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Parlay
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A parlay, accumulator (or acca), combo bet, or multi is a single bet that links together two or more individual wagers, usually seen in sports betting. Winning the parlay is dependent on all of those wagers winning together. If any of these bets in the parlay lose, the entire parlay loses. If any of the plays in the parlay ties, or "pushes", the parlay reverts to a lower number of wagers with the payout odds reducing accordingly. Parlay bets are high-risk, high-reward; linking the possibilities drastically reduces the chance of the bet paying off overall. The benefit of the parlay is that there are much higher pay-offs, although as usual, casinos and bookkeepers offering parlays often exploit the poor calculation of gamblers by not increasing the pay-out as much as the odds truly demand, with the effect of the house edge increasing in parlays.
Although a variety of bets can be used to build a parlay bet, correlated parlays are usually not allowed by traditional bookmakers. Correlated parlays are two or more bets from the same game that rely on a closely related outcome: for example, betting that a football (soccer) team might both score more than three goals in a match, and also win the match. These are not independent events, as a team that scores more than three goals is also very likely to win the match. A naive application of odds that treated these events as uncorrelated would not accurately reflect the probability of the linked bet. However, with the rise of sports betting through mobile gambling apps in the late 2010s–2020s, this traditional hesitance has weakened. These newer apps often allow "microbets" on propositions such as if the current possession will end in a score, and further allow these props to be bundled into parlays. The system then attempts to compensate on how correlated these props are. While these systems usually prefer to lean heavily in the house's favor, the increased volatility from these bundles has resulted in some notable cases where bettors have found favorable odds. This isn't always a windfall for the bettors, though, as these newer-style sportsbooks have sometimes simply refused to pay out in those cases if the parlay comes through.[1]
History
[edit]![[icon]](https://en.wikipedia.org/wiki/File:Wiki_letter_w_cropped.svg){kind=small} | This section needs expansion. You can help by adding to it. (October 2024) |
Parlays were introduced into New York-area racetrack gambling in 1988, but a 1989 newspaper article indicated that they still weren't very popular, perhaps due to the large surcharges and fees charged by off-track betting (OTB) parlors.[2]
Odds and payout
[edit]Parlay bets are paid out at odds higher than the typical single game bet, but still below the "true" odds. For instance, a common two-team NFL parlay based entirely on the spread generally has a payout of 2.64:1. In reality, however, if one assumes that each single game bet is 50/50, the true payout should instead be 3:1.
Examples
[edit]Typical payouts for up to 10 team parlay bet
[edit]The following is an example of a traditional Las Vegas Parlay Card, which shows the typical payouts for an up to 10 team parlay bet based on −110 prices (amount won is assuming $100 is bet) and if every match is 50/50:[citation needed]
| Number | Odds | Amount won | Payout |
|---|---|---|---|
| 2 Team Parlay | 2.6 to 1 | $260 | $360 |
| 3 Team Parlay | 6 to 1 | $600 | $700 |
| 4 Team Parlay | 11 to 1 | $1,100 | $1,200 |
| 5 Team Parlay | 22 to 1 | $2,200 | $2,300 |
| 6 Team Parlay | 45 to 1 | $4,500 | $4,600 |
| 7 Team Parlay | 90 to 1 | $9,000 | $9,100 |
| 8 Team Parlay | 180 to 1 | $18,000 | $18,100 |
| 9 Team Parlay | 360 to 1 | $36,000 | $36,100 |
| 10 Team Parlay | 720 to 1 | $72,000 | $72,100 |
Profitability of parlays in sports betting
[edit]The best way to analyze if a parlay is profitable in the long term is by calculating the expected value. The formula for expected value is: . Since the probability of all possible events will add up to 1 this can also be looked at as the weighted average of the event. The table below represents odds.
![{\displaystyle E[X]=x_{1}p_{1}+x_{2}p_{2}+x_{3}p_{3}\dots x_{k}p_{k}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5ab576c98ef452ad76ee97d13593707f4f27935a)
Column 1 = number of individual bets in the parlay
Column 2 = correct odds of winning with 50% chance of winning each individual bet
Column 3 = odds payout of parlay at the sportsbook
Column 4 = correct odds of winning parlay with 55% chance of winning each individual bet
| Number of individual bets | Correct odds at 50% | Odds payout at sportsbook | Correct odds of winning parlay at 55% |
|---|---|---|---|
| 2 | 3 to 1 | 2.6 to 1 | 2.3 to 1 |
| 3 | 7 to 1 | 6 to 1 | 5.0 to 1 |
| 4 | 15 to 1 | 12 to 1 | 9.9 to 1 |
| 5 | 31 to 1 | 24 to 1 | 18.9 to 1 |
| 6 | 63 to 1 | 48 to 1 | 35.1 to 1 |
| 7 | 127 to 1 | 92 to 1 | 64.7 to 1 |
| 8 | 255 to 1 | 176 to 1 | 118.4 to 1 |
| 9 | 511 to 1 | 337 to 1 | 216.1 to 1 |
| 10 | 1,023 to 1 | 645 to 1 | 393.8 to 1 |
| 11 | 2,047 to 1 | 1,233 to 1 | 716.8 to 1 |
The table illustrates that if a 55% chance of winning each individual bet were achievable, parlays would be profitable in the long term against the usual house edge. Compare the expected value received on an individual bet at a typical price of −110 with a 55% chance of winning: ((100/110+1)*.55)−1 = .05 (exactly 5 cents won for every dollar bet on average), multiplied by 11 = .55, to the expected return on the 11 game parlay ((1234/717.8)−1) = .719 (72 cents won for every dollar bet on average).
