Mathematical expectation in the lottery. How to win the lottery based on mathematical expectation Theory of mathematical expectation and lottery
IN AN HOUR
EXPECTED VALUE
Expectation is the amount of money that, on average, can be won or lost on a given bet. This is an extremely important concept for the player, since it is key to assessing most game situations. Expectation is also the best tool for analyzing most poker hands.
Let's say you and a friend are playing a coin game, betting equally $1 each time, regardless of which side it lands on. Tails means you win, heads means you lose. The odds of getting heads are 1 to 1, and you bet $1 to $1. Therefore, your expected value is exactly zero, because mathematically you cannot expect to be leading or losing after two rolls or after 200.
Your hourly gain is zero. Hourly winnings are the amount of money you expect to win in an hour. You can toss a coin 500 times in an hour, but since your odds are neither positive nor negative, you will neither win nor lose. From the point of view of a serious player, this betting system is not bad. But this is just a waste of time.
But let's say some sheep wants to bet $2 against your $1 in the same game. Then you immediately have a positive expectation of 50 cents per bet. Why 50 cents? On average, you win one bet and lose another. Bet the first dollar and lose $1, bet the second and win $2. You bet $1 twice and are ahead by $1. Therefore, each of those one-dollar bets earned you 50 cents.
If the coin came up 500 times in an hour, your hourly winnings are now $250, since on average you lost $1 250 times and won $2 250 times. $500 minus $250 equals $250, which is the total winnings. Notice again that the expectation, which is the average amount you win per bet, is 50 cents. You won $250 by betting a dollar 500 times: that's 50 cents per bet.
Expectation has nothing to do with short-term results. The Ram could win the first ten flips in a row, but with a 2 to 1 betting edge at even odds, you still get 50 cents on every $1 bet. It makes no difference whether you win or lose a single bet or a series of bets, as long as you have enough cash to easily cover your expenses. If you continue to bet the same way, you will win, and over a long period of time your winnings will closely approach the sum of the expectations in individual throws.
Every time you place a bet with the best outcome,(that is, it can be expected to be profitable in the long run), when the odds are in your favor, you win something on it regardless of whether you lose it or not on a particular hand. Conversely, if you make bet with the worst outcome(unprofitable in the long run) When the odds are against you, you lose something regardless of whether you win or lose on a particular hand.
You bet with the best outcome when the expectation is positive, and it is positive when the odds are in your favor. By betting with the worst outcome, you have a negative expectation, and this happens when the odds are against you. Serious players only bet on the best outcome; they fold on the worst outcome.
What does that mean the odds are in your favor? This means that you end up winning more than the real chances give you. The real odds of getting heads are 1 to 1, but you get 2 to 1 due to the ratio of bets. The odds are in your favor in this case. The best outcome is guaranteed with a positive expectation of 50 cents per bet.
But the example of mathematical expectation is a little more complicated. A friend writes numbers from one to five and bets $5 against your $1 that you will not guess this number. Should you accept this bet? What is the expectation here?
On average, you will miss four times and guess once. Total odds against What you guess correctly are 4 to 1. The odds are that you will lose a dollar on one attempt. However, you are getting $5 to $1 with a 4 to 1 chance of losing. So the odds are in your favor, you can hope for the best outcome and it is worth taking the bet. If you bet this way five times, on average you will lose $1 four times and win $5 once. So in five tries you will earn $1 with a positive expectation of 20 cents per bet.
Betting seizes chances when he thinks he will win more than he bets, as in the example above. And he ruins chances when he plans to win less than he bets. The bettor can have either a positive or negative expectation, depending on whether he catches the chances or ruins them. If you bet $50 to win $10 when the odds of winning are only 4 to 1, you have a negative expectation of $2 per bet because on average you will win $10 four times but lose $50 once, for a total loss of $10 after five bets. On the other hand, if you bet $30 to win $10 when the odds of winning are 4 to 1, you have a positive expectation of $2 because you will again win four times on S10 and only lose $30 once, for a total profit of $10. Waiting shows that the first bet is bad and the second bet is good.
Mathematical expectation is at the center of every game situation. When a bookmaker requires football fans to bet $11 to win $10, he has a positive expectation of 50 cents for every $10 he makes. When a casino pays even money on a craps pass line, it has a positive expectation of about $1.40 on a $!00 bet. since this game is designed in such a way that a bettor on this line loses on average 50.7%, and wins 49.3% of the total time. Undoubtedly, it is this seemingly minimal positive expectation that creates colossal profits for casinos around the world. As the casino owner noted Vegas World Bob Stupak, “A one-thousandth of one percent negative probability over a long enough period will ruin the richest man in the world.”
