The quiet way books tax your parlay: compounding vig
You already know the book bakes in vig on every line. What most bettors don’t fully feel is how nasty that vig gets when you stack legs. A parlay isn’t just “three bets multiplied.” It’s three pieces of juice multiplied. That’s why a 3-legger can pay less than it should even when each leg looks totally normal on its own.
Let’s use the most common building block in sports betting: a -110 point spread. Two-sided market, -110 both ways. The implied probability on -110 is:
Implied p(-110) = 110 / (110 + 100) = 0.5238 (52.38%)
But that 52.38% isn’t “true.” It’s juiced. If both sides are -110, the total implied is 52.38% + 52.38% = 104.76%. That extra 4.76% is the overround (vig).
To estimate the fair probability for one side in a symmetric -110/-110 market, you normalize:
Fair p ≈ 0.5238 / 1.0476 = 0.5000 (50%)
That’s the whole story in one line: a -110 “coin flip” is priced like 52.38% when it’s really 50%. When you parlay three of them, you don’t just pay that tax once. You pay it three times.
Fair win probability for three true 50/50 legs: 0.5 × 0.5 × 0.5 = 0.125 (12.5%). Fair decimal odds: 1 / 0.125 = 8.00. That’s +700.
If you instead multiply the book’s implied probabilities (the juiced ones): 0.5238³ = 0.1436 (14.36%). That corresponds to decimal odds 1 / 0.1436 = 6.96, which is about +596.
Read that again. A “fair” 3-leg coin-flip parlay is +700, but the juiced math points toward +596. That’s the compounding vig effect. And it’s exactly where recreational bettors get crushed while thinking they’re just “having fun with a small stake.”
Fair odds vs book odds: the exact math you should run
If you want to know whether a parlay payout is objectively bad, you need one clean habit: convert everything to fair probabilities, multiply, then convert back to odds. Don’t eyeball it. Don’t trust the “boosted” badge. Do the math.
Here’s the repeatable method I use:
- Step 1: Convert each leg’s odds to implied probability.
For American odds:
Negative odds (-A): p = A / (A + 100)
Positive odds (+A): p = 100 / (A + 100) - Step 2: Remove vig (estimate fair probability).
Best method: use both sides of the market. If Team A is -115 and Team B is -105, compute both implied probs, sum them, then normalize: fair pA = pA / (pA + pB).
If you only have one side, you’re guessing. (Sometimes you can approximate, but don’t pretend it’s precise.) - Step 3: Multiply fair probabilities across legs.
p_parlay_fair = p1_fair × p2_fair × p3_fair × ... - Step 4: Convert that fair probability back to fair odds.
Decimal: odds_fair = 1 / p_parlay_fair
American (if decimal ≥ 2.00): + (decimal - 1) × 100 - Step 5: Compare to the book’s parlay payout.
If the book pays worse than your fair number by a meaningful margin, it’s a bad price even if every leg individually is “fine.”
If you want the fastest refresher on stripping vig and break-even prices, keep this bookmarked: Vig vs True Odds: Find Your Break-Even Price in 10 Seconds. Same concept, just applied to parlays.
Example #1: Three -110 legs (the “looks harmless” parlay)
Let’s make it painfully concrete. You build a 3-leg parlay with three spreads, each priced -110. The book offers +600 (decimal 7.00). Most people see “6-to-1” and fire.
Run the fair math.
Each leg fair probability: In a -110/-110 market, fair p ≈ 0.50 (as shown earlier).
Parlay fair probability:
0.50 × 0.50 × 0.50 = 0.125
Fair odds:
Decimal = 1 / 0.125 = 8.00
American = +700
Book payout: +600 (decimal 7.00)
That’s not a small difference. You’re getting paid like the parlay wins 1/7 = 14.29% of the time, when it should win 12.5% if those legs are true 50/50. The book is basically saying: “Thanks for donating an extra chunk of edge.”
