Winning at gambling and sports betting with math ?

Betting on sports (or any other form of betting) is risky, that's not a new story.
Mathematics seems to be involved, or at least allows for understanding and predicting random events. This is not a new story either.
Two questions about math and gambling can be answered categorically:


Gambling and mathematics

We talk about "pure random" chance like casino roulette, lotto, etc.
For this type of game, there is no strategy that allows you to change the mathematical expectation of the game: that's a mathematically proven mathematical property !
For example, if you play Heads or Tails, winning 1€ when Tails comes up and losing 1€ when Tails comes up, the expectation is zero. On average, over a large number of plays of this game, you neither win nor lose much.
Well, for this type of random game for example, there is no strategy that changes this expectation. Neither martingale nor statistical study changes the mathematical expectation.
In the same way, when we look at sports betting as purely random games, no strategy changes the expectation, and in particular no mathematical game formula allows you to become a winner in the long term.
This result is studied and demonstrated mathematically on this page, for a martingale, accumulator bets and some other sports betting formulas.
In summary
No strategy can reverse chance


And with statistics ? against chance ?

Games of chance also escape statistics. In particular, the laws of probability associated with games of chance such as lotto or roulette are said mathematically to be memorylessness probability laws, i.e. knowledge of past results does not influence the results to come.
Such a simple example: if we toss a (well balanced) coin and get heads 10 times in a row, then the probability of getting heads by tossing it again is … 1/2 … just like getting Tails this 11th times. (On the other hand, the overall probability of getting Tails 10 times consecutively is quite low, 1 chance in 1024).

Wrong use of the law of large numbers: explanations

The law of large numbers tells us that, the more the number of tosses of the coin, the more the probabilities of getting Heads and that of getting Tails approach the probability 1/2. Hence the following reasoning, for example if after 100 throws I have already obtained 60 times the result Heads, therefore 40 times Heads, statistics are 60/100 = 0.6 of Tails and 40/100 = 0.4 Heads. As the two "must balance" towards 1/2, obviously, to catch up, Tails must "slow down" a little, and Tails the opposite. So, to do this, Face would have to catch up in the next draws.
This reasoning is erroneous and comes from a misuse of the law of large numbers which "only" asserts that the statistics of Heads and Tails will tend towards their probability, here 1/2.
We can for example imagine that from now, after previous 100 draws, we draw exactly as many heads and tails (i.e. 50 each), during the following 100 draws, leading to the statistics 110/200 = 0.55 Tails and 90/200 = 0.45 Heads.
We thus got very closer to 0.5 for both results, without Face having "caught up".
We can still imagine that over the next 1000 draws, after the previous 200, Pile goes on with "its advantage" with 510 draws in his favor. We then arrive at the stats 620/1200 ≃ 0,51 of Pile and 580/1200 ≃ 0.49 from Face, and we are still getting closer to 0.5 for both sides.
Be careful therefore, in "pure random" games the statistics calculated form past outcomes have no say: in mathematical terms, these laws of probability are called memorylessness probability laws.
This type of mathematical error is now well known, and referred to as the gambler's fallacy. This is now a fairly well-known general cognitive bias, see the page on the gambler's fallacy.

Maths are definitely useless against chance ?

Yes, they are, against pure random.
But many other applications exist: such as trading, horse racing, sports betting in general, etc.
We must (we have no choice!) see these categories as being a matter of chance. But not only that: history matters, and history = statistics !
For instance, a player still unknown until then and who reveals himself will drastically increase his chances of winning, which is not yet shown by either probability or statistics, but by a knowledgeable eye... Mathematical strategies therefore do indeed exist, and are effective, but in areas where additional expertise can be provided.

Mathematics and sports betting

Everyone knows it, says it and repeats it: sporting events contain their share of chance ! The most assured match can turn against the favorite team, as certain as its victory seemed.
Betting on sporting events is risky. So can math help in this case ?

This time, we can nevertheless affirmatively answer; Sports betting is not just about chance, not just pure random.
Making good pronostics systematically is impossible, as we have just said. Any good tipster knows this and must have the humility to accept being wrong... We would rather measure the effectiveness a good tipster calculating his percentage of good forecasts.

In addition, specificity of sports betting, what interests us is not only the number of good pronostics, but to have both good forecasts and high pay off (the easy pronostic, on almost certain events have an odd very weak and yield very little profit, therefore are not very interesting; in sports betting, we speak of value bet).

Math comes into play here.
Imagine for a moment being able to leave, even to an average tipster (yourself ?) two chances out of three to be a winner, there the rate of bad predictions should be very low, even zero.
Mathematics allows this precisely. It is a mathematical strategy of calculating exact bets to be a winner by betting on two different outcomes of the same event (for example, victory and a draw) and to be a winner in both cases. Many other similar mathematical strategies exist.
Thus, mathematics combined with some studies, knowledge, statistics, etc. can make you a winner in sports betting.

And with statistics? against the chance of sports betting ?

Unlike the pure chance of certain games, against which stats can't do anything, it's a different story for sports betting: Betting strategies exist. These are ineffective against pure chance (the expectation of winning never changes, read for example this article and its math expectation calculations), on the other hand they can be ineffective for sports betting such as for example for the martingale on draws.

An alliance: sports expertise and mathematics

In summary, math alone does not allow you to win at purely random games, but that's a category in which sports betting is not restricted.
With sporting expertise (previous results, statistics, particular sporting element such as the absence of players, injuries, etc.) we can calculate mathematical strategies to best secure sports betting (such as Double chance and Refunded if, draw no bet, formulas , or some martingales, among many other betting formulas).
The know-how then comes down to knowing which is the right betting formula to use, the right mathematical strategy, depending on the sporting knowledge you have.

The use of an Elo rating system is also a very good example of a mathematical method allowing to combine sports expertise and statistics/mathematical model.

With this method or another, it must be clear that:

Winning at sports betting ? a work !

Finally, we must insist on a fundamental point: becoming a winner in sports betting is largely possible and conceivable, but it requires personnal investment: time and intellectual (mathematical) investments (and also, of course, some money):
In summary: winning at sports betting yes, but it takes time, knowledge and investment: it's called work, right ? and the winnings are then called a salary, right ?

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