Guided course - 5 chapters

Game theory: A Practical Course with Liam Foster

Liam Foster teaches Game theory through five practical chapters that move from a clear foundation to guided work, applied decisions, and revision. You will finish with an annotated scenario and decision log, a tutor-ready capstone, saved notes, and a repeatable way to continue practicing.

Math learners, strategy-game players, debate students, and curious adults 2 hrs 30 min Practice and checkpoints Free curriculum

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What you will learn

Build knowledge, use it, and leave with evidence of progress.

Explain the essential Game theory vocabulary through a connected mental model.
Follow and explain a reliable strategic decision making workflow in guided practice.
Apply Game theory to a realistic scenario with visible constraints and tradeoffs.
Evaluate and revise an annotated scenario and decision log using evidence-based success criteria.
Complete a capstone and leave with a specific next-practice plan.

Before you start

Know the basic rules of the chosen activity or review them with the tutor
Use responsible-play boundaries where money or competition is involved

Useful materials

A board, replay, map, or scenario sheet
Notebook or annotation tool
Timer for selected practice rounds

Suggested rhythm

Complete one 30-minute chapter at a time: learn for 10 minutes, practice for 15, then use 5 minutes for the checkpoint and notes.

Course capstone

Game theory decision dossier

Analyze a sequence of Game theory decisions, compare realistic alternatives, and extract a reusable decision rule.

What you will submit

Three annotated decision points
A candidate-and-risk comparison
A post-review with one reusable rule

How it will be reviewed

Key information is noticed
Alternatives are plausible
Tradeoffs are explicit
The review separates process from outcome

Course chapters

Learn, practice, check, and record what matters.

2 hrs 30 min total

Chapter 1

Game theory: Foundations and vocabulary

Build a dependable mental model for Game theory before trying to memorize isolated details. You will define the essential vocabulary, inspect a worked example, and turn the ideas into a reference you can actually use.

27 min Not complete

Learning objectives

Explain the purpose of Game theory in your own words.
Use the chapter vocabulary accurately in a short example.
Distinguish a strong example from a common misconception.
Create a compact reference for later practice.

Key terms

Start with the purpose

Place Game theory inside a game or decision scenario with limited information, competing options, and consequences. Name the result a learner is trying to produce and the constraints that make the skill useful.

How Game theory actually works

These are the load-bearing ideas. Everything later in the course is an application of one of them, so it is worth reading slowly and returning to when something stops making sense.

Judge the decision, not only the result. Good decisions sometimes lose and poor ones sometimes win, because outcomes contain chance. Reviewing the reasoning available at the time is how skill actually improves.
Compare candidates before committing. The first plausible move is rarely the best one. Generating two or three options and comparing them is the habit that separates strong players and planners from quick ones.
Position beats immediate gain in most systems. Choices that improve your future options usually outperform ones that take the visible reward now. Naming which type a move is clarifies the trade being made.

Misconceptions worth clearing early

Each of these is common, understandable, and expensive to leave in place. Recognising them now saves rework later.

Playing or deciding by pattern recognition alone. Familiar shapes feel safe and fast. Fix: Pause on important decisions and check what has changed from the pattern you are recalling.
Judging past decisions by how they turned out. Outcomes are the most visible information. Fix: Ask what you knew at the time; a losing decision made on good reasoning should be repeated.
Ignoring what the opponent or environment intends. Focus naturally sits on your own plan. Fix: Before committing, name the strongest reply available to the other side.

Build the mental model

Connect the key terms as a process rather than a word list. Use this sequence: read the position, generate candidates, compare risks, choose, and review the decision rather than only the result.

Catch the common miss

Compare a surface-level attempt with one that shows relevant observations, viable alternatives, explicit tradeoffs, and an honest post-decision review. Explain the single difference that matters most.

Equation in context

Expected value

EV = \sum_i p_i \cdot v_i

Weigh every outcome by its probability; a decision can be good even when one result was bad.

Live decision model

Price a risky choice before taking it

Set the chance and the payoffs. The running total shows what repeating the choice really does.

A single round can lose even when the decision is good. Expected value is the slope of the long run, not a promise about the next round.

Find the break-even chance where the expected value is exactly zero.
Set up a positive-EV bet, then Re-roll until you find a run that still loses.

Side-by-side comparison

Two reviews of the same game

Both attempts look plausible from a distance. Toggle the highlights and study where they part ways.

