Chapter 36 Exercises: The Psychology of Betting

Instructions: Complete all exercises in the parts assigned by your instructor. For written responses, provide structured arguments with supporting evidence. For programming exercises, include type hints, docstrings, and sample output. For self-assessment exercises, answer honestly --- these are tools for personal development, not graded evaluations of your character.

Part A: Cognitive Bias Identification

Each problem is worth 5 points. Answer in complete sentences.

Exercise A.1 --- Anchoring Bias in Line Movement

A sportsbook opens the line for a Monday Night Football game at Chiefs -7.5. By Sunday evening, the line has moved to Chiefs -5.5 due to injury reports and sharp action. You run your model and it outputs Chiefs -4.8. Explain how anchoring bias might affect a bettor who saw the opening line but not the closing line movement. What specific decision error is likely, and how would you structure your process to avoid it?

Exercise A.2 --- Confirmation Bias Audit

You believe the Denver Nuggets are undervalued this season and have been betting their moneyline consistently. Over the last 20 games, they are 11-9 against your model's spread. Describe three specific behaviors that would indicate confirmation bias in how you evaluate this position. For each behavior, propose a concrete countermeasure.

Exercise A.3 --- Gambler's Fallacy Scenario

A bettor has lost seven consecutive NFL spread bets. She tells you, "I'm due for a win --- the law of averages has to kick in eventually." Write a mathematically precise explanation (using probability notation) of why this reasoning is fallacious. Then explain the related concept of regression to the mean and why it does not apply to independent events.

Exercise A.4 --- Availability Bias Case

After watching a dramatic last-second three-pointer win a nationally televised NBA game, a bettor increases his bet size on NBA underdog moneylines by 50% for the next week. Identify the specific cognitive bias at work, explain the mechanism by which the televised event distorted his probability assessment, and calculate the expected bankroll impact if his normal edge on these bets is +2.5% and the increased sizing pushes him above his optimal Kelly fraction by 40%.

Exercise A.5 --- Sunk Cost Fallacy

You placed a $500 futures bet on the Tampa Bay Buccaneers to win the Super Bowl at +2500 before the season. They are now 4-8 with a 0.3% implied probability of making the playoffs. A sportsbook is offering cash-out at $12. Explain the sunk cost fallacy in this context, derive the mathematically correct decision framework, and discuss why emotional attachment to the original bet amount distorts decision-making.

Exercise A.6 --- Hindsight Bias Self-Test

Describe a protocol for testing your own susceptibility to hindsight bias. Your protocol should include: (a) a pre-game prediction recording method, (b) a post-game recollection task, (c) a quantitative comparison metric between predictions and recollections, and (d) a threshold for determining whether hindsight bias is affecting your decision-making. Explain why this self-test must be conducted over at least 50 events to be reliable.

Part B: Emotional Management and Tilt

Each problem is worth 5 points.

Exercise B.1 --- Tilt Trigger Inventory

List seven common tilt triggers specific to sports betting (not generic emotional triggers). For each trigger, rate its likely intensity on a 1-10 scale and describe the characteristic behavioral response a bettor on tilt would exhibit. Design a personal "tilt scorecard" that could be used during a betting session to monitor emotional state.

Exercise B.2 --- Physiological Response Mapping

Research has shown that cortisol levels increase by an average of 30-50% during gambling activities. Describe how elevated cortisol affects the prefrontal cortex's ability to process probabilistic information. Then propose three physical interventions (not cognitive ones) that a bettor could use during a session to reduce physiological arousal before making a betting decision.

Exercise B.3 --- Stop-Loss Rule Design

Design a three-tiered stop-loss system for a bettor with a $10,000 bankroll who bets an average of 8 bets per day at 1-3% of bankroll per bet. Tier 1 should trigger a 30-minute break, Tier 2 should end the session for the day, and Tier 3 should require a 48-hour cooling-off period. Specify the exact thresholds for each tier in terms of both units lost and percentage of bankroll, and justify your choices using the concept of expected daily variance.