In most games, such as crepe and casino roulette, the odds are constant for any bet. In others, they change over the course of the game, and the expectation can tell you how to evaluate a particular situation. In blackjack, for example, to determine the correct play, mathematicians calculated the expected value when playing boxes in various ways. The tactic that gives you the maximum positive expectation or the minimum negative expectation is the correct one. For example, if you have 16 against the dealer's 10, you will most likely lose. However, if the 16 consists of two eights, your best bet would be to split the eights by doubling your bet. If you split the dealer's eights against the dealer's 10, you will still lose more money than you win, but in this case the negative expectation is lower than if you simply drew a card every time with 8.8 against 10.
– the number of boys among 10 newborns.
It is absolutely clear that this number is not known in advance, and the next ten children born may include:
Or boys - one and only one from the listed options.
And, in order to keep in shape, a little physical education:
– long jump distance (in some units).
Even a master of sports cannot predict it :)
However, your hypotheses?
2) Continuous random variable – accepts All numerical values from some finite or infinite interval.
Note : the abbreviations DSV and NSV are popular in educational literature
First, let's analyze the discrete random variable, then - continuous.
Distribution law of a discrete random variable
- This correspondence between possible values of this quantity and their probabilities. Most often, the law is written in a table: 
The term appears quite often row
distribution, but in some situations it sounds ambiguous, and so I will stick to the "law".
And now very important point: since the random variable Necessarily will accept one of the values, then the corresponding events form full group and the sum of the probabilities of their occurrence is equal to one:
or, if written condensed:
So, for example, the law of probability distribution of points rolled on a die has the following form: 
No comments.
You may be under the impression that a discrete random variable can only take on “good” integer values. Let's dispel the illusion - they can be anything:
Example 1
Some game has the following winning distribution law: 
...you've probably dreamed of such tasks for a long time :) I'll tell you a secret - me too. Especially after finishing work on field theory.
Solution: since a random variable can take only one of three values, the corresponding events form full group, which means the sum of their probabilities is equal to one: 
Exposing the “partisan”: 
– thus, the probability of winning conventional units is 0.4.
Control: that’s what we needed to make sure of.
Answer:
It is not uncommon when you need to draw up a distribution law yourself. For this they use classical definition of probability, multiplication/addition theorems for event probabilities and other chips tervera:
Example 2
The box contains 50 lottery tickets, among which 12 are winning, and 2 of them win 1000 rubles each, and the rest - 100 rubles each. Draw up a law for the distribution of a random variable - the size of the winnings, if one ticket is drawn at random from the box.
Solution: as you noticed, the values of a random variable are usually placed in in ascending order. Therefore, we start with the smallest winnings, namely rubles.
There are 50 such tickets in total - 12 = 38, and according to classical definition:
– the probability that a randomly drawn ticket will be a loser.
In other cases everything is simple. The probability of winning rubles is:
Check: – and this is a particularly pleasant moment of such tasks!
Answer: the desired law of distribution of winnings: 
The following task is for you to solve on your own:
Example 3
The probability that the shooter will hit the target is . Draw up a distribution law for a random variable - the number of hits after 2 shots.
...I knew that you missed him :) Let's remember multiplication and addition theorems. The solution and answer are at the end of the lesson.
The distribution law completely describes a random variable, but in practice it can be useful (and sometimes more useful) to know only some of it numerical characteristics .
Expectation of a discrete random variable
In simple terms, this is average expected value when testing is repeated many times. Let the random variable take values with probabilities 
respectively. Then the mathematical expectation of this random variable is equal to sum of products all its values to the corresponding probabilities:
or collapsed: 
Let us calculate, for example, the mathematical expectation of a random variable - the number of points rolled on a die:
Now let's remember our hypothetical game: 
The question arises: is it profitable to play this game at all? ...who has any impressions? So you can’t say it “offhand”! But this question can be easily answered by calculating the mathematical expectation, essentially - weighted average by probability of winning:
Thus, the mathematical expectation of this game losing.
Don't trust your impressions - trust the numbers!
Yes, here you can win 10 or even 20-30 times in a row, but in the long run, inevitable ruin awaits us. And I wouldn't advise you to play such games :) Well, maybe only for fun.
From all of the above it follows that the mathematical expectation is no longer a RANDOM value.