Aspect	Result-based review	Decision-based review
Judgment	A win means the plan was right	Each decision judged by what was knowable at the time
Alternatives	The move played is the only one considered	Two candidate moves compared honestly
Lesson	"Play better next time"	One reusable rule extracted and written down

Results are noisy. Decisions are the only thing you can actually train.

Practice round

Match the Game theory vocabulary

Tap a term, then the definition it belongs to. Wrong guesses cost nothing but honesty.

Retrieval beats rereading: pulling a definition from memory strengthens it far more than recognizing it on the page.

Clear the board once, shuffle, and beat your attempt count.
Say each definition aloud before tapping — then check yourself.

Practice activity - 12 min

Make a one-page field guide

Create a compact field guide that would help a new learner recognize and begin using Game theory.

Write a one-sentence definition and purpose.
Add the four key terms with a plain-language example.
Include one non-example and explain why it misses.
Finish with a three-step starter checklist.

Deliverable

One annotated page or slide that can be reused in later chapters.

Success looks like

The definition is specific.
Examples match the vocabulary.
The checklist is usable without extra explanation.

Knowledge check

Which response best shows a usable foundation in Game theory?

1 question

AIt defines the idea, shows it in context, and explains why the example fits. BIt copies a list of terms without connecting them. CIt starts the final project before identifying the purpose. DIt chooses an answer without checking the situation.

Chapter notes Not started

2
Chapter 2
Probability: Guided demonstration

Follow a complete Probability example from setup to result, pausing at the decisions that experts often make silently. Then repeat the process with support and check your work against visible criteria.

29 min Not complete
Learning objectives

Sequence the main steps in a reliable Probability workflow.

Explain why each important decision is made.

Complete a supported example without skipping verification.

Use a checklist to identify one correction.
Key terms
1

Watch the whole process

Trace a model from the initial prompt to an annotated scenario and decision log. Mark each point where the learner must observe, choose, or verify rather than act automatically.
2

Worked example: Positive predictive value of a highly accurate test

Follow each step and predict the next before you read it. Predicting first is what turns a demonstration into practice.

Assume a condition affects 1% of people, the test detects 99% of true cases, and it wrongly flags 5% of healthy people.

Among 10,000 people, 100 have the condition and 99 of those test positive.

Of the 9,900 without it, 5% test positive, which is 495 false positives.

Total positives are 99 + 495 = 594, so the chance that a positive result is genuine is 99/594, about 16.7%.

When the base rate is low, most positive results are false no matter how impressive the accuracy figure sounds on its own.
3

Where this usually goes wrong

Watch for these while you work through the demonstration rather than afterwards.

The gambler's fallacy. A long run of one outcome feels like it is owed a correction. Fix: Independent trials have no memory. A fair coin that has landed heads nine times still lands heads next with probability one half.

Confusing the two directions of a conditional. The two read almost identically when stated in English. Fix: Write both out with explicit populations. The chance a positive test means disease is very different from the chance a diseased person tests positive.

Playing or deciding by pattern recognition alone. Familiar shapes feel safe and fast. Fix: Pause on important decisions and check what has changed from the pattern you are recalling.
4

Practice with scaffolding

Repeat the model with one detail changed. Keep the prompts visible and say or write the reason for each choice before continuing.

5

Check before feedback

Use relevant observations, viable alternatives, explicit tradeoffs, and an honest post-decision review as the quality test. Make one self-correction before asking the tutor to review the result.
Live probability
Roll until the pattern shows itself

Choose an event and a number of rolls, then watch luck wobble around the true probability.

Small samples lie. The gap between observed and expected shrinks as trials grow — the law of large numbers, seen instead of stated.

Run 20 rolls three times with Re-roll. How different are the outcomes?

Now run 400 rolls a few times. How different can they be?

Which event needs more rolls to look stable: 1-in-6 or 1-in-2?
Guided flowchart
A complete Probability practice run

flowchart LR N1["Read the task"] N2["Model one step"] N3["Try with support"] N4["Verify the result"] N1 --> N2 N2 --> N3 N3 --> N4

Pause at each arrow and explain the decision before moving to the next step.

Step 1 of 4: Read the task
Practice round
Rebuild the Probability method

The steps of this chapter's method, shuffled. Arrange them so they would actually work.

