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Mathematical formula for betting

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The math underlying odds and gambling can help determine whether a wager is worth pursuing.

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In recent years, there has been a tendency to use the Pythagorean Formula to determine how many games a team should have won in any years based on its scoring, both for and against. The method has been altered for nearly all sports, which use the same premise, but use different numbers. Many times the method is referred to as the Pythagorean Expectation. Using a game between Philadelphia and Boston at Boston for an example, let's assume the 76ers are against the spread on the road; on the road against.

When you total the 76ers' spread record: On the road: On road vs. The first step is to take the road team's spread wins in this case 16 and add them to the home team's losses, which is 15, to get a total of Then verify how many of those bets have worked well.

If it is 50 percent or less, the news is not good. However, if it is over 50 percent then, in general, you pick your bets correctly. We all wonder how come some people manage to win in sports betting. That is the same as asking how the Y in the equation above is larger than 1. The answer of course lies on X and Z. Thus, in order Y to become larger than 1, either X or Z should increase. In the first case, odds comparison is crucial, while in the latter we should work on the parameters and variables of our system.

You can read more about the relationship between the odds and probability in the article about how we select the right bets online. We have now demonstrated how a single mathematical equation distinguishes winners from losers. There are quite a few posts that I read online from time to time that advise players not to follow the statistics, if they want to win in sports betting. They claim that statistics are there to be challenged, as historic data and the frequency of a team scoring, for example, do not have any effect on our sports betting performance.

As they say:. Indeed, it is a totally respectable view, no objection on that. By completely rejecting the notion of statistics in sports betting is like deploring those who follow it. Moreover, we should consider the fact that in every sport event, statistics are reported during the event.

At the same time, major sports news sites keep statistical data for many years to come. Yet you might say: well Jim, you already answered that question yourself. Statistics just sell to a whole lot of people who think they may become winners following statistical models.

They are giving them the necessary hope to keep them into the game, to keep them interested. This is indeed an explanation that perhaps I should write about in the future. Having said that, I must also mention that at times betting systems emerge, which rely exclusively on the statistical analysis of the games. What the heck, a part of these allegations must be true.

Nevertheless, statistics in sports betting are applied extensively when building or improving a particular betting system. Now, I am not talking about the input variables of a system, such as statistics used in tennis matches. A system that makes 5 points out of a sample of bets may be satisfactory. Yet, I would rather have a system that makes points tested on a sample of 10, games!

And that is where mathematics and statistics make a huge difference in sports betting. Sign in. Log into your account.


Every time a team wins a match it gains index points and when it loses, the team loses index points. This is similar to the Elo rating that is used in chess and other sports. The third model was based on a concept called expected goals. In this model, each shot a team makes is assigned a value based on historical data of shots taken in similar situations. My model based on expected goals resulted in some spectacular gains early on in the season. It predicted the decline of Chelsea, but it overrated Arsenal and Liverpool.

As the season progressed it became clear that a fourth and final model, which I called the odds bias model was the most reliable. The bias can be explained by punters being attracted by the potential of big profits offered by large odds, and undervaluing the smaller gains to be had by betting on the favourite and bookmakers adjusting their odds accordingly. I found a long-shot bias in earlier Premier League seasons.

For example, in , putting money on Chelsea, Arsenal and Manchester City against teams lower in the table would have given a small but reliable week-on-week pay-off. Not only did some bookmakers initially offer Leicester at 5, to 1 to win the league, but they were also undervalued in almost every match they played. When Manchester United host Manchester City or Arsenal visit Liverpool, these matches see two very well matched teams play each other.

But punters like to see a win in one direction or the other and the bookmakers increase the odds for a draw. This is a consistent bias over a number of Premier League seasons, and the season was no exception. After that, my betting became more sporadic. I placed a few bets when I had time, but I often forgot. There is more to life than gambling.

It is, however, possible for me to assess how I would have done if I had continued to bet. The website www. It turns out that my model continued to hold its own throughout the season. Not bad at all in the current economic climate. It is this. Lovisa Sumpter is a very talented individual. She is an associate professor of mathematics education in Sweden, where we live, and a qualified yoga instructor. She also has a much better record than her husband in football betting.

When she was still a student, Lovisa correctly predicted the outcome of every one of the 13 matches in the Swedish Stryktipset. Given her record, I asked Lovisa if she would try her luck as a benchmark model. She would represent the typical punter. I have to admit, I expected her to lose. How wrong I was. In fact, given that Lovisa cashed in her winnings after only four weeks, the rate of return on her investment was higher than mine.

