It is crucial to understand the relation between probability and expected value.
The idea is that the statistical anomalies and variance all level out after a huge volume of rounds.
And then at those points, the results should line up with theexpected valueof the wagers.
Defining Expected Value
The expected value is how much money you will make if your bet wins.
But it will always be a little larger than the real possibility of winning.
This is because the house applies a littlejuice, or vig, skimming a little money off your winnings.
It is easiest explained withroulette bets.
Playing a game of European roulette, you have 37 segments on the wheel.
When playing a 1:1 wager, you cover 18 of those segments.
That additional 1.35% is thehouse edge.
The straight up bets are priced at 35:1, but you are only covering 1 from the 37 segments.
That means, your real chances of winning are 2.70%, but the implied probability is 2.77%.
Should you win 1 round from 37 tries, you will spend $37 and win $36 again.
Defining House Edge
The house edge is made by providing you withnegative expected value bets.
In card games or roulette, we can definitively calculate this edge.
Simply by counting theexact probability of winningand measuring it against the expected value’s implied probability.
But in slot machines and crash games, it is not as apparent.
These games have RTP values, provided by game auditors who thoroughly test each game’s algorithms.
They are designed to provide completely randomized results, but a house edge remains.
This is because some statistical anomalies and frequencies cannot be precalculated.
The key word here isvariance.
This is the amount and frequency of the winnings that deviates from what is mathematically optimal.
These are the anomalies that can occur by chance.
In the long run, the streaks and variance should diminish, as the results balance out.
But that may take an infinite number of rounds to achieve.
In the short run, variance is a lot higher, and anything can happen.
Dangers of Variance
Though variance can play tricks on gamers.
These are allgambler’s fallacies, and make similar kinds of assumptions as the gambler’s ruin.
But the latter is based on maths and fact, whereas the fallacies are misconceptions.
It is not simply something that you will experience in casino games.
The Gambler’s Ruin is not as straightforward in sports betting as it is in casino games.
The casino has no say in what happens on the field in a sports game.
They define the odds based on previousgame statistics, historical data, trends and other metrics.
Oddsmakers feed the data into complex algorithms to generate the odds.
But some so many external factors and variables can come into play.
Variance is generally a lot higher in sports betting than casino gaming.
Especially when the odds on a bet are overestimated, or severely underestimated.
Expert sports bettors don’t just pick out bets based on who they think will win.
Analysing the odds and finding golden opportunities is just as part of the game as picking amoneyline winner.
The sportsbooks always add a little juice to your winnings.
It ensures that in the long run, the house will make its money.
Plus, it makes it more difficult forhedge bettorsto bet on all outcomes and guarantee a profit.
It takes the assumption that after countless hands, the results will reflect the actual probabilities.
The gamblers ruin can be offset by adding a few tricks of your own.
Such as changing your stake after each round.
By usingprogressive betting systems, you could minimize your losses when the variance is high.
Alternatively, some systems such as themartingale systemcan aggressively push to make a profit.
But these are dangerous, as they can lead to tremendous losses if you cant keep up.
Another way of avoiding the gamblers ruin is by implementing targets.
Specifically, targets that are quite achievable, and dont require huge variance.
In either case, a bigger bankroll is needed to maintain your gaming.
Ideally, you should have enough money to last a long gaming session without going bust.
Therefore, it’s crucial that you rely on variance.
And considering how it can also play against you, be prepared for losses along the way.
Daniel has been writing about casinos and sports betting since 2021.
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