bettor's probability estimates are miscalibrated (as overconfidence implies), concentrated positions amplify the cost of errors. A properly calibrated bettor acknowledges uncertainty in each individual estimate and diversifies accordingly, allowing the law of large numbers to work in their favor.Section 4: Scenario Analysis (5 questions, 4 points each = 20 points)
Question 21. A professional bettor has been profitable for three years running. In the fourth year, he experiences a 20% drawdown over two months. He begins to question whether his edge still exists. Outline a structured framework (at least four steps) for distinguishing between a variance-driven drawdown and genuine edge degradation.
Answer
**Step 1: Analyze CLV.** Check whether the bettor is still beating the closing line. If CLV remains positive despite negative P&L, the drawdown is likely variance, not edge loss. If CLV has deteriorated, investigate further. **Step 2: Compute expected drawdown range.** Using the bettor's historical edge, win rate, and stake size, run a Monte Carlo simulation to determine the probability of a 20% drawdown within any two-month period. If this probability exceeds 5-10%, the drawdown is within normal variance. **Step 3: Segment performance.** Break down results by sport, bet type, market, and time of week. If the drawdown is concentrated in one segment while others remain profitable, the issue may be localized rather than systemic. If all segments are declining uniformly, systemic edge loss is more likely. **Step 4: Check for environmental changes.** Investigate whether anything has changed in the markets the bettor operates in: sportsbook algorithm updates, new competing sharp bettors, changes in data availability, or line movement patterns. Edge degradation often has identifiable external causes. **Step 5: Apply a waiting rule.** Absent evidence of systemic edge loss, continue operating the system for a pre-specified additional period (e.g., 200 more bets) before making any strategic changes. This prevents knee-jerk reactions to variance that could destroy a still-functional strategy.Question 22. Two friends start a sports betting partnership. Friend A is the modeler who builds the quantitative system. Friend B provides the bankroll. After three months and a 12% drawdown, Friend B wants to reduce the bankroll allocation. How might each partner's cognitive biases be contributing to this conflict?
Answer
**Friend B (bankroll provider) likely biases:** - **Loss aversion:** The pain of watching a 12% decline in capital is psychologically more intense than the pleasure of equivalent gains, driving a desire to reduce exposure. - **Outcome orientation:** Friend B may evaluate the strategy based on the three-month result rather than the process quality or CLV performance. - **Recency bias:** The current drawdown looms larger than the initial agreement, which was made when the future felt abstract. **Friend A (modeler) likely biases:** - **Overconfidence:** Friend A may be too certain that the model is sound and dismiss Friend B's concerns without adequate consideration. - **Sunk cost fallacy:** Friend A has invested significant time building the model and may resist acknowledging potential problems. - **Confirmation bias:** Friend A may selectively focus on metrics that show the model is working (e.g., CLV) while dismissing metrics that suggest problems. **Resolution framework:** Pre-agreed drawdown review thresholds and decision protocols, established before any bets are placed, would reduce the role of biases in this decision. Both partners should review CLV data, conduct a segmented performance analysis, and compare the actual drawdown to the Monte Carlo-simulated drawdown distribution before making allocation changes.Question 23. You have built a model that identifies +EV bets at a 3% average edge. During a live betting session, your model fires a signal on a bet you "feel" strongly is wrong based on your watching the game. Describe the psychological conflict, identify the biases that could be operating on each side, and propose a decision rule for resolving such conflicts.
Answer
**The conflict:** Your analytical system (the model) and your intuitive system (gut feeling from watching the game) are in disagreement. This is a classic System 1 (fast, intuitive) vs. System 2 (slow, analytical) conflict. **Biases on the "trust the model" side:** - Automation bias: over-trusting the model because it is quantitative, even when it may be using stale inputs or missing live-game context. **Biases on the "trust the feeling" side:** - Narrative bias: constructing a story from the game action ("this team looks sluggish") that may not reflect probabilistic reality. - Availability bias: the visual impressions from the last few minutes of play are disproportionately salient. - Overconfidence in subjective observation: eye-test impressions are notoriously unreliable for probability estimation. **Decision rule:** 1. If the disagreement is about information the model does not have (e.g., you see a player limping who is not listed as injured), this is legitimate new information. Reduce the stake by 50% or pass. 2. If the disagreement is about the "feel" of the game without specific new information, follow the model. Your model has been validated over thousands of data points; your feeling has not. 3. Record the conflict in your journal. Over time, analyze whether your gut overrides improve or harm performance. This data will calibrate your future decision rule.Question 24. A recreational bettor tells you he bets on sports "for entertainment" and that he "knows he'll lose in the long run." He bets approximately $200 per week on NFL games. At what point, if any, does this recreational approach become problematic, and what warning signs would you watch for?
Answer
Recreational betting with acknowledged negative expected value is a legitimate entertainment choice, analogous to spending money on concerts or dining out. It becomes problematic when: **Financial warning signs:** - Betting more than he can afford to lose (defined as money allocated for essentials like rent, food, or debt payments). - Increasing bet sizes to "make up for" previous losses. - Borrowing money to fund betting. - Hiding the extent of betting from a partner or family. **Behavioral warning signs:** - Preoccupation with betting that interferes with work or relationships. - Irritability or restlessness when unable to bet. - Using betting to escape negative emotions (anxiety, depression, boredom) rather than as genuine entertainment. - Repeatedly attempting to cut back or stop without success. - Chasing losses --- continuing to bet after a losing session to try to get back to even. **Specific threshold analysis:** $200/week is approximately $10,400/year. The appropriateness depends entirely on his income and financial situation. As a guideline, gambling expenditure exceeding 1-2% of net income warrants self-reflection, and exceeding 5% is a strong warning sign. The key question is not the absolute amount but whether he can lose his entire weekly allocation without financial stress or emotional distress.Question 25. Explain the concept of "process journal" in sports betting. What should it contain that a standard bet log does not? How often should it be reviewed, and what specific patterns should the reviewer look for?