Creative task for independent research:
Example 4
Mr. X plays European roulette using the following system: he constantly bets 100 rubles on “red”. Draw up a law of distribution of a random variable - its winnings. Calculate the mathematical expectation of winnings and round it to the nearest kopeck. How many average Does the player lose for every hundred he bet?
Reference : European roulette contains 18 red, 18 black and 1 green sector (“zero”). If a “red” appears, the player is paid double the bet, otherwise it goes to the casino’s income
There are many other roulette systems for which you can create your own probability tables. But this is the case when we do not need any distribution laws or tables, because it has been established for certain that the player’s mathematical expectation will be exactly the same. The only thing that changes from system to system is
May 6, 2013 at 11:46 amProbability theory and the anthropogenic factor
- Mathematics
Introduction
There is an opinion among people that a person who enters the Faculty of Mathematics will definitely come out as a mathematics teacher. I didn’t come up with this, it’s from experience, because quite a large number of not very educated people asked where I was going to go to work after graduating from university. Of course, you can find much more extensive areas of application of your knowledge. One of them is related to the theory of probability. I don't want to delve into the complex details of the subject, because... people who do not have the right mathematical background are likely to get confused. But I don’t want to talk about anything at all. Therefore, I want to write about the connection between a person and this very theory of probability, and in a simple language that anyone can understand. If interested, please see cat.general information
I will nevertheless introduce a couple of definitions in order to formalize what has been written at least a little.1) If there are several possible random outcomes that are “equally possible” among themselves, then classical probability is the ratio of the number of “good” random (elementary) events to their total number. For example, if you have 5 balls, 2 of which are white, then the probability of taking the white ball will be 2/5.
2) Random value- this is a quantity that, as a result of experiment, takes on one of many values, and the appearance of one or another value of this quantity cannot be accurately predicted before its measurement. A classic example is the dice. By throwing it, you can randomly get one of six possible values.
3) Expected value A random variable is the sum of all its possible values multiplied by their probability. In simple terms, this is the “average value” of the random variable taken. For a dice it is equal to (1+2+3+4+5+6)*1/6=3.5. What does this give us? The fact is that when you throw a die many (for example, 100) times, on average each time you will get 3.5, and in total you will get approximately 100*3.5=350. As the number of throws increases, the relative error of the real result and its mathematical expectation, multiplied by the number of throws, will decrease more and more.
The essence
Now the essence of what I actually wanted to tell you: mathematical calculations predict various events quite well if they do not directly depend on a person’s choice. If an anthropogenic factor intervenes, then making any plans based only on the theory of probability must be done with caution. Let me give you a couple of simple examples. They may be a little far-fetched, but they are simple and understandable.Coin
Case once
During a class at the university (a lesson at school, a work day), you became bored and you invited your desk neighbor (work colleague) to play the following game: toss a coin; if it lands on heads, your friend pays you 5 rubles, but if it lands on tails, then you pay 5 rubles. Out of boredom, a person may agree. You will play like this all day, and in the end you will both be left with almost the same money as you started with. The probability of any side of the coin appearing is 1/2 and, as a consequence, the mathematical expectation of your winnings is zero. So on average, the win/loss will be around plus or minus 10 rubles. Well, maybe a little more. In any case, it is not critical for the budget.Case two
The situation is the same, but you suggested paying not 5, but 1000 rubles for a loss. Most likely your friend/colleague will refuse. Because you don’t want to just lose a significant amount of money.What has changed? The mathematical expectation of winning is still zero. From a mathematical point of view, everything is almost the same. And then the human factor intervened, and your plan to while away a boring day failed.
Lottery
You have decided to organize a lottery. They made tickets priced at 10 rubles with a fifty percent chance of winning 15. The mathematical expectation of winning is 15 * 0.5 = 7.5 rubles, but since the ticket costs 10, it turns out -2.5 rubles. Yes, it’s not very profitable for the client, but you’re not going to work at a loss, right? However, it is unlikely that such a lottery will be popular. Because it is proposed to spend 10 rubles with a dubious chance of winning 15. The difference is small.You change the conditions and make the lottery almost charitable. Now the winnings are 25 rubles. The mathematical expectation of winning minus the cost of the ticket is 2.5 rubles! You will even be at a loss! But the majority of people will still not favor your lottery, because the winnings are little more than the ticket price. Only schoolchildren who do not have enough change for ice cream will play the lottery.