A method is a sequence, not a bag of tips — if the order surprises you, that is exactly the gap worth closing now.

Order the steps, then explain to yourself why step 2 cannot go last.

Shuffle again and solve it in fewer moves.
Practice activity - 15 min
Complete the guided run

Use the chapter workflow to produce an annotated scenario and decision log for a slightly changed Probability example.
1. Restate the task and constraints.
2. Follow the model one decision at a time.
3. Record the reason for two key choices.
4. Check the result and revise one issue.
Deliverable
A completed guided example with two decision notes and one correction.
Success looks like

The workflow is complete.

Decisions have reasons.

The final check produces a visible correction.
Knowledge check
During guided Probability practice, when is the best time to explain a choice?

1 question

During guided Probability practice, when is the best time to explain a choice? AAt the decision point, before seeing whether the final result works. BOnly after the tutor supplies the correct answer. COnly when the result is wrong. DAfter deleting the draft and starting over.

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Ready to complete this chapter? Submit the guided example with decision notes, one self-correction, and the checkpoint response.
3
Chapter 3
Risk literacy: Applied scenario

Transfer Risk literacy into a realistic scenario where the prompt is less tidy and more than one option may be reasonable. You will define the constraints, choose an approach, and defend the tradeoff.

32 min Not complete
Learning objectives

Extract the relevant facts and constraints from a realistic scenario.

Generate at least two plausible approaches to Risk literacy.

Choose an approach using explicit criteria.

Explain the likely consequence of the choice.
Key terms
1

Read the situation

Translate the scenario into a clear task. Separate facts, assumptions, constraints, and information that is interesting but not relevant to Risk literacy.
2

Choosing well under real constraints

Applied work is mostly judgement under limits: less time, less information, and more competing goals than a textbook example allows. These are the decision rules that hold up in practice.

Two options seem equal: Prefer the one that keeps more future options open.

You are behind: Accept more variance deliberately; the safe line only helps when you are ahead.

You are reviewing a loss: Find the last point where a better option existed, not just the final mistake.
3

Reading the situation before acting

Before choosing an approach, state three things explicitly: what result the situation actually requires, which constraints are fixed rather than preferences, and what evidence would tell you the approach is working. Skipping this step is the most common reason competent work solves the wrong problem.

Judge the decision, not only the result. Good decisions sometimes lose and poor ones sometimes win, because outcomes contain chance. Reviewing the reasoning available at the time is how skill actually improves.
4

Compare real options

Generate two workable approaches and test both against the purpose. Do not hide the tradeoff; name what each option improves and what it gives up.

5

Make the reasoning visible

Produce an annotated scenario and decision log and attach a short decision note. The note should make the result auditable, not merely confident.
Live decision model
Price a risky choice before taking it

Set the chance and the payoffs. The running total shows what repeating the choice really does.

A single round can lose even when the decision is good. Expected value is the slope of the long run, not a promise about the next round.

Find the break-even chance where the expected value is exactly zero.

Set up a positive-EV bet, then Re-roll until you find a run that still loses.
Practice round
Match the Risk literacy vocabulary

Tap a term, then the definition it belongs to. Wrong guesses cost nothing but honesty.

Retrieval beats rereading: pulling a definition from memory strengthens it far more than recognizing it on the page.

Clear the board once, shuffle, and beat your attempt count.

Say each definition aloud before tapping — then check yourself.
Practice activity - 18 min
Solve the scenario

Apply Risk literacy to a scenario from school, work, home, or community life that includes at least two constraints.
1. Write the task, audience, and constraints.
2. Sketch two possible approaches.
3. Choose using three criteria from the chapter.
4. Produce the result and explain one tradeoff.
Deliverable
A scenario response with an option comparison and a short decision note.
Success looks like

Constraints are visible.

Both options are plausible.

The final choice follows the stated criteria.
Knowledge check
What makes an applied Risk literacy decision defensible?

1 question

What makes an applied Risk literacy decision defensible? AThe chosen approach follows stated constraints and criteria, with the tradeoff acknowledged. BIt is the first idea that came to mind. CIt avoids mentioning uncertainty. DIt copies the guided example without adapting it.

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Ready to complete this chapter? Finish the scenario response, compare two options, and explain the selected tradeoff.