Exercise B.4 --- Bad Beat Analysis

You bet $300 on an NBA spread at -4.5. Your team leads by 12 with 45 seconds remaining and the opposing team is dribbling out the clock. An inadvertent foul leads to free throws, then a meaningless three-pointer at the buzzer makes the final margin exactly 4, losing your spread bet. Write a structured "bad beat analysis" that separates (a) the quality of the decision from (b) the quality of the outcome. Then calculate the pre-game win probability implied by -4.5 at -110, and compare it with the in-game win probability at the 45-second mark to quantify how much value you actually captured versus what variance took away.

Exercise B.5 --- Decision Fatigue Protocol

Research in cognitive psychology suggests that decision quality degrades after approximately 3-4 hours of continuous decision-making (ego depletion). Design a betting session schedule for a full Saturday of college football (12 hours of games) that manages decision fatigue. Include: session length limits, break durations and activities, a maximum number of decisions per session, and a rule for prioritizing decisions when there are more opportunities than your cognitive budget allows.

Exercise B.6 --- Emotional Journaling Template

Design a structured emotional journal entry template that a bettor would complete after each betting session. The template should capture: pre-session mood (5-point scale), specific emotions experienced during the session, any tilt triggers encountered, decisions made while emotionally elevated, whether the stop-loss protocol was needed, and a post-session self-assessment. Explain why capturing this data enables pattern recognition that purely quantitative bet logs miss.

Exercise B.7 --- Variance Tolerance Calibration

Using the formula for the standard deviation of a bettor's bankroll after $n$ bets at flat stake $s$ with win probability $p$ and decimal odds $d$, calculate the 95% confidence interval for bankroll after 100, 500, and 1000 bets for a bettor with a 53% win rate on -110 bets at 2% of initial bankroll per bet. Present the results as a "what to expect" guide that would help a new bettor calibrate their variance tolerance.

Part C: Applied Bias Analysis

Each problem is worth 10 points. These require both written analysis and code.

Exercise C.1 --- Recency Bias Detector

Write a Python program that analyzes a bettor's historical record and detects recency bias. The program should: (a) compare the bettor's actual bet sizing to what their model recommended, (b) measure whether bet sizes systematically increase after wins and decrease after losses (or vice versa), (c) compute the autocorrelation of bet size changes with prior outcomes, and (d) produce a report quantifying the degree of recency bias. Test with synthetic data.

Exercise C.2 --- Overconfidence Calibration Analyzer

Write a Python program that takes a bettor's prediction log (predicted probability, actual outcome) and produces a calibration analysis. The program should: (a) bin predictions into deciles, (b) compare predicted probabilities to actual frequencies, (c) compute the Expected Calibration Error (ECE), (d) produce a reliability diagram, and (e) generate a written assessment of whether the bettor is overconfident, underconfident, or well-calibrated. Include a specific analysis of whether overconfidence is worse at extreme probabilities.

Exercise C.3 --- Narrative Bias Filter

Design and implement a "narrative bias filter" that screens betting decisions for narrative contamination. The filter takes as input: (a) the bettor's written reasoning for a bet, (b) the model's numeric output, and (c) the magnitude of deviation between the two. It should flag bets where the written reasoning contains narrative language (e.g., "momentum," "due," "revenge game," "statement game") and the bet deviates from the model by more than a specified threshold. Implement keyword detection with appropriate sports betting context.

Exercise C.4 --- Loss Aversion Profit Impact

Simulate 10,000 seasons of 1,000 bets each for three bettor profiles: (a) Rational bettor who follows the model exactly, (b) Loss-averse bettor who reduces stake by 25% for 5 bets after each loss, and (c) Aggressive loss-chaser who increases stake by 30% for 3 bets after each loss. Assume a true edge of 3% on average -110 bets and a base stake of 2% of bankroll. Compare the distributions of final bankroll, maximum drawdown, and probability of ruin across the three profiles.

Exercise C.5 --- Bias Interaction Effects

Many cognitive biases interact with and reinforce each other. Write an analytical essay (500-800 words) describing three specific pairs of interacting biases in sports betting. For each pair, explain: (a) the individual bias mechanisms, (b) how they reinforce each other, (c) a concrete sports betting scenario where the interaction occurs, and (d) a combined countermeasure. Then implement a simulation demonstrating one of these interaction effects.