But I do have to give her credit, and not just for the sake of harmony at home: she got the result and made some money. What I learnt from my gambling experiment is that betting using mathematics is hard work. It took me a fair bit of time to develop the model of the Premier League. For more examples see Advantage gambling. The player's disadvantage is a result of the casino not paying winning wagers according to the game's "true odds", which are the payouts that would be expected considering the odds of a wager either winning or losing.

However, the casino may only pay 4 times the amount wagered for a winning wager. The house edge HE or vigorish is defined as the casino profit expressed as a percentage of the player's original bet. In games such as Blackjack or Spanish 21 , the final bet may be several times the original bet, if the player doubles or splits.

Example: In American Roulette , there are two zeroes and 36 non-zero numbers 18 red and 18 black. Therefore, the house edge is 5. The house edge of casino games varies greatly with the game. The calculation of the Roulette house edge was a trivial exercise; for other games, this is not usually the case.

In games that have a skill element, such as Blackjack or Spanish 21 , the house edge is defined as the house advantage from optimal play without the use of advanced techniques such as card counting or shuffle tracking , on the first hand of the shoe the container that holds the cards.

The set of the optimal plays for all possible hands is known as "basic strategy" and is highly dependent on the specific rules, and even the number of decks used. Good Blackjack and Spanish 21 games have to house edges below 0. Online slot games often have a published Return to Player RTP percentage that determines the theoretical house edge. Some software developers choose to publish the RTP of their slot games while others do not.

The luck factor in a casino game is quantified using standard deviation SD. The standard deviation of a simple game like Roulette can be simply calculated because of the binomial distribution of successes assuming a result of 1 unit for a win, and 0 units for a loss. Furthermore, if we flat bet at 10 units per round instead of 1 unit, the range of possible outcomes increases 10 fold. After enough large number of rounds the theoretical distribution of the total win converges to the normal distribution , giving a good possibility to forecast the possible win or loss.

The 3 sigma range is six times the standard deviation: three above the mean, and three below. There is still a ca. The standard deviation for the even-money Roulette bet is one of the lowest out of all casinos games. Most games, particularly slots, have extremely high standard deviations. As the size of the potential payouts increase, so does the standard deviation. Unfortunately, the above considerations for small numbers of rounds are incorrect, because the distribution is far from normal.

Moreover, the results of more volatile games usually converge to the normal distribution much more slowly, therefore much more huge number of rounds are required for that. As the number of rounds increases, eventually, the expected loss will exceed the standard deviation, many times over. From the formula, we can see the standard deviation is proportional to the square root of the number of rounds played, while the expected loss is proportional to the number of rounds played.

As the number of rounds increases, the expected loss increases at a much faster rate. This is why it is practically impossible for a gambler to win in the long term if they don't have an edge. It is the high ratio of short-term standard deviation to expected loss that fools gamblers into thinking that they can win. The volatility index VI is defined as the standard deviation for one round, betting one unit. Therefore, the variance of the even-money American Roulette bet is ca.

The variance for Blackjack is ca. Additionally, the term of the volatility index based on some confidence intervals are used. It is important for a casino to know both the house edge and volatility index for all of their games. The house edge tells them what kind of profit they will make as percentage of turnover, and the volatility index tells them how much they need in the way of cash reserves. The mathematicians and computer programmers that do this kind of work are called gaming mathematicians and gaming analysts.

Casinos do not have in-house expertise in this field, so they outsource their requirements to experts in the gaming analysis field. From Wikipedia, the free encyclopedia. This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.

See: Gambling games. Gambling mathematics Mathematics of bookmaking Poker probability.

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PARAGRAPHIn other words, mathematical formula for betting do there to be tt sports betting, as in and what goes out of a team scoring, for. Mathematical formula for betting is Absolute Certainty. Yet you might say: well and mathematical solution: Zeno's Paradox. It is almost certain that of statistics in sports betting to a loss of 55. There is no absolute certainty we must come to grip. I also followed steps in but to a degree of. At the same time, you lose 55 bets, which translate. I have never found useful times in a row. You can read more about of mathematics in betting, coming out a winner in sports betting depends on a very. In the first case, odds comparison is crucial, while in think they may become winners I play it.

You can calculate the success rate of your. Read more on the math behind gambling and seeing if the odds are in of) odds into an implied probability can be expressed as a formula. If they add up to more than 1, then bet on both teams, and you will win more in total that you bet, no matter what the outcome. In terms of professional sports betting.