A complete quantitative case

Combine conditional evidence, price, sensitivity and an auditable final explanation.

15 minutes · advanced · Original Poker4Quant lesson

What you will learn

Integrate the curriculum into one explicit model while separating data, assumptions and conclusions.

Prerequisites: The value of information · Decision robustness · Information and incentives

Keep the chain of reasoning modular

A complete case should make it possible to audit information, inference and payoffs separately. Define the states and prior, state evidence likelihoods, normalize the posterior, then map the posterior state weights to action payoffs.

Do not treat “strong opponent hand” as automatically equivalent to your probability of losing. That mapping needs its own assumption. Here the toy case explicitly says you beat every weak hand and lose to every strong hand, with no ties; real ranges can contain more complicated outcomes.

A final answer includes a failure mode

Calculate the point-estimate decision and a meaningful sensitivity case. Check the probability direction and whether payoff accounting includes the opponent’s bet. Explain the strongest remaining uncertainty and what evidence would change the recommendation.

This exercise is an educational modeling case, not a hiring assessment, certification or claim about a real player. Communicating a conditional conclusion precisely is more useful than pretending the available assumptions make uncertainty disappear.

Worked example

The opponent is strong 20% before a bet. Bet rates are 80% when strong and 20% when weak. You beat every weak hand and lose to every strong hand. After the bet, the pot is 120 and a final call costs 40. No ties, fees or later bets.

Strong-and-bet mass is 0.20×0.80=0.16; weak-and-bet mass is 0.80×0.20=0.16.
Posterior strength is 0.16/0.32=50%, so the stated win probability is 50%.
Break-even equity is 40/(120+40)=25%; call EV is 0.50×120−0.50×40=40.
If the weak-hand bet rate were only 5%, weak bets would contribute 0.04. Posterior strength becomes 80%, win probability 20%, and call EV becomes −8.

The point model favors calling at +40 chips. The sign reverses under the changed behavioral assumption, so the weak-hand betting likelihood is decision-relevant and needs evidence.

Hands-on: Build and challenge an end-to-end quantitative case

Construct betting evidence, normalize posterior weights, map states to outcomes, fund the call and reconcile three conserved counterfactual ledgers. Isolate behavioral and showdown sensitivity.

Reading quantitative case…

Common mistakes

Using P(bet|strong) directly as posterior strength.
Equating posterior strength with showdown loss without stating that mapping.
Stopping at the point estimate without examining a plausible assumption change.

Keep these ideas

Separate the information, inference and payoff layers.
Connect state probabilities to outcome probabilities explicitly.
Give a conditional conclusion and a concrete way it could fail.