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Online Casinos: The Mathematics of Bonuses
Casino players who play online know that these casinos provide various bonuses. These bonuses may look attractive but are they actually beneficial? Do they generate income for the gamblers who make use of these bonuses? The answer to this question depends on a variety of variables. Mathematics can assist us in answering this question.

Let's begin with an ordinary bonus upon deposit: you make $100, and then receive another $100, which it will be possible to receive after you have staked $3000. This is an illustration of a bonus you receive on your first deposit. Although the size of a deposit and bonus will vary, so too will the stake requirement, one thing is constant the bonus amount will be available for withdrawal once the wagering requirement is met. At present, it's impossible to withdraw money in the majority of cases.

This bonus is a fantastic method to earn money when you are planning to play on the internet casino for quite some time. If you play slots with 95% pay-outs, a bonus will allow you to make on average extra 2000 $ of stakes ($100/(1-0,95)=$2000), after that the amount of bonus will be over. There are a few pitfalls. For example, you may want to look around an online casino that doesn't require you to play for long, or you might prefer roulette, which is not allowed by the rules of casinos for cash-back bonuses that are a winner. If you don't play the games of casinos, the majority do not permit players to withdraw their money. They may even return the deposit. If you're keen on blackjack or roulette, and a bonus is earned only by playing slots, place the required $3000 of stakes, in the course of 95% of pay-outs you'll lose an average of $3000*(1-0,95)=$150. You will not only lose your bonus, but you'll also have to pay $50 out of the pocket. In this case it's recommended to decline the bonus. In any case, if blackjack and poker can be used to return the bonus and a casino's profit only about 0,5%, so it can be expected that once you have repaid the bonus you will have $100-$3000 plus 0,005 = $85 from the casino's profit.
"sticky" or "phantom" benefits:

The popularity of casinos is gained by "sticky" or "phantom" bonuses - similar to casino chips that are lucky in real life. It is not possible to cash out the bonus. The bonus money has to remain in the account until it is totally lost or cancelled on the first cash withdrawal (like the Phantom). It may appear as if a bonus isn't worth it, as it is not going to earn cash. However, this isn't accurate. If you win, there's no reason in the bonus, but even if you lose, it may be of use to you. If you don't have a bonus, you've lost your $100 and that's it, bye-bye. However, with a bonus even if it's one that is "sticky" one, the $100 are still on your account, which could assist you in getting out of the problem. In this situation the odds of winning back the bonus is lower than 50%. (For this, you'll need only to bet the whole amount at roulette). In games people play to maximize profits from "sticky" bonuses one needs to use the strategy "play-an-all-or-nothing game". Really, if you play small stakes, you will gradually and eventually lose because of the negative math expectation in games, and the bonus will only make you feel worse, and will not assist you in winning. Clever gamblers usually try to realize their bonuses quickly - somebody stakes the entire amount on chances, in the hope to double it (just imagine, you stake all $200 on chances, with a probability of 49% you'll win neat $200, with a probability of 51% you'll lose your $100 and $100 of the bonus, that is to say, a stake has positive math expectancy for you $200*0,49-$100*0,51=$47), some people use progressive strategies of Martingale type. You should set a target amount, such as $200, and try to get there by making a bet. If you have contributed a deposit in the amount of $100, obtained "sticky" $150 and plan to enlarge the sum on your account up to $500 (that is to win $250), then a probability to achieve your aim is (100+150)/500=50%, at this the desired real value of the bonus for you is (100+150)/500*(500-150)-100=$75 (you can substitute it for your own figures, but, please, take into account that the formulas are given for games with zero math expectancy, in real games the results will be lower).


Cash Back Bonus:

It is not often seen variant of a bonus, specifically, the return of a lost deposit. Two types of bonuses can be distinguished - an entire return of the deposit that was lost in which the amount returned is typically repaid in the same way as a regular bonus, or a part (10-25%) reimbursement of the loss over a predetermined duration (a month, a week). The first option is almost identical to the "sticky bonus" - the bonus is not worth it in the event of winning, but it is useful if you lose. Math calculations are identical to the "sticky" bonus, and the strategy is similar - we risk and try to win as much as we can. The cash back in the event that we lose and are unlucky. This will minimize the chance of losing. best play games may have a slight advantage in the games by providing a portion of losing money to active gamblers. If you are playing blackjack with math expectancy - 0,5%, after you have staked 10 000 dollars, you'll lose $50 on average. You'll get $10 back if you get 20 percent return. That means you will lose 40 dollars. The math expectation increases to 0,4%. Bonuses are not the sole benefit. You can also get benefits from playing more. There is only one chance to win very high stake, like $100, on the same bets on roulette. played games of the cases we again win $100, and 51% of times we lose $100, however at the end of the month, we receive our 20% that's $20. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. As you see, the stake then has positive math expectancy, but it's a big dispersion, as you to play this way very rarely - every week, or every month.

I'll allow myself to offer a few words which is a minor deviance from the topic. On a casino forum one of the gamblers started to assert that tournaments were not fair, arguing it as follows: "No normal person will ever make a single stake in the final 10 minutes of the event, which 3,5-fold surpasses the prize amount ($100) as a result of a maximal losing, so that they can win. What's the point?"

Does it really be logical? It is like a variation that returns the losing stake. We're in the black when a stake is won. If it loses - we'll get a tournament prize of $100. So, the math expectancy of the above-mentioned stake amounting to $350 is: $350*0,49-($350-$100)*0,51=$44. We could be losing $250 right now, however we we'll be able to win $350 next day and, over the course of a year playing every day, we'll accumulate pretty 365*$44=$16 000. If we solve a basic mathematical equation, we can realize that stakes as high as to $1900 are profitable. We'll need a lot of money for this type of game but we don't have to blame casinos or the gamblers.

Return to our bonuses. Let's examine the "freeloaders"- - those who don't require a deposit. In recent years, more advertising has been spotted promising $500 free of charge without deposit. The pattern is like this - you really get $500 on a special account and limited time for playing (usually one hour). After one hour, you'll only be able to claim the amount of the winnings. It's nonetheless $500. The gain is transferred on an actual account, where you are required to return it as with any bonus typically after having played it 20 times through slot machines. What is the actual cost of $500 in free bonus money? In the first place, you must be able to win $500. It is possible to calculate the chance of winning with a simple formula. In practice, this is even lower. Second part to win back the bonus, you must place a bet of at least $10 000 on slots. The casino doesn't publish the payout percentages for slot machines. They average 95% but can range from 90-98 percent. If we get at an average slot, then at the end of our bet we'll have a total of $500-10 000*0,05=$0 in our account. Not a bad game... If we select an option with the highest payouts, then we can anticipate $500-10 000*0.02=$300. Even though the likelihood of selecting the slot that pays effectively is just 50% (you've been listening to the opinions of other gamblers and the probability by random selection will be hardly more than 10%-20 percent), in this case, the value of the deposit-free bonus will be $300*0.50*0.50=$75. This is less than $500, however isn't bad. We can also see that the amount of bonus is cut by seven-fold when using the best assumptions.

single player games of bonus calculations can be beneficial to gamblers. If you want to win, you just need to do some calculations and think.

Arthur Prudent is the developer of casino bonuses mathematics web site, which covers gambling news. provides reviews of casinos, Poker rooms, bingos, Sports Betting bonuses promotions and more.



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