Predict before you run. Keep every marginal probability fixed, then tighten dependence from Conservative to Aggressive and watch joint hit rate rise while fair payout falls.
Leg-level probabilities are marginal. A parlay needs a joint probability. This simplified chain exposes every intermediate term so the result can be checked rather than trusted.
Phi dependence adds covariance to the independent intersection, then Frechet bounds keep the result inside a valid probability range.
Select a mode, commit to a prediction, and run the weave to expose the conditional chain.
Each leg's 62%, 58%, or 54% estimate ignores whether another leg has already hit.
Run the model to derive P(B|A) and P(C|B) from the two pair intersections.
The chain multiplies P(A), P(B|A), and P(C|B). Independent multiplication is only a special case.
"If each leg has analysis, I can multiply the three probabilities." Test that claim against the dependency field.
A shared game script can make all three legs hit together more often. That raises joint probability. A fair price must respond by paying less. Value exists only when your probability is better than the offered price, and this lesson does not provide live odds.
Worked contrast: at rho .05, the chain lands near independence: 20.9% versus 19.4%. At rho .45, the same marginal legs land at 34.2%, while the fair decimal payout contracts from 4.80x to 2.93x. The legs did not improve; their dependence changed.
Correction will appear here when the independence shortcut fails.
The marginal probabilities stay fixed, but positive dependence rises. What should happen to a fair payout before bookmaker margin?
Mastery: 0 / 3 Predict, recover, transfer.
Hypothetical inputs and a simplified three-node Markov chain. No live odds, sportsbook margin, betting advice, or claim about LineProphet's proprietary implementation. Correlation alone does not establish positive expected value.