See also
[edit]References
[edit]- ^ Funt, Danny (January 17, 2024). "He hit three monster bets — and then the sportsbook wouldn't pay". The Washington Post. Retrieved January 17, 2024.
- ^ Crist, Steven (March 17, 1989). "OTB's Parlay Still an Unpopular Bet". The New York Times.
Parlay
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Fundamentals
Definition
A parlay, also known as an accumulator or combo bet, is a type of wager in gambling that combines two or more individual bets, referred to as "legs" or "selections," into a single bet.[10][11] For the parlay to succeed and pay out, every leg must win; if even one leg loses, the entire parlay is lost.[12][13] In parlays, a "push" occurs when a leg results in a tie, such as the score exactly matching the spread or total; in this case, that leg is typically voided and removed from the parlay without causing a loss, allowing the remaining legs to determine the outcome.[14][15] Unlike straight bets, where each wager stands alone and can win independently, parlays multiply the risks across all legs, resulting in a lower probability of winning but offering higher potential payouts due to the aggregated odds.[11][10]Key Components
A parlay bet is constructed from individual wagers known as "legs," which can include a variety of eligible bet types such as moneylines, point spreads, over/under totals, and prop bets, though the ability to mix these depends on the specific sportsbook's guidelines.[10] For instance, many sportsbooks permit combining moneylines from different games with over/under totals, but prop bets may be restricted in certain combinations to maintain fairness.[16] This flexibility allows bettors to tailor parlays to their predictions across multiple markets, but operators enforce rules to prevent exploitative selections. The structure of a parlay requires a minimum of two legs to qualify, with most sportsbooks setting a maximum between 10 and 15 legs, though this can vary up to 20 depending on the platform.[17] Parlays can be same-sport, focusing on outcomes within one league or event, or cross-sport, spanning different sports like combining an NFL moneyline with an NBA total, which broadens the scope but increases complexity in tracking.[1] Sportsbooks strictly prohibit correlated legs in parlays, where the outcome of one bet directly influences or is likely to influence another, to preserve betting integrity and house edge.[18] For example, a bet on a team to win (moneyline) cannot be paired with an over on that team's player points in the same game, as a victory often correlates with higher scoring opportunities.[16] Uncorrelated legs, such as independent moneylines from separate games, are permitted and form the basis of most standard parlays.[19] Within parlay frameworks, bettors can choose between straight parlays, which use the original odds of each leg for higher potential payouts, and teasers, a modified parlay that adjusts point spreads or totals in the bettor's favor (e.g., moving a spread by 6 points) at the cost of reduced overall odds.[1] Teasers typically require at least two legs and are limited to spread and total bets, excluding moneylines or props, as the adjustment mechanism applies only to those formats.[20] This distinction allows for strategic risk adjustment while adhering to the all-legs-must-win rule common to both.Historical Development
Origins
The concept of parlay betting traces its roots to the Paroli system, a positive progression betting strategy originating in 16th-century Italy for card games like basset, later adapted to casino games including roulette.[21] The term "parlay" derives from the French "paroli," meaning to double a bet, rooted in 18th-century gambling practices.[5] This practice of letting stakes "ride" laid the groundwork for combined wagering, evolving from single-event risks to informal multi-bet arrangements in gambling dens across Europe. Betting in horse racing evolved from private wagers to more structured systems in the 19th century.[22] In the early 20th century, parlay betting began to formalize in U.S. bookmaking operations amid the growth of underground gambling.[23] This development was influenced by the parallel rise of accumulator bets in the United Kingdom, which emerged as a distinct yet similar form in early 20th-century betting on horse races and football pools—starting with the launch of fixed-odds pools in 1923—allowing cumulative stakes across selections but differing in regional terminology and regulatory contexts.[24] A pivotal milestone occurred in the 1920s, when parlay cards, allowing low-stake multi-game wagers, gained popularity in American sports wagering, especially for baseball and boxing, through the widespread distribution of printed parlay cards in taverns and stores amid the era's booming interest in professional sports.[25]Evolution in Sports Betting