At the same time, your enterprising neighbor is also organizing his own lottery. Only he charges 50 rubles for a ticket, and the winnings are a car worth 500,000 rubles. The probability of winning is 0.001%. The mathematical expectation of winning is 5 rubles. Minus the cost of the ticket, we get -45 rubles. Yes, the neighbor's lottery is simply extortionate! Having sold a sufficiently large number of tickets, even by raffling off a car, he will still become significantly rich. People may well buy tickets, because what is 50 rubles compared to the prospect of getting a good car for free?
The reader may decide that it is simply a matter of the quantitative size of the winnings. But this is far from necessary. Let me give you another rather far-fetched, but illustrative example:
Very big lottery
You are offered a gift of unparalleled generosity. "Super lottery." One of two, to choose from. You can play it just one time. In the first “lottery” you are guaranteed to pay a million dollars. And in the second, with a 50% chance you will receive 2 million, with a 40% chance a million and with a 10% chance you will leave with nothing. The mathematical expectation of winning in the first “lottery” is 1 million. In the second - 1.4 million. But what will you choose? Some may choose the second option, but a survey of a number of people will show that the majority will probably choose the first option. After all, as they say, a bird in your hands is better... Especially if a bird is a million, and in the second “lottery” there is a chance of not getting anything. And a hypothetical 2 million doesn’t solve anything.Last example
You have written a good and high-quality application for your phone. We spent a lot of effort and money. You list it in the store for $9.99. For such a high-quality product, this does not seem to be very much. Yes, and you need to pay off and earn extra money. But no one buys your app. People thought it was expensive. Downloads are minimal. In desperation, you lower the price to $0.99. Furor, people download your program only this way, but not enough money comes from them. Then you raise the price again, but to $4.99. Yes, the download flow is decreasing relative to the lowest price, but it is still higher than at the beginning. And lo and behold, you get quite a good profit from your product. From the point of view of primitive calculations, the number of people who want to have this program has always been the same. However, you reduced the price relative to the original one, and the profits increased. Again, a purely human factor.So what's the end result?
As a result, on the one hand, mathematical calculations can give results that are not entirely obvious from a mathematical point of view. A person can choose strictly one from almost identical conditions, and among several offers, take the one that is more unfavorable for himself. Why? This is how man is made. The benefit of one specific person cannot always be easily calculated.On the other hand, if you look from the point of view of various companies, corporations, etc., then having many clients, you can get good money, even if, from a mathematical point of view, the offer for the client is not the most profitable. That is why banks, lotteries, and insurance companies exist. And people take out loans at wild interest rates, buy dubious lottery tickets and insure things that, most likely, will be fine.
This means that if you try to apply some kind of “stupid” calculations to people, thinking like a robot, most likely nothing worthwhile or useful will come of it. But if you act wisely, imagine yourself in other people’s shoes, then you can move mountains and earn billions with the help of mathematics.
In general, think like people, but don’t forget about mathematics either.
P.S. If I wrote some nonsense somewhere (I took examples from my head), don’t kick me too hard, tell me. I'm interested in other people's opinions.
Mathematical expectation (ME) is the sum of the product of the probabilities of making a profit from a transaction, multiplied by the actual result of each trade:
Where n is the number of trades.
Unprofitable trades are substituted into the formula with a negative sign and subtracted when summing, so the expectation takes on both positive and negative values.
The probabilities of a positive outcome (or risk) for each trade are replaced by its actual value, adding the ratio of the arithmetic average of profit and loss. In this case, the formula looks like this:
Where the actual probability is equal to the real percentage of profitable trades from the total number of completed trades.
The average profit is calculated as the sum of profitable transactions divided by their number. The average loss (average loss) is also calculated by summing up the negative values and averaging the results of trades.
The relationship between a flat and a trend changes unpredictably, so it is impossible to accurately calculate the probability when directional movements that have grown to a maximum will bring an amount of loss that cannot be “worked off” with small takes.
Rule for collecting statistical data to calculate the mathematical expectation of profit
Calculations of mathematical expectation are considered reliable if:
the data includes a historical period from 2000 to 10,000 candles or "working timeframe" bars; tests equally contain areas of rising, falling trends and flats; volatility does not significantly deviate from historical values (there are no crisis phenomena or panic sales).
Tactical techniques for increasing the value of mathematical expectation
The mathematical expectation strongly depends on the choice of tactics for taking profits and limiting losses. Before deciding to part with the found or developed strategy due to the low results of MO, you should pay attention to the ratio of stops and takes.
A small size of loss limitation leads to an increase in the number of negative transactions and the accumulation of losses. If a trader trades the EUR/USD pair intraday, he must take into account that the “trading noise” is on average 30 points and will often trigger stop losses located in this zone.
