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Online Casinos: The Mathematics of Bonuses
Online casino players are aware that the latter ones offer various bonuses. While "Free-load" may seem appealing, they're not really worthwhile. Are they profitable for gamblers? The answer to this question depends on many factors. Mathematical knowledge can assist us in answering this question.

Let's begin with a typical bonus on deposit. You deposit $100 and receive another $100. This is possible after you stake $3000. This is an example of a bonus you receive on your first deposit. The size of the bonus and deposit may differ and so can the required stake rates, but one thing remains unchangeable - the amount of the bonus is available for withdrawal after the required wager. In general, it is not possible to withdraw money.

The bonus is free money if you are playing at the casino online for a prolonged duration and you are consistent. 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 some complexities. In particular, if your goal is to just take a peek at the casino without spending a lot of time there, or you like roulette or other games that are not permitted under bonus rules, you could be denied access to the bonus. In technology there is no way to withdraw money or will simply refund a deposit when a wager isn't made on games permitted in the casino. If you're keen on blackjack or roulette and a bonus is earned only by playing slots, make the required stakes of $3000 during 95% of pay-outs you'll lose $3000*(1-0,95)=$150. The loss is $50 and you also lose the bonus. In this scenario it's better not to take the bonus. If find out here or poker can win back the bonus with a casino profit of 0.5 percent, it's possible that you will get $100-3000*0,005=$85 after you have won back the bonus.
"Sticky" as well as "phantombonus

Casinos are becoming more popular for "sticky" and "phantom bonuses. These bonuses are the equivalent to lucky chips in real casino. It's not possible to withdraw the bonus amount. The bonus has to be stored on the account as if it "has stuck". It might appear as if an offer isn't worth the effort. You won't be able to withdraw any money, but this is not true. If you are a winner, there's really no use to the bonus. However, if you have lost the money, it could be of use to you. You've already lost $100, without a bonus. But with a bonus, even if it is one that is "sticky" one, the $100 are still on your account, which could assist you in getting out of the situation. There is a chance to win back the amount of bonus is less than 50% (for it is only necessary to bet the whole amount on the chances in roulette). In order to maximize profits from "sticky" bonuses one needs to use the strategy "play-an-all-or-nothing game". You'll lose slowly and sure if you only stake tiny amounts. The math expectancy that is negative of the game means you will not win any bonuses. 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. It is advised to determine the desired amount you wish to gain, for example $200, and try to win it by taking risks. 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:

The most common bonus noticed is the return of lost funds. Two types of bonuses can be distinguished: the complete return of the deposit. At this point the money is usually to be returned just as an ordinary bonus. Also, a partial return (10-25 percent) over a time period (a month or a week). The first situation is similar to the "sticky bonus" The bonus is not worth it if you win however, it is beneficial when you lose. Math calculations are identical to "sticky" bonus, and the game's strategy is similar - we risk and try to win as many times as we can. If we are not lucky and we have lost then we are able to play again using this money, thus decreasing the risk. Casinos in games can offer a partial return on losing for gamblers who are active. If you play blackjack with math expectancy of 0,5%, then after you have staked 10 000 dollars, you'll lose an average of $50. If you earn 20% of the money, the amount of $10 is returned to you, which means that the amount your loss will be 40 dollars, which is equal to the increase in math expectancy to 0,4% (ME with return = theoretical ME of the game * (1-% of return). It is possible to still benefits from the bonus however, you'll need to play less. You only make one, however an extremely high stake, such as $100, using the same roulette stakes. We can win $100 in 49% of the cases, while $100 is taken home by 51% of players. We have to lose $100 in 51% of the cases. When we finish each month, we get back 20% of our $20 winnings. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. The stake then has positive math expectancy, but its dispersion is huge, since you to play in this manner very rarely - every week, or once a month.

Let me make a brief remark. I am slightly off-topic. One of the forum members claimed that tournaments weren't fair. He claimed, "No normal person will ever stake a single stake during the final 10 minutes." The 3,5-fold increase is more than the prize amount ($100) in nomination of maximum loss, meaning it's impossible to lose. What is the point?"


What is the sense? The situation is identical to the scenario that involves losing a stake. If a stake has won it is already in the black. If it has lost - 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. Yes, we may be losing $250 right now, however we win $350 tomorrow in the course of a year. playing each day, we'll earn $16,000. If we can solve a basic equation, we'll find out that stakes of up to $1900 are profitable for us! Of course, to play this kind of game, we'll require hundreds of dollars in our account, but we certainly can't accuse casinos of dishonesty or gamblers who are foolish.

Let's look back at our bonus offers, especially the most "free-load" ones- without any deposit. Of late one has been able to notice more and more advertisements promising as much as $500 free , with no cost and with no deposit. The pattern is the following you actually get $500 when you sign up for a specific account, and a limited amount of time to playing (usually one hour). After an hour, you receive only the amount of your gains, but not greater than $500. You have to win the bonus back on a real account. In most cases, you've run it 20 times in slot machines. It sounds wonderful, but what's the actual cost of this bonus? The first aspect is that you must get $500. Using a simplified formula, we can determine the odds of winning are 50 percent (in practice, it is certainly even smaller). In order to win the bonus back and you have to bet $10 000 in slots. We do not know the percentages of pay-outs from slot machines, but they are provided by casinos, and make up on average approximately 95 percent (for various kinds they fluctuate around 90-98 percent). The average slot gives us between $500 and 000*0.05=$0. That's not a bad amount. We can expect $500-10 000*0.02=$300 If we're fortunate enough to find a high-paying slot. The likelihood of picking one with the highest payout is 50 percent. However, you have been influenced by the opinions of other gamblers as the probability of winning will be between 10-20 10%. In this case the bonus for depositing is generous of $300*0.5*0.5=$75. While it's less than $500, it's still an excellent amount. But, we can find that the bonus's final value has decreased sevenfold, even with the most accurate assumptions.

I'm hoping this look into the mathematics realm of bonuses can prove beneficial to gamblers. If you'd like to win, all you need is to think and make calculations.

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