Saturday morning, games still hours away, and a football-pool simulator is already running. A participant pulls up the week's schedules, selects a game, flips the result, and watches the standings shift to reflect the change. Kansas City holds its position in the division. Buffalo moves into the second wild-card spot. The simulator runs the tiebreaker process through head-to-head record, division record, conference record, and strength of victory, each set in stone and applied in the order required by the league. The outcome is mutable. The past is immutable.
One Click, Three Cascades
A single flip in the simulator alters two records simultaneously. The winner's column is increased, the loser's is decreased, and all the downstream calculations related to those two teams are recalculated. A division title can change hands. The loser moves into the wild-card comparison and is now compared to teams which were previously higher than them. Strength of victory, the combined winning percentage of all the teams a team has beaten, shifts for all the teams that have beaten the two teams in question during the season.
The tiebreaker cascade eventually resolves standings, but only after simulating every possible permutation. There is something inherently entertaining to football fans about seeing how one single change would ripple through the system. At swiper online casino, there is a different type of environment to test this. The mathematics that govern the outcomes are fixed by design rather than by the rules of a football league. There are no tiebreakers or head-to-head records. Instead, outcomes are governed by a system of probabilities that remain constant no matter what the participants do. There are different ways to handle uncertainty in football pools, prediction markets, and casino games, and the difference between a flexible scoreline and a house edge is where these systems diverge.
There is a lot of drama packed into one button click. The cascade is made possible by the quirks of the NFL seeding system, which the simulator has to mimic. No wild-card team is seeded higher than a division winner. A 10-7 division champion is seeded higher than a 12-5 wild-card team, for example. Because of this rule, a result that determines a division winner is more valuable than almost all the other games that can be simulated.
When two teams have the same number of wins, losses, and ties in a division, the league goes through its tiebreaker list and stops at the first point where the records differ. The list includes: head-to-head record, division record, common-game record, conference record, strength of victory, strength of schedule, combined conference points ranking, combined overall points ranking, net points in common games, net points in all games, net touchdowns, and finally, a coin toss. The league stops at the first criterion that separates the two teams. Eleven steps come before the coin toss. A good simulator applies them in this order. The list is always the same, but the input can be altered.
This is the mechanical heart of What-If modelling. Rules are always the same but the results of the hypotheticals can change. People can alter the input and predict what the outcome of the rules will be. This type of tinkering with the fixtures is interesting because the framework is always the same.
The Market That Never Sits Still
Prediction markets are based on a completely different philosophy. The number that is important is a price, and that number is always changing based on what the participants of the market believe, and is updated whenever more information is revealed.
A contract in a prediction market has a value between 0 and 1 dollar. A contract pays out 1 dollar if the event happens, and 0 dollars if it does not happen. So a contract that is worth 70 cents means the market, according to all the trades that are happening, places a 70% probability on the event happening. There is no spread to decode, no odds format to convert. The price of the contract answers the question, how likely is the event to happen?
The price of the contract is determined by the information that is available. Let's say one of the key players in the event goes on the injury report on Friday. A contract that is worth 55 cents might trade for 35 cents within a few minutes, even though the game has not been played yet. The outcome is still open, but the market has updated its estimate of the probability of that outcome. This is what researchers call probability repricing. The market instantaneously updates the number that it displays to all the participants to reflect the new information.
The prediction market contrasts sharply with a simulation. A simulation keeps the rules fixed and allows the participant to change the outcomes. A prediction market keeps the event fixed and allows the participants to change the probabilities. In a simulation, the participant moves the number by assigning a fictitious outcome. In a prediction market, the number moves by itself in response to what the traders collectively know or believe.
Letâs look at football again. In the simulator, a user can select âBuffalo winsâ and then sees the standings change. Meanwhile, in a prediction market for the same game, the price for a Buffalo contract is rising. A statistical trader in Toronto has found something in the weather forecast or the injury report that the rest of the market has not seen.
Your Division Race, Priced in Real Time
When run through prediction-market logic, the contrast with the simulator sharpens. Picture two teams in the same division, with the second-place team trailing the leader by one game. In Week 13, the two teams are scheduled to play against each other. Before the game, the trailing team's contract for the division title is priced at 28 cents, representing the marketâs opinion of a team that needs a win and then needs some help.
The game has started and the team that is trailing has a 14-0 lead after the first quarter. So far, no result has been determined and the event is still active. The market, however, has been moving. Traders that think a 14-point lead is significant buy the contract, while other traders that know this team has given up big leads sell the contract. The price of the contract is rising and is potentially valued at 52 cents. Each trade represents a real dollar value that is being put at stake for a perceived probability. The market is not trying to guess the outcome of the game, but is continuously repricing the probability of that outcome.
By half time, if the lead holds, the contract could be trading at 68 cents. A second half collapse puts it back at 40. A late field goal has it trending toward 80. The final whistle locks it at either one dollar (if the team won the division) or zero (if they did not). Every single cent of movement from kickoff to the final whistle is generated by traders processing information and trading on it.
This is completely different from a simulator. A simulator takes a specific hypothetical and spits out a standings table. The market creates a continuously updating real money estimate of probability. One provides insight on the consequences; the other takes a crowd-sourced guess at the likelihood.
