How parlays are priced

1. Leg probability

p_i = clamp(side = YES ? q_i : 1 − q_i, 0.03, 0.97)

q_i is the market's implied probability for the outcome. Taking NO inverts it. The result is clamped into the 3%–97% band so a single near-certain leg cannot dominate the product or push the multiplier to absurd values.

2. Average pairwise correlation

ρ = min(0.60, ( Σ_{i<j} w_ij ) / pairs),  w_ij = 0.55 same cluster, 0.14 same category, else 0

Correlation is averaged over the number of pairs, not summed. That matters: summing would mean three unrelated legs looked more correlated than two, purely because there are more pairs. Averaging keeps diversification honest.

A cluster is a single underlying event (one match, one CPI print, one coin). A category is broader (all of Crypto). ρ is capped at 0.60 — even identical-looking legs retain some independence in this model.

3. Joint probability

P_ind = Π p_i    P_joint = P_ind + ρ · ( min(p_i) − P_ind )

With ρ = 0 the legs are independent and the joint probability is the plain product. With ρ = 1 the parlay collapses to its weakest leg, because everything either happens together or not at all. Real parlays sit between the two, and this interpolation is exactly that line.

4. Multiplier and house margin

M_naive = 1 / P_ind    M_fair = 1 / P_joint    M = M_fair × (1 − 0.045)

The naive multiplier is what a correlation-blind book would offer. The fair multiplier reflects the true joint probability. Predct applies a 4.5% house margin to the fair price — the same margin on every parlay, disclosed here rather than buried.

Because P_joint ≥ P_ind whenever ρ > 0, correlated parlays always price below the naive number. That gap is the 'payout trimmed' warning on the slip.

5. Model edge

P_model = joint( m_i, ρ )    edge = P_model × M − 1

m_i is the Predct model's own probability for the leg, derived from the market price extrapolated along its 24-hour drift. Where the model disagrees with the price, edge appears. Positive edge means the offered multiplier is generous relative to the model; negative means it is not, and most parlays are negative after margin.

6. Break-even and expected value

P_breakeven = 1 / M    EV(stake) = stake × edge

Break-even is the win probability at which the bet is a coin flip in credit terms. If your honest estimate of the parlay is below it, the bet loses money in the long run. Expected value scales linearly with stake — it never turns a negative-edge parlay positive.

7. Margin floor

M = (1 − m) / max( P_market , P_model )

Settlement samples the model probability, so a multiplier priced purely off the market price would pay more than it charged whenever the model is the more optimistic of the two. Predct therefore prices off whichever joint probability is higher. The consequence is exact and holds for every possible combination of legs: the long-run return to the trader is 1 − m, never above it, whether the parlay is a single leg, eight diversified legs, a stack from one cluster or a hedge. Multipliers are additionally capped at 2,000x and payouts always round down to the cent.

8. All-or-nothing settlement

return = stake × M  if every leg lands, else 0

A parlay pays only on a full hit. The joint probability that drives the multiplier is the same correlated distribution the settlement engine draws from, so the long-run return of a correlated parlay and a diversified one is identical — the trimmed payout is matched by a genuinely higher chance of landing.

Positions placed while the earlier payout ladder existed carry their rungs and keep settling exactly as they were priced, so historical balances are never rewritten.

Limits of the model

Correlation weights are fixed constants, not estimates from historical joint outcomes. Cluster tagging is editorial. The model probability is a drift extrapolation, not a forecast with a track record. Treat the outputs as a teaching tool for how parlay pricing behaves, not as a prediction of anything in the real world. The Risk Disclosure covers this in full.