The legalization of sports betting in Nevada in 1949 facilitated the expansion of parlay betting within major professional leagues, including the NFL and NBA, by permitting wagers on these sports alongside horse racing.[26] This development made parlays especially attractive for bettors seeking to link multiple game outcomes, such as those spanning NFL or NBA weekends, capitalizing on the growing popularity of organized sports schedules.[25] Parlay cards, a common format for such multi-leg bets, had already gained traction in earlier decades but found renewed vigor in this regulated environment, contributing to Nevada's emergence as the epicenter of U.S. sports wagering.[27] During the 1990s, the proliferation of sportsbooks across Las Vegas casinos and the surge in television coverage of live sports events drove a significant boom in parlay betting volume.[23] By the end of 1993, Nevada's sports betting handle reached $2 billion annually, reflecting heightened engagement with multi-game wagers amid broader accessibility.[23] This era's expanded infrastructure and media exposure laid the groundwork for more sophisticated parlay variations, including the eventual rise of same-game parlays, which combine multiple outcomes from a single contest.[28] The U.S. Supreme Court's 2018 repeal of the Professional and Amateur Sports Protection Act (PASPA) dismantled federal restrictions, enabling states nationwide to legalize sports betting and spurring innovations in online parlay formats.[29] This shift accelerated the integration of player prop bets—wagers on individual athlete performances—into parlay structures, offered through digital platforms for greater customization and accessibility.[30] Post-repeal, the industry saw over $200 billion in total wagers since 2018 by 2023, with online operators like FanDuel pioneering these hybrid products to attract a broader audience.[31] In recent years, parlay betting has increasingly merged with daily fantasy sports (DFS) ecosystems and mobile applications, amplifying overall volume through seamless integration and promotional features.[32] Platforms such as DraftKings and FanDuel, dominant in both DFS and sportsbooks, have embedded parlay builders into their apps, enabling users to combine DFS-style picks with traditional bets.[32] This convergence has propelled parlay wagers to represent 50-67% of revenue in states like New Jersey and Illinois, with monthly volumes exceeding $300 million in some markets during peak seasons.[32]Betting Mechanics
Odds Calculation
In sports betting, parlay odds are typically presented in the American format, which requires converting individual leg odds to their decimal equivalents before combining them. For positive American odds (underdogs, denoted as +X), the decimal conversion is calculated as (X / 100) + 1; for example, +100 converts to 2.00.[33] For negative American odds (favorites, denoted as -Y), the decimal is 1 + (100 / Y); for instance, -110 converts to approximately 1.909.[33] The core formula for determining parlay odds involves multiplying the decimal odds of each leg to obtain the combined decimal multiplier, then subtracting 1 to isolate the profit factor, and finally converting back to American odds. If the resulting decimal multiplier D exceeds 2.00, the American odds are +( (D - 1) × 100 ); if below 2.00, they are - ( 100 / (D - 1) ). This multiplicative process reflects the compounded probability and payout potential across all legs, ensuring the parlay's overall odds capture the joint outcome requirements.[33] Handling favorites and underdogs in parlays adjusts the risk profile through these conversions, as favorites contribute lower decimal values (closer to 1.00), tempering the overall multiplier, while underdogs amplify it with higher values. For a two-leg parlay with -110 (favorite, 1.909 decimal) and +150 (underdog, 2.50 decimal), the product is 4.7725; subtracting 1 yields 3.7725, converting to approximately +377 American odds. This method maintains consistency across bet types but inherently incorporates bookmaker adjustments.[33] Bookmakers incorporate a house edge into parlay odds by applying vig (or juice) to each leg, typically reducing the true odds by 5-10% to ensure profitability; in parlays, this edge compounds multiplicatively as the implied probabilities of each leg (e.g., 52.4% for -110 instead of true 50%) are multiplied, resulting in a higher effective hold—such as 12.5% for a three-leg parlay at -110 odds.[34][35] This compounding effect amplifies the bookmaker's advantage, making parlays riskier for bettors despite the allure of higher payouts.[9]Payout Determination
In parlay betting, the total payout is calculated by multiplying the wager stake by the parlay's overall decimal odds, which encompasses both the return of the original stake and any profit earned. This formula applies uniformly across sportsbooks, where the decimal odds represent the combined probability-adjusted multiplier from all legs of the bet. For example, a $100 stake on a parlay with decimal odds of 5.00 would yield a total payout of $500, including $400 in profit.[10][1] Sportsbooks determine parlay payouts by offering odds that are reduced from true mathematical probabilities to incorporate the vigorish, or house edge, on each individual leg, which compounds across the bet. True odds reflect the actual likelihood of all outcomes occurring without adjustment, such as approximately 64:1 for a fair six-team parlay at even-money probabilities per leg, whereas sportsbooks typically pay around 40:1 or less to ensure profitability. This reduction varies by the number of legs and the vig applied (often 4.76% per leg at -110 odds), making longer parlays particularly advantageous for the house. The parlay decimal odds are derived from multiplying the decimal equivalents of each leg's American odds.