Chapter 4

Decision trees: Review and improve

Learn to diagnose and improve Decision trees work with a focused rubric instead of vague judgment. You will separate symptoms from causes, revise the highest-value issue, and document the before-and-after difference.

29 min Not complete

Learning objectives

Evaluate a draft using explicit Decision trees criteria.
Identify the cause behind the most important weakness.
Choose a revision with high impact and reasonable effort.
Explain how the revision changes the result.

Key terms

Use the rubric, not a feeling

Review the work for relevant observations, viable alternatives, explicit tradeoffs, and an honest post-decision review. Record evidence for each judgment so feedback points to something observable.

Diagnostic checklist

Run this before you revise anything. Diagnosing first prevents the common failure of polishing the parts that were already fine.

Check: Playing or deciding by pattern recognition alone — is this present in your work?
Check: Judging past decisions by how they turned out — is this present in your work?
Check: Ignoring what the opponent or environment intends — is this present in your work?

The quality bar

This is what finished work looks like in this field. Use it as the standard for your revision rather than a general sense of improvement.

Decisions are recorded with the reasoning available at the time
At least two candidates were compared before committing
Review separates process quality from outcome luck

Diagnose before editing

Name the symptom, then ask what decision or missing step produced it. Choose the cause you can address rather than changing everything at once.

Revise and compare

Make one purposeful revision and compare the two versions. Keep the change only if it improves the intended result without creating a larger problem.

Live decision model

Price one branch of a decision tree

Every branch is a probability times a value. Set both and read what the branch is worth before you choose it.

A single round can lose even when the decision is good. Expected value is the slope of the long run, not a promise about the next round.

Find the break-even chance where the expected value is exactly zero.
Set up a positive-EV bet, then Re-roll until you find a run that still loses.

Revision flowchart

Evidence-led improvement loop

flowchart LR
    N1["Inspect evidence"]
    N2["Find the likely cause"]
    N3["Revise one issue"]
    N4["Compare versions"]
    N1 --> N2
    N2 --> N3
    N3 --> N4

Revise the cause of the highest-value issue, then compare the new result with the original criteria.

Step 1 of 4: Inspect evidence

Side-by-side comparison

Two reviews of the same game

Use this pair as your revision rubric: find which column your current draft sits in, one row at a time.

Aspect	Result-based review	Decision-based review
Judgment	A win means the plan was right	Each decision judged by what was knowable at the time
Alternatives	The move played is the only one considered	Two candidate moves compared honestly
Lesson	"Play better next time"	One reusable rule extracted and written down

Results are noisy. Decisions are the only thing you can actually train.

Practice round

Rebuild the Decision trees method

The steps of this chapter's method, shuffled. Arrange them so they would actually work.

A method is a sequence, not a bag of tips — if the order surprises you, that is exactly the gap worth closing now.

Order the steps, then explain to yourself why step 2 cannot go last.
Shuffle again and solve it in fewer moves.

Practice activity - 16 min

Run a focused revision cycle

Review a previous Decision trees artifact or the supplied flawed example, then improve the most consequential issue.

Score the draft against three criteria.
Quote or point to evidence for the weakest score.
Name the likely cause and revise it.
Write a before-and-after comparison.

Deliverable

A marked-up draft, revised version, and four-sentence change note.

Success looks like

Feedback cites evidence.
The revision addresses a cause.
The comparison explains a measurable or observable improvement.

Knowledge check

Which feedback is most useful for improving Decision trees?

1 question

AA specific observation linked to a criterion and a realistic next action. BA general statement that the work is good or bad. CA complete replacement made by someone else. DA list of unrelated preferences.

Chapter notes Not started

5
Chapter 5
Tournament strategy: Capstone integration

Integrate the course methods in a compact Tournament strategy capstone. You will define the brief, plan milestones, produce a complete result, gather tutor feedback, and leave with a repeatable next-practice plan.

36 min Not complete
Learning objectives

Translate the capstone brief into milestones and checks.

Combine the course methods without losing the central purpose.

Present evidence for the quality of the final result.

Choose the next skill to practice from the final review.
Key terms
1

Define a finishable brief

Choose a specific audience, result, and boundary for the Tournament strategy capstone. Reduce scope until the project can be finished and reviewed in one focused cycle.
2

Bringing the parts together

A capstone is judged on coherence, not on the number of techniques it includes. Return to the core ideas and make sure the work demonstrates them rather than decorating them.