Want to quantify the hold on this parlay price? Compare the implied win rate from the payout to the fair win rate:
- Fair p = 12.50%
- Paid-as-if p = 14.29%
- Difference = 1.79 percentage points
That 1.79% doesn’t sound huge until you realize it’s relative to a 12.5% event. You’re giving up about 1.79 / 12.50 = 14.3% of the fair value. On a $100 bet, fair EV at fair odds is $0 (break-even). At +600 when fair is +700, your EV is negative.
Compute it:
At +600, profit if win = $600. Loss if lose = -$100.
EV = (0.125 × 600) + (0.875 × -100) = 75 - 87.5 = -$12.50
You’re lighting $12.50 on fire per $100 in the long run, assuming the legs are truly fair. That’s the “quiet worsening” in dollars.
Example #2: “Good legs” don’t save a bad parlay price
This is where people get defensive: “But I like all three picks.” Cool. You can like the legs and still hate the parlay payout. Those are different questions.
Let’s say you’re betting three moneylines in a parlay. The book shows:
- Leg 1: -150
- Leg 2: -160
- Leg 3: -170
The parlay payout offered is +250 (decimal 3.50). Looks reasonable, right? Three favorites, moderate payout.
We need fair probabilities. To do this properly, you should look at the other side of each market (the opponent price) and normalize. I’ll use a realistic setup where each market has typical vig.
- Market 1: Team A -150 / Team B +130
Implied p(-150) = 150/250 = 0.6000
Implied p(+130) = 100/230 = 0.4348
Sum = 1.0348
Fair p1 = 0.6000 / 1.0348 = 0.5798 - Market 2: -160 / +140
p(-160)=160/260=0.6154
p(+140)=100/240=0.4167
Sum=1.0321
Fair p2=0.6154/1.0321=0.5964 - Market 3: -170 / +150
p(-170)=170/270=0.6296
p(+150)=100/250=0.4000
Sum=1.0296
Fair p3=0.6296/1.0296=0.6114
Multiply fair probabilities:
p_parlay_fair = 0.5798 × 0.5964 × 0.6114
First two: 0.5798 × 0.5964 ≈ 0.3457
Then × 0.6114 ≈ 0.2113 (21.13%)
Fair decimal odds = 1 / 0.2113 ≈ 4.73
Fair American odds ≈ +373
But the book offers +250 (decimal 3.50). That’s brutal. +250 implies a win rate of 1/3.50 = 28.57%. You’re being paid like the parlay is way more likely than it truly is.
EV on $100 at +250:
Profit if win = $250. Loss if lose = -$100.
EV = (0.2113 × 250) + (0.7887 × -100)
= 52.8 - 78.9 = -$26.1
And that’s with “normal” favorites you might actually handicap well. If you truly have an edge on one leg, you can still get smoked by a trash parlay price. That’s why you need to separate pick quality from price quality.
A simple checklist to spot an overpriced parlay in 60 seconds
You don’t need to be a quant. You just need a routine. Here’s the checklist I use before I click “Place Bet.”
- 1) Can you see both sides of each leg?
If you can’t see the opposite price, you can’t cleanly remove vig. That’s where books hide the most nonsense. If you’re building from a parlay tab that only shows one side, be careful. - 2) Strip vig per leg (normalize), don’t assume -110 = 50/50 if it isn’t.
Totals at -115/-105, player props at -130/+100, alternate lines… these are not symmetric. Normalize each one. - 3) Multiply fair probabilities, not implied probabilities.
If you multiply implied probs, you’re literally compounding the book’s margin. That’s the whole problem. - 4) Convert to fair odds and compare to payout.
If your fair price is +700 and you’re being offered +600, that’s a “no” unless you have a real edge that more than covers the gap. - 5) Watch for “same-game” correlation rules.
SGPs often have extra padding because legs aren’t independent. Books adjust, and they usually don’t adjust in your favor. If you can’t explain the correlation, you’re guessing. - 6) Don’t let a tiny stake fool you.