A take/stop ratio of 2 to 1 increases the expected value. It is believed that takes and stops should not be below parity (1 to 1).
A decrease in the number of transactions can lead to an increase in the value of MO. Traders use time filters, trading during the session in areas that coincide in time with the work of the stock exchanges of the countries to which the pair’s currencies belong.
Improving the quality of entries - purchases or sales of currency pairs. Filters are introduced into the trading system to allow transactions at significant points. These are historical highs and lows, candles that coincide in trend on lower and higher timeframes, indicator readings with a long period (from 50), etc.
Features of mathematical expectation when scalping
Scalping is characterized by a large number of intraday trades with a low positive MO value. The small size of stops in this case is an exception, justified by high trading activity. With a slight prevalence of profit over loss, earnings come from a large number of intraday trades.
There are no exceptions to the remaining tactical rules - the scalper applies a fixed take value that exceeds the stop level. The search for the optimal value of the expected value is achieved by selecting the time for holding the transaction; the scalper should not “sit out” or work when there is no volatility.
The parameter under consideration does not alone determine the feasibility of adopting a strategy. Performance assessment is based on a comprehensive analysis of test results.
Today, software from NetEnt and not only is at the top of its popularity. The online gambling market is actively developing, which means it is in maximum demand. From this fact it follows that many players are actively searching for information that will increase their chances of getting maximum winnings. We invite you to estimate the probability of winning at any gambling establishment, relying on mathematics and statistics. We will tell you how to increase the mathematical expectation of winning.
In modern online casinos, each client’s chances of receiving a positive mathematical expectation of winning are at the highest level. And all because operators are introducing various innovations in the field of bonus policy. But dumping is often used (note: Dumping is the sale of goods or services at artificially low prices). Please note that obtaining the above expectation is simple and completely legal. You will not violate the rules of the gambling establishment, since bonuses will be used. By the way, one trend is clearly visible in modern online gambling - the closure of new virtual casinos and numerous refusals to pay winnings to clients due to the use of dumping.
The statement that all casino slot machines have a negative mathematical expectation leads to the thought: “Is it worth playing at all?” That is why we recommend reading our article and finding out whether it is possible to obtain a positive mathematical expectation.
Ways to obtain a positive mathematical expectation of winning at a casino
You should know that there are several rules that need to be followed for the strategy to work. So, we choose slot machines that have a high expected payout percentage. RTP should be above 97%. Also, the account must have bonuses with certain wagering requirements. The best option is a wager of less than x40. Please note that this strategy usually produces small but stable payouts. But you can hope for a big win. This is due to the fact that when using this method, the mathematical expectation will be moved towards the player. Don’t forget that some casinos have begun to exclude the most profitable slots from NetEnt from the list of games for wagering bonuses.
Statistics
The developers do not hide what payout percentage (RTP) is valid in any slot. Operators also always provide information on wagering requirements for bonus offers. Our experts have revealed hidden data. These are the cycle length and the dispersion of winnings. Recommendations from experienced testers are also available. All these statistics will help you get a positive expectation of winning. The main thing is to know how to use indicators.
So, a negative expectation of winning always applies to the rules of any gambling establishment. In any case, after several very successful spins, any slot will level out the statistics. He will not allow you to leave as a winner and, in the end, losing is simply inevitable. But the operator always leaves the opportunity to correct this state of affairs. This is why the bonus policy is applied. Especially at NetEnt casinos.
Selecting a bonus offer
Each gambling establishment offers different types of bonuses. You can take advantage of the welcome offer. For example, for topping up your account with 100 euros you can get another 100 euros bonus. Wagering requirements are usually up to 35x of the bonus amount. In simple words, you need to place bets amounting to 3,500 euros. Then the bonus will be wagered in full. Be sure to choose bonus offers that have a low wager.
Slot machine selection
When choosing an online slot, be sure to study all the offers. On our website you can find information on each game. The return percentage requires special attention. RTP is indicated everywhere. Now let's decipher this indicator. For example, you chose a slot machine with an expected payout percentage of 96%. This means that out of 100 euros spent on bets, you can get back 96 euros. All NetEnt games have a payout percentage that varies from 90% to 99%. The spread of the indicator is large. But based on this data, you can choose the most profitable slot. Thanks to it, you can get more payouts and win back your bonus. The higher the RTP and the lower the wagering requirement, the lower the risk of spending your money. We invite you to learn how to use all these values to obtain a positive mathematical expectation of winning in an online casino.
