Casino players who play online know that casinos that offer various bonuses. Although "Free-load" might sound appealing, they're not worthwhile. Are they profitable for gamblers? This is a question that depends on a variety of factors. This question can be answered with mathematics.

Let's start with a normal bonus on deposit. You transfer $100 and get $100 more. This is feasible after you stake 3000. This is an example of a bonus you receive on your first deposit. While the amount of a deposit or bonus may vary, so can the stake rates. However, one thing is sure: the bonus amount is still able to be withdrawn following the wagering requirement has been met. It is currently impossible to withdraw cash in the majority of cases.

If you plan to play at the online casino for a lengthy period of time, and you are persistent about it, this bonus will aid you, and it could be considered as free money. 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 in the event that you simply want to have a look at a casino, but not playing for a long period of time, if you prefer roulette or any other game, forbidden by casinos' rules for winning back bonuses. In the majority of casinos there is no way to withdraw money or will just return your deposit if a wager is not made on the games allowed at the casino. You can win a bonus when you play roulette or blackjack, but only if you meet the minimum stakes of 3000. If you're lucky enough to win 95% payouts that you'll lose an average of $3000* (1-0,95) which is $150. In other words, you are not just losing the bonus, but also have to take out of your wallet $50. In this case it is better to not accept the bonus. If poker or blackjack could win back the bonus by earning a profits of 0.5 percent, it's possible that you'll get between $100 and $3000, which is equal to $85 after you have won back the bonus.
"sticky" or "phantom" bonus:

A growing amount of popularity in casinos is derived from "sticky" or "phantom" bonuses - similar to lucky chips in real casinos. It isn't possible to cash out the bonus. The bonus has to be stored on the account like it "has stuck". It might appear as if a bonus is not worth the effort. It isn't possible to withdraw any money, however this is not true. If you win, there's no reason in the bonus, but even if you lose the money, it could be useful to you. You have already lost $100 without a bonus. If the bonus is not "sticky", $100 will still be on your account. This could help to get out of the situation. There is a chance to win back the bonus in this case is less than 50 percent (for that you only need to bet the whole amount on the odds of roulette). In order to maximize profits from "sticky" bonuses one needs to use the strategy "play-an-all-or-nothing game". You will lose slowly and certainly if you play with in small amounts. The negative math expectation of the game means you will not receive any bonus. 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 the amount you wish to gain, such as $200, and then take the risk to make it. 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 recognized is the possibility of returning money lost. Two types of bonuses could be distinguished: the complete return of the deposit. At this point the money is usually to be returned as an ordinary bonus. A partial return (10-25%) for a set period (a month or a week). The first situation is the same as the "sticky bonus" - the bonus will not be worth anything in the event of winning, but helps if you lose. The "sticky bonus" mathematical calculation will be analogous. The principle of the game is similar that we bet, win as often as possible. You can gamble with the money we've won, even if we fail to win. Casinos with games offer an opportunity to earn a portion of the loss for gamblers who are active. If you are playing blackjack with the math expectation of 0,5%, after you have staked 10 000 dollars, you'll lose an average of $50. You will receive $10 back when you make a loss of 20 dollars. This is equivalent to the math expectancy rise of 0.4%. But, from the bonus, you can also gain benefit, for that you need to be playing less. With the same stakes in roulette, we place one, but it is the largest stake. The majority of instances, we again win $100, and 51% of the time we lose $100, but at the end of the month we win back 20% which is equal to $20. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. It is evident that the stake has a positive math expectation, however the its dispersion is huge, since you to play in this manner very rarely - every week, or once per month.

I will allow myself to make a brief remark, but slightly digressing from the main topic. One forum member said that tournaments were unfair. He claimed, "No normal person will ever be able to stake a single stake in the final 10 minutes." The 3,5-fold increase is more than the amount of prize ($100) in the case of maximum losing, so it's impossible to lose. What's the point?

And really does it make sense? It's similar to the one with loss of money. We're in the black if a stake has been won. We'll receive a tournament prize of $100 if it fails to win. So, the math expectancy of the above-mentioned stake amounting to $350 is: $350*0,49-($350-$100)*0,51=$44. Sure, we could lose $250 today, but we will win $350 next day. In the course of a year of playing each day and earning a total of 365, our earnings will be pretty impressive at 365*$44=$16 000. After completing a simple equation, we'll find out that stakes of up to $1900 can be profitable for us! It is essential to have thousands on our accounts for this kind of game, but we don't have to blame casinos for being shady or naive.

Let's look back at our bonuses, to the best "free-load" ones- with no requirement for any deposit. Recently, one has noticed more and more advertisements promising up to $500 absolutely free , with no cost and without deposit. You will receive $500 in exchange for an account that is unique, and only a certain amount of time to play (usually one hour). After an hour, you receive just the amount of your gains, but not more than $500. You have to win the bonus back in a real bank account. Usually, you have been able to play it for 20 times in slot machines. It sounds wonderful however, what is the real price of the bonus? The first aspect is that you need to win $500. Based on more here simplified formula, we can determine the odds of winning are 50 percent (in the real world, it's certainly even smaller). In order to win the bonus it is necessary to bet at least $10 000 in slots. The pay-out rates in slot machines aren't known. They average around 95% and fluctuate between 90-98% for different types. An average slot will give us between $500 and 000*0.05=$0. This isn't a bad amount. If we are lucky to choose a slot with high pay-outs, we can await $500-10 000*0,02=$300. Even though the probability to choose a slot with payouts that are high is 50 percent (you have listened to the opinions of other gamblers , since by random choice this probability will be less than 10-20% since there are only a handful of slots with high payouts), in this case the value of a huge deposit free bonus amounts to $300*0,5*0.5%=$75. It's less than $500 however, it's still not poor, although we can see that even with the most ideal suppositions, the final value of the bonus has diminished seven times.

I hope this exploration into the mathematical realm of bonuses will be useful for gamblers. If you'd like to win, all you need is to think and make calculations.