Game Theory and Two Team Parlays
As sports betting becomes legal in more states across the US, betting has emerged as a major part of sports. It is a massive industry that allows fans to have more engagement in the games they watch, as well as have the hopes of making money off of their presumed knowledge of the games. One of the most enticing sports bets is the parlay, which is a bet where you try to predict the outcome of multiple events. In order to win this bet all outcomes must be correct, making it a high-risk/high-reward type of bet. If you bet $100 that two underdogs will both win at, for example, +250 and +180 odds (meaning $100 to win $250 and $180, respectively) you would win $880. However, the odds of winning this bet are very low since both teams are the underdog. Many people will look at the games that have the closest odds between the two teams, and try to parlay them due to a higher chance that the underdog will win because they are less of an underdog.
I have seen challenges online where two people make a parlay, each choosing one team, where the other player’s choice is unknown. This challenge can be looked at through game theory, but there is a slight twist because instead of choosing a strategy, each player is predicting an outcome that may or may not occur. For example, let’s consider this challenge were to be played for week 2 of the NFL season where the Cincinnati Bengals (+115) vs the Chicago Bears (-135) and the Dallas Cowboys (+150) vs the Los Angeles Chargers (-170) are the two closest games in terms of moneyline odds. If player 1 is required to choose one team from the CIN vs CHI game and player 2 is required to choose one team from the DAL vs LAC game, there can be four total outcomes. Given that the combined choices will result in a $100 parlay being bet, the combinations would yield returns of: (CIN, DAL) = $437.5, (CIN, LAC) = $241.5, (CHI, DAL) = $335.2, and (CHI, LAC) = $176.5.
This challenge differs from a simple game theory because the outcomes aren’t guaranteed, so the players might consider either the highest payout, or the highest possibility of the bet winning. If the players are focused on the highest payout, the Nash Equilibrium would be (CIN, DAL), but if the players are focused on the likelihood the bet actually wins, the Nash Equilibrium would be (CHI, LAC).
Sports betting is a fascinating topic to examine in terms of game theory, because the combinations of outcomes can relate to simple games, except with the addition of alternative motives. Some bettors look for the largest payouts, while others look for the greatest probability of winning. In the end, the only people who actually win are the book makers because they adjust the odds to ensure they make money. Many people think they are able to beat the system and win these unlikely parlay bets, but that’s what draws the betters back to the games, and why the industry is growing to be so large
Source: https://www.njonlinegambling.com/parlay-sports-betting-explored/