The Edge That Always Remains
There is a third kind of number found in online casino games that is set in stone by the mathematical design of the game and remains fixed for the life of the game, regardless of what the participants of the game do.
Let's start with roulette. In European roulette, the house edge is 2.70% because the wheel only has one zero. In contrast, the house edge is 5.26% in American roulette because the wheel has two zeros. The edge is a result of the design of the wheel and the payouts. The edge is built into the game because the payouts sit below the true probability of each bet. It does not matter how many spins of the wheel have occurred, the edge remains the same for the 10th spin as it does for the 100th spin. No matter what the player does, the edge always remains. It is built into the structure of the game, and it is not affected by how much the player bets, what the previous results of the spins were, or what betting strategy the player uses.
When played optimally, blackjack has a house edge of around 0.5%. On the other hand, slot games have house edges that range from 2% to over 10%. There are many different types of games, but once you select a game, the house edge is set. The edge is determined by the rules of the game and the payout, and it is verified by an independent organization that tests the game.
Understanding this verification process is important. The organizations that perform these audits are testing laboratories that analyze vast numbers of outcomes from a gameâs random number generator. When performing these audits, the testing laboratories are not concerned with whether the player won or lost. Their focus is on whether the outcomes over the large sample are aligned with the mathematical model that the game is built upon. After a game has passed this audit, players can be assured that the probability architecture is as represented in the game. The architecture is known and fixed.
The important distinction from the first two systems is that in the simulator, it is the player who alters the inputs, and in the prediction market, it is new information that alters the prices. In a casino game, the player alters nothing structural whatsoever. Each spin or hand is a new draw from a fixed probability distribution. The outcome of any individual round is uncertain; that is the nature of the game, but the mathematical framework that is generating the outcomes is constant.
Three Grids, One Football Sunday
Take a single moment in time. A divisional game, 4th quarter, visiting team trailing by 3, with 2 minutes left, and the ball. This moment will look completely different in each of the processing systems.
This moment in the simulator is still hypothetical. For now, a participant can assign a win to the visiting team and see what happens to the standings. The home team, which currently leads its division by one game, drops into a tie with that team. The tiebreaker list is active. This year, the two teamsâ head-to-head record is 1-1, so the tiebreaker steps cascade to the division record. The simulator processes the tiebreaker steps in order, because the participant has defined the outcome and the ruleset supports it.
In a prediction market, this fourth quarter is live. All quarter, the contract for the visiting team to win the division title has been active. With two minutes remaining in the game and the visiting team trailing by three, it could be valued at 38 cents. The market is pricing in a field goal as a real possibility and a touchdown as less likely. If the visiting team's drive is stopped on fourth down, the contract value would drop. If the visiting team scored a touchdown to take the lead, the contract value could rise to well over 70 cents in a few seconds, with traders purchasing the contract to win the division title.
On a casino floor, it's a different story on Sunday night. During a roulette spin, the house edge is 2.70% on every single bet, regardless of what's happening in the other football games. The outcome of a football game has no relation to the outcome of a casino game. Each spin of the roulette wheel is drawn from the same distribution as the previous spins. The football game produces no signal that the roulette wheel can read. The only thing the two activities share is that they occur on the same day.
This contrast actually produces the sharpest result of all the observations. The market's numbers are generated by collective estimates of the uncertain event, while the casino game's numbers are sealed into the game itself. The numbers produced by the simulation are logical consequences of the inputs.
The Numbers Feel Different
In the end, the difference in these three systems is the type of uncertainty the user is faced with.
In the simulation, uncertainty is structural and sequential. While the rules are known, the unknown is which results will actually occur. The user of the simulation explores this uncertainty by manipulating inputs and observing the outcomes. The fun is in the discovery of how a given input affects the entire system.
In a prediction market, uncertainty is collective and informational. The mechanics for setting prices are the same for all contracts. Prices must be between 0 and 1, and the price should reflect the probability that the outcome of the contract is true. Settlement is binary. Since new information is revealed over time, prices are constantly changing. Having a division race contract for a live game is not the same as looking at a probability estimate. The division race contract will show people making informed arguments and will provide real time price updates.
In a casino game, the uncertainty is mathematical and individual. The house always has an edge, and the potential outcomes of the game are determined before players start. What is unknown is which outcome will happen with this particular spin, this particular hand. The game does not remember what happened in previous rounds. Each new hand is a new draw. A football fan who spends their time on wild-card scenario simulations and division contract price hedging during live games is doing something fundamentally different from a game where the mathematical framework for each spin is determined before the game starts.
Reading the Uncertainty
All of these examples have a number that is associated with some meaning. Understanding why the number changes and what causes it to remain the same is the objective of each example.
The standings in the simulator update when a user changes a result. The tiebreaker list is static, but the inputs are not. The price in the prediction market is fluid, and the settlement rules are fixed. The edge in the casino game is static, but the individual outcomes of each round are not.
Football fans intuitively understand the concepts expressed here without formally recognizing them. Picturing various outcomes when watching a wild-card race with three weeks left is What-If modelling. Watching the betting line adjust after an injury report is probability repricing. A crude understanding of how a fixed probability structure interacts with changing conditions is seeing that a team playing at home in January has different odds than a team playing at home in September. The three systems in this comparison formalize these notions, and the distinctions between them are the focus of the interesting work.
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