[36][37] Many modern sportsbooks provide partial cash-out features for parlays, enabling bettors to secure a portion of their potential winnings early by settling some legs while allowing the remaining ones to continue, with the cash-out value based on the real-time performance and implied probability of unsettled legs. This option, available on platforms like DraftKings and FanDuel, helps mitigate risk but often comes at a discounted rate compared to a full successful payout.[1] In the United States, parlay winnings are considered taxable income, with sportsbooks required to issue a Form W-2G for payouts exceeding $600 in a single wager if the winnings are at least 300 times the bet amount or meet other IRS thresholds, though actual tax liability depends on the bettor's total income and is reported on their federal tax return. Withholding may apply for larger wins over $5,000, at a rate of 24% for federal taxes.[38]Practical Examples
Basic Parlay Scenarios
A two-leg parlay represents one of the simplest forms of this betting structure, combining outcomes from two separate events across different sports. For instance, a bettor might select the moneyline for an NFL game where an underdog team is listed at +150 odds, meaning a $100 wager would return $150 in profit if they win outright, alongside an over/under total for an NBA game at -110 odds, where the bettor risks $110 to win $100 if the combined score exceeds or falls below the line as chosen.[39] Similar combinations, such as pairing an underdog win in a soccer match with an over goals bet, can yield high overall odds of 5–10x or more, though a single wrong pick results in losing the entire bet.[40] High-odds parlays, particularly multi-leg soccer accumulators, exemplify this potential. On January 31, 2026, one available express prediction featured four football selections with a combined decimal odds of 12.89: Arsenal victory over Leeds at 1.52, Liverpool victory plus over 1.5 total goals against Newcastle at 2.00, Atlético Madrid victory plus under 3.5 total goals against Levante at 2.45, and Barcelona scoring in both halves against Elche at 1.73. Other daily expresses offered coefficients ranging from 2.38 to 4.87, often focusing on leagues like the Premier League.[41] The combined parlay odds for these legs calculate to approximately +378 in American format, reflecting the multiplied risk and potential reward.[39] With a $10 stake on this parlay, a successful outcome yields about $37.85 in profit, for a total payout of $47.85, demonstrating how even modest wagers can amplify returns if both selections hit.[39] Expanding to a three-leg parlay introduces greater complexity by mixing selections from diverse sports, such as an MLB point spread (e.g., a team covering -1.5 runs at -110 odds), a soccer moneyline (e.g., a favorite to win outright at -110 odds), and a tennis match winner (e.g., a top seed at -110 odds).[42] This multi-sport approach allows bettors to leverage perceived edges across unrelated events, with overall odds reaching approximately +600 for -110 legs.[16] A key feature in such parlays is the handling of pushes, where one leg ties—such as a tennis match ending in a set tie adjusted by the bookmaker line—resulting in that selection being voided and the parlay reducing to a two-leg bet with recalculated odds and a partial refund or adjusted payout based on the remaining outcomes.[14] Same-game parlays consolidate multiple bets within a single contest, enhancing engagement by linking correlated outcomes. In an NBA example, a bettor could combine a team moneyline (e.g., home favorite at -150) with player props like a star forward exceeding 25.5 points and the game total going over 220.5, yielding combined odds around +500.[43] This structure ties the wager to one game's flow, where all elements must align for success, often appealing to fans with detailed knowledge of team dynamics.[44] Parlay outcomes hinge on the collective performance of all legs, with variations dictating the final result. If every selection wins, the full parlay pays out at the multiplied odds, delivering the enhanced profit.[1] Conversely, a single loss in any leg voids the entire bet, resulting in a total loss of the stake, underscoring the high-risk nature of these wagers.[45] In cases of a partial push, such as one leg tying while others win, the pushed selection is removed, transforming the parlay into a smaller version with adjusted odds and a corresponding payout.[14]Payout Tables for Multi-Team Bets
Payout tables for multi-team parlays consisting of even-money legs at -110 odds illustrate the scaling potential returns, derived from converting each leg's American odds to decimal format (approximately 1.909) and multiplying across legs before reconverting to American odds. This approach yields approximate true odds adjusted for the built-in vigorish on -110 lines. The following table summarizes standard payouts for 2 to 10 teams based on this calculation:| Number of Teams | Approximate Payout (American Odds) |
|---|---|
| 2 | +265 |
| 3 | +597 |
| 4 | +1228 |
| 5 | +2435 |
| 6 | +4740 |
| 7 | +9140 |
| 8 | +17500 |
| 9 | +33500 |
| 10 | +64200 |