Wager requirement 35x and calculation
You have a bonus of 100 euros and need to place bets totaling 3,500 euros. Therefore, you should choose the most profitable slot machine. If you choose a slot with an RTP of 97.14%, you can get a positive mathematical expectation. After all, such games will help you play the required number of bets. And when a lower wager is in effect, the probability of waiting for a win will increase several times. Be sure to familiarize yourself with the list of games that are most suitable for obtaining a positive mathematical expectation of winning in an online casino.
| Logo | A game | RTP (payout percentage) |
Winning on every 100€ bets |
Probability bonus |
Cycle length | Probability loss bonus |
Fund distribution main / bonus |
Dispersion winnings |
| 99% | 1.86 | No | Long | no data | no data | Extremely high | ||
| 98.86% | 1.72 | No | Average | - | - | Extremely high | ||
| 98% | 0.86 | 0.5%/ 2.1% | Fast | 0.5%/ 2.1% | 65% /12,1%/ 20,1% | Very low | ||
| 97.8% | 0.66 | 0.94% | Average | 0.94% | 80,3% / 17,6% | Low | ||
| 97.6% | 0.46 | no data | The longest | no data | no data | Extremely high |
||
| SimSalabim | 97.5% | 0.36 | 1,87% | Fast | 1,87% | 68,8% / 15,9% / 12,8% |
Average | |
| 97% | - 0.14 | no data | Long | no data | 77,3% / 19,7% | High |
Having carefully examined the presented table, we can conclude that many slot machines allow you to get the highest expectations. In our rating, the first places are occupied by the Mega Joker and Jackpot 6000 slots. We will separately focus on the latter, in which you are guaranteed to return up to 98.86 euros. If you play this particular slot machine, you can make a profit of 1.72 euros. Also pay attention to the last slot machine on our list. The Jack Hammer slot has a return rate of 97%. Even using a 35x wager, you can get only 0.14 euros in profit. Therefore, this game is not suitable for our strategy. Important! Based on the above, you can only get a positive expectation of winning if you have an active 35x bonus and play on a slot with an RTP that is above 97%.
Calculation for wager requirements 40x
Now let’s look at the calculation for a bonus with a 40x wager and choose the optimal slot machine. So, you have a 100 euro bonus, to win it back you need to place bets in the amount of 4,000 euros. In this case, you need to choose games that have an RTP that is higher than 97.5%. We have selected three of the best slot machines that are ideal for the strategy of obtaining a positive mathematical expectation of winning.
Representatives of large gambling establishments usually exclude high-variance slot machines, since they have the greatest winning potential. And all because bonus hunters can take advantage of this opportunity. For example, create several accounts, deposit large sums, receive maximum bonuses and win them back at high rates on any of the high variance slots. Having lost a large amount and significantly replenished the prize fund, the player will receive an impressive win at the last count. After all, in a casino, any game does not distinguish what money was bet - bonus or real. So bonus hunters could make big profits.
Country restrictions
Operators also use country restrictions for bonus programs. In the list you can always see which offer is not available to residents of a particular region. This is due to the fact that countries have different standards of living. Some people are willing to spend more than 100 euros daily on bets, but somewhere they can only afford 10 euros. The program excludes countries in which clients receive maximum winnings using bonuses from the list of those eligible for participation in bonus offers. The strategy of obtaining a positive mathematical result is very profitable. It really works, so gambling houses admit their defeats to active and knowledgeable players, adding entire countries to the list of prohibited countries.
The Welcome Bonus is given only once. What should I do?
You probably have a question about how to regularly make a profit using this scheme. After all, in any casino you can only get one welcome bonus. Don’t despair, because gambling establishments regularly offer other bonuses. For example, for replenishing a deposit on certain days or hours. There are various promotions that you must participate in to win.
Summary
Let's summarize and highlight the main aspects that relate to obtaining a positive mathematical expectation of winning. So:
- All bonus offers with a wager of 35x and slots with an RTP above 97% allow you to get a positive mathematical expectation of winning.
- When choosing a bonus with a wager of x40, you must choose a slot machine with a payout percentage above 97.5%. In this case, only a few games that are described in this article will suit you.
- Using a strategy for choosing a profitable slot significantly increases your chances of winning at NetEnt casinos.
- The use of repeated reload bonuses and other personal offers from casinos that have lower wagering requirements is the most profitable and allows you to get the maximum positive expectation.
- Be sure to carefully study the wagering conditions for the selected bonus.
- Follow casino news and take part only in the most profitable promotions.
