Open your ticket. Multiply the decimal odds of each leg together. Write down that number. Now look at what the sportsbook is actually offering. If the second figure is smaller—and with same-game parlays it almost always is—you are staring at what the industry calls the correlation tax. The question is whether that haircut is justified by real statistical dependency, or whether you are simply paying extra for the convenience of a single slip.
Why Independence Fails
Standard parlays treat each leg as its own coin flip. A $10 bet on three -110 lines multiplies out to roughly $70 in return because the book assumes one outcome tells you nothing about the next. Same-game parlays violate that assumption from the start. When Caesars Sportsbook explains its pricing, it notes that SGP odds begin with individual leg prices but are then run through a correlation model that measures how those outcomes relate to one another. The reason is simple: a quarterback throwing for 300 yards makes it more probable, not less, that his top receiver clears 100. The legs are not independent, and any pricing model that pretends otherwise is fantasy.
BetSmart defines a correlated parlay as one where one leg winning changes the odds that another leg wins, with positive correlation meaning the true joint probability sits higher than the simple product of individual probabilities. Sportsbooks understand this. Rather than multiplying prices and hoping, they estimate the joint probability directly and price from there. The math has moved on from the parlay formula you learned in a sportsbook's FAQ.
The Pricing Gap
Caesars illustrates the mechanics with concrete numbers. Three -110 legs in a standard parlay pay $70.00. The same three legs in a same-game parlay pay anywhere from $46.00 to $58.00 when positively correlated, and $64.00 to $70.00 when largely uncorrelated. That gap—between $70 and the offered price—is what OddsIndex terms the “vig differential” and more colorfully labels the “correlation tax.”
OddsIndex explains that sportsbooks apply a correlation discount to reflect dependency between same-game legs, with the result that SGP prices fall below what an independent parlay calculation would produce. The more correlated the legs, the steeper the discount. This is not a bug in the system. It is the system. The book is charging you for the fact that your legs are not random events drawn from separate contests.
When the Gap Is Justified
A lower payout is not automatically robbery. The Wizard of Odds notes that positive correlation makes the parlay more likely to hit than independence would suggest, which means the sportsbook must offer shorter odds to maintain its edge. If the true joint probability of your legs is genuinely elevated by their relationship, then a price below the naive product can still be fair—or at least fairer than it appears.
Caesars confirms this with its example: positively correlated legs pay less because the outcomes cluster together more often than random chance would predict. A quarterback's big day and his receiver's big day are not separate events occurring in isolation. They are entangled. The book's correlation model attempts to measure that entanglement and price accordingly. Your job is not to complain about the haircut, but to judge whether the model has overestimated or underestimated the link.
How to Test a Slip
Here is the practical checklist. First, convert each leg to decimal odds. American -110 becomes 1.909, +150 becomes 2.5, and so on. Multiply them together. That product is what the parlay would pay if the legs were independent. Second, compare that figure to the SGP price offered on your ticket. The difference is the correlation tax. Third, and this is where most bettors fail, ask whether the legs are actually correlated enough to justify the gap.
A quarterback over 2.5 touchdown passes and his team to win is obvious positive correlation. The same quarterback over 2.5 touchdowns and the opposing running back over 100 rushing yards is less clear—negative game script could link them, but the relationship is weaker and harder to model. The book's correlation discount may be too steep or too shallow for any given combination. Your edge, if you have one, lives in that mismatch.
OddsIndex puts this plainly: the sportsbook's price reflects its estimate of joint probability, not yours. When your estimate diverges from theirs by more than the tax, you have found value. When it does not, you are paying for a story about how your legs fit together.
What Books Do Under the Hood
The Wizard of Odds documents the methods that power these adjustments. Gaussian copulas, empirical frequency tables, correlation matrices—these are not marketing terms. They are the statistical machinery that translates individual leg prices into a joint probability distribution. A copula, in plain terms, is a function that links marginal probabilities into a coherent multivariate structure. Empirical tables draw from historical data about how often certain outcome combinations actually occur. Correlation matrices quantify the directional relationships between variables.
You do not need to build these models yourself. You do need to understand that the book has already built them, and that the price on your screen reflects thousands of simulations and historical observations. The naive product of leg odds is a fiction. The offered SGP price is the book's best guess at reality. Your test is whether your guess is better.
The Practical Takeaway
Same-game parlays are not priced like independent bets because they are not independent bets. The correlation tax is real, permanent, and defended by sophisticated modeling. The only defensible way to judge one is to calculate the naive product, compare it to the offered price, and ask whether the leg relationship is strong enough to survive the haircut.
If your calculated product is $70 and the book offers $58, you need those legs to be substantially more correlated than independence suggests. Not slightly. Substantially. The book has already priced in the obvious connections. Your edge lives in the connections it has mispriced or missed entirely. Most bettors skip the calculation and trust the narrative. The test is simple. The discipline is not.