Judge the decision, not only the result. Good decisions sometimes lose and poor ones sometimes win, because outcomes contain chance. Reviewing the reasoning available at the time is how skill actually improves.

Compare candidates before committing. The first plausible move is rarely the best one. Generating two or three options and comparing them is the habit that separates strong players and planners from quick ones.

Position beats immediate gain in most systems. Choices that improve your future options usually outperform ones that take the visible reward now. Naming which type a move is clarifies the trade being made.
3

Standards that make the work credible

These are the marks of work that would be taken seriously by someone who does this professionally.

Decisions are recorded with the reasoning available at the time

At least two candidates were compared before committing

Review separates process quality from outcome luck
4

Build with checkpoints

Plan foundation, first draft, verification, and revision milestones. At each checkpoint, save evidence instead of relying on memory.

5

Present and continue

Present an annotated scenario and decision log with a concise rationale. Use the final rubric to choose one strength to retain and one next practice target.
Rating lab
Seeding is Elo arithmetic

Brackets and seeds are expected scores in disguise. Set two ratings and read what the format assumes about you.

Elo is a probability engine: 400 points means a 10:1 favorite, and the points exchanged after a game are exactly the surprise the result contained.

Find the gap that makes you a 75% favorite.

Why does beating a much higher rating pay so well?
Visual model
Capstone learning loop

The capstone is a complete cycle: define a finishable brief, build, review evidence, then choose the next practice target.
Practice round
Match the Tournament strategy vocabulary

Tap a term, then the definition it belongs to. Wrong guesses cost nothing but honesty.

Retrieval beats rereading: pulling a definition from memory strengthens it far more than recognizing it on the page.

Clear the board once, shuffle, and beat your attempt count.

Say each definition aloud before tapping — then check yourself.
Practice activity - 22 min
Complete the capstone sprint

Create a complete Tournament strategy artifact for a defined audience and purpose, using the course rubric to review it.
1. Write a brief with scope and success criteria.
2. Create the first complete version.
3. Run a self-check and request focused tutor feedback.
4. Revise, present, and set one next-practice target.
Deliverable
A finished capstone, evidence of one revision, and a next-practice note.
Success looks like

The result answers the brief.

Course methods are visible.

Revision follows feedback or evidence.

The next step is specific and achievable.
Knowledge check
When is the Tournament strategy capstone ready to finish?

1 question

When is the Tournament strategy capstone ready to finish? AIt meets the written brief and criteria, includes a reviewed revision, and has a clear next-practice target. BIt contains every possible feature or idea. CThe learner can no longer think of any improvement. DIt looks exactly like the tutor example.

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Ready to complete this chapter? Submit the completed capstone, revision evidence, rubric review, and one concrete next-practice target.

Make it personal

Turn the public curriculum into your own learning path.

Ask Liam Foster to adapt the sequence to your level, available time, and goal. The personalized path can then be saved in your workspace.

0 of 5 chapters complete

Build knowledge, use it, and leave with evidence of progress.

Before you start

Useful materials

Suggested rhythm

Game theory decision dossier

What you will submit

How it will be reviewed

Learn, practice, check, and record what matters.

Game theory: Foundations and vocabulary

Learning objectives

Key terms

Start with the purpose

How Game theory actually works

Misconceptions worth clearing early

Build the mental model

Catch the common miss

Which response best shows a usable foundation in Game theory?

Probability: Guided demonstration

Learning objectives

Key terms

Watch the whole process

Worked example: Positive predictive value of a highly accurate test

Where this usually goes wrong

Practice with scaffolding

Check before feedback

During guided Probability practice, when is the best time to explain a choice?

Risk literacy: Applied scenario

Learning objectives

Key terms

Read the situation

Choosing well under real constraints

Reading the situation before acting

Compare real options

Make the reasoning visible

What makes an applied Risk literacy decision defensible?

Decision trees: Review and improve

Learning objectives

Key terms

Use the rubric, not a feeling

Diagnostic checklist

The quality bar

Diagnose before editing

Revise and compare

Which feedback is most useful for improving Decision trees?

Tournament strategy: Capstone integration

Learning objectives

Key terms

Define a finishable brief

Bringing the parts together

Standards that make the work credible

Build with checkpoints

Present and continue

When is the Tournament strategy capstone ready to finish?

Turn the public curriculum into your own learning path.