Part D: Self-Assessment and Reflection

Each problem is worth 7 points. These exercises require honest self-reflection.

Exercise D.1 --- Personal Bias Profile

Complete the following self-assessment for each of the six major cognitive biases discussed in Chapter 36 (anchoring, confirmation, availability, gambler's fallacy, sunk cost, hindsight). For each bias: rate your susceptibility on a 1-10 scale with a specific justification from your betting history, identify the context where you are most vulnerable, and describe one concrete countermeasure you will implement. Compile these into a "Personal Bias Profile" document.

Exercise D.2 --- Tilt History Analysis

Recall three specific instances where you experienced tilt (or made an emotionally compromised betting decision, or a decision in any domain where emotions overrode analysis). For each instance, document: the trigger, the emotional state, the decision made, the outcome, and what you would do differently. If you have not bet before, use analogous decision-making scenarios from other high-stakes contexts.

Exercise D.3 --- Process vs. Outcome Journal

For the next 20 betting decisions (or hypothetical evaluations of betting opportunities), maintain a dual-scored journal. Before learning the outcome, score the quality of your decision process on a 1-10 scale. After the outcome, record the result. After all 20 decisions, compute the correlation between process quality and outcome. Discuss what this correlation (or lack thereof) tells you about process-versus-outcome thinking over small samples.

Exercise D.4 --- Dunning-Kruger Self-Assessment

Estimate your percentile ranking among sports bettors in each of the following skills: probability estimation, bankroll management, emotional control, model building, and market knowledge. Then describe what evidence (quantified where possible) supports each self-assessment. Finally, identify the skill where you have the least evidence to support your self-assessment and explain what data you would need to collect to calibrate your confidence accurately.

Exercise D.5 --- Mental Resilience Plan

Write a one-page mental resilience plan for surviving a 15% bankroll drawdown that occurs despite making positive-EV bets. Your plan should include: (a) a mathematical demonstration that this drawdown is within normal variance, (b) specific actions you will take each day during the drawdown, (c) criteria for distinguishing a variance-driven drawdown from genuine model degradation, (d) a support system you will activate, and (e) conditions under which you would stop betting entirely versus continuing.

Part E: Synthesis and Application

Each problem is worth 5 points.

Exercise E.1 --- Debiasing Protocol Design

Design a comprehensive debiasing protocol that a small group of bettors (3-5 people) could implement collectively. The protocol should include: pre-decision bias checks, independent prediction recording before group discussion, structured disagreement processes, post-decision reviews, and a quarterly bias audit. Explain why group-based debiasing can be more effective than individual efforts.

Exercise E.2 --- Cognitive Bias in Market Pricing

Select three cognitive biases from Chapter 36 and explain how each contributes to specific, documented market inefficiencies in sports betting. For each, cite the relevant academic or practitioner literature and describe how a quantitative bettor can exploit the bias-driven mispricing while being careful not to exhibit the same bias themselves.

Exercise E.3 --- Psychology of Winning Streaks

A bettor has won 12 of her last 15 bets. Describe three psychological dangers she faces and three specific actions she should take. Then calculate the probability that a bettor with a 55% long-term win rate would experience a 12-of-15 stretch or better at some point during a 500-bet sample, and use this calculation to explain why hot streaks are less meaningful than they feel.

Exercise E.4 --- Cross-Domain Bias Comparison

Compare how cognitive biases manifest differently in sports betting versus financial trading. Address at least four biases and explain why the structure of sports betting (fixed-duration events, binary or near-binary outcomes, public information environment) amplifies or attenuates each bias relative to financial markets. What can sports bettors learn from the behavioral finance literature?

Exercise E.5 --- Teaching Bias Awareness

You are asked to give a 15-minute presentation to a group of recreational sports bettors about cognitive biases. They have no background in psychology or statistics. Design the outline of your presentation, including: three biases you would focus on (and why those three), one interactive demonstration for each, and three actionable takeaways they can implement immediately. Explain your pedagogical choices.