“It’s only $10” is how bad habits become expensive habits. Negative EV is negative EV.
If you want a quick way to quantify how different books price the exact same legs, ThunderBet’s Parlay Builder is useful. Build the same 3 legs across books and you’ll see which shop is quietly shaving the payout. That’s not theory—it’s free information you can use immediately.
When to bet singles (or smaller combos) instead of the full parlay
Parlays aren’t automatically evil. Most parlays are sucker bets because of pricing, not because combining outcomes is sinful. Your job is to put the bet in the form that gives you the best expected value.
Here’s the decision framework I actually use:
A) If your parlay is priced worse than fair by more than ~2–3% of win probability, pass.
Example: fair parlay p = 12.5%, book payout implies 14.3%. That’s a big haircut. You need a real edge across the legs to make up for it. Most bettors don’t have it.
B) If one leg is your strongest edge, prioritize the single.
This is where people screw up. They find one great bet and then “decorate” it with two coin flips to chase a bigger payout. That decoration often flips your overall EV from positive to negative.
Quick illustration. Suppose you have one legit edge:
- Leg A: You bet -110 but you think true win probability is 55% (that’s a solid edge).
- Leg B and C: true 50/50 at -110 (no edge).
Single EV on Leg A for $100:
Win profit = $90.91 (because -110).
EV = (0.55 × 90.91) + (0.45 × -100) = 50.00 - 45.00 = +$5.00
Nice. That’s what you want.
Parlay EV if the book pays +600 (decimal 7.00):
True parlay p = 0.55 × 0.50 × 0.50 = 0.1375 (13.75%).
Profit if win = $600. Loss if lose = -$100.
EV = (0.1375 × 600) + (0.8625 × -100) = 82.50 - 86.25 = -$3.75
You turned a +$5 single into a -$3.75 parlay because the payout didn’t match the true risk. That’s the trap: one good leg can’t carry two juiced coin flips when the book underpays the combo.
C) Consider a 2-leg parlay if the pricing is fair and you have edges on both legs.
Two legs means less compounding vig, and it’s easier for your edges to overcome the tax. Three and four legs get expensive fast.
If you’re consistently finding +EV singles and want to keep your card sharp, ThunderBet’s Positive EV Finder helps you separate “good bets” from “fun opinions.” Then you can decide whether combining them makes sense or just feeds the book.
The most common parlay mistakes (and how you stop making them)
You can know the math and still punt money if you fall into the same three habits everyone falls into.
- Mistake #1: Treating the parlay payout as “automatic.”
Books don’t have to offer a true multiplication of fair odds. They offer what bettors will accept. Your fix: always compute your own fair parlay price first, then decide if the payout clears it. - Mistake #2: Mixing markets with huge hidden vig.
Player props and alt lines often carry bigger margins than main spreads/totals. Stack three high-vig legs and your parlay price gets wrecked. Your fix: build parlays from the cleanest, most efficient markets when possible. - Mistake #3: Ignoring correlation and thinking “different sports” means “independent.”
Same-game legs can be correlated (obvious), but even across games you can create correlation through weather, injuries, lineup news timing, or just betting markets that move together. Your fix: assume legs are independent only when you can justify it. - Mistake #4: Chasing a target payout instead of a target edge.
“I want +500” is not a strategy. It’s a dopamine request. Your fix: start with bets that beat the number, then decide how to size and structure them. - Mistake #5: Not shopping the parlay.
Different books price the same parlay differently. Sometimes by a lot. Your fix: compare payouts before you commit. If you don’t want to do it manually, use a tool that shows the differences quickly (that’s literally what a parlay builder is for).
If you like this kind of nuts-and-bolts betting education, the rest of the blog lives in the same lane, especially the pieces in /blogs/education/ and /blogs/strategy/.
Responsible gambling note: Parlays are high-variance and can chew through a bankroll fast. Bet sizes you can afford to lose and take breaks when it stops being fun.
