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Online Casinos: Mathematics of Bonuses
Online casino players know that the latter ones offer various bonuses. "Free-load" appears attractive, however, are they really worth such bonuses? Are they lucrative for gamblers The answer to this question depends on a variety of factors. This question can be answered with mathematics.

Let's start with a normal bonus when you deposit. You deposit $100 and receive another $100. This is possible after you have staked $3000. This is a common example of bonus on your first deposit. The size of the bonus and deposit can be different, as well as the required stake rates however one thing is unchangeable - the amount of bonus can be withdrawn after the required wager. In general, it is not possible to withdraw any funds.

If you intend to play in the online casino for a long period of time, and you are persistent about it the bonus can help you, it can be considered to be 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 want to simply take a look at a casino without playing for a long time or if you like roulette or other gamesthat are which are not permitted by the rules of casinos to win back bonuses. If you don't wager on any of the allowed games, the majority of casinos will not let you withdraw cash. If you are keen on blackjack or roulette and you can 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 lose $50, and forfeit the bonus. In this scenario it's best not to accept the bonus. Anyway, if blackjack and poker can be used to win back the bonus with a casino's profit only about 0.5%, it can be expected that after winning back the bonus, you'll be left with $100-$3000, which is a total of 0,005 or $85 for.
"sticky" or "phantom" benefits:

A growing amount of popularity in casinos is gained by "sticky" or "phantom" bonuses - the equivalent of luck chips in real casinos. The bonus amount is impossible to withdraw and must stay on the account (as if it "has been glued" to it) until it's entirely lost or is canceled after the first time you withdraw cash means (disappears as if it were a phantom). It might appear as if bonuses are not worth the effort. It isn't possible to withdraw any money, but this isn't the case. It's not worth the cost if you win. However, if you fail, the bonus might prove useful. Already, you've lost $100 with no bonus. Even if the bonus was not "sticky" it remains on your account. This can help you get out of the situation. There is a chance to win back the bonus is a bit less than 50% (for it is only necessary to put 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 in small amounts. The negative math expectancy of games means that you will not win 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 win, for instance $200, and be willing to take chances to be successful. 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 a rare variant of a bonus, which is the return of lost. Two kinds of bonuses can be distinguished: the full return of the deposit. In this case, the money is usually to be returned as an normal bonus. A partial return (10-25%) for a set period (a month or a week). The first scenario is almost similar to a "sticky bonus" which is not worth it if you win however, it is beneficial in the event that you lose. In the second case, the "sticky bonus" calculation of math will be similar. The strategy of the game is identical that we bet, win as often as possible. We can still bet with the money that you've earned even if we do not succeed. Casinos that offer games may provide some kind of compensation for losses for gamblers who are active. If you play blackjack with the math expectation of 0,5%, then, having made stakes on $10 000, you will lose an average of $50. play free will receive $10 back if you lose $20. This is the equivalent of the math expectancy increase of 0.4 percent. You can still derive benefits from the bonus however, you'll need to be playing less. We make only one but very high stake, for example $100, on the same stakes in roulette. We win $100 in 49% of cases, while $100 is won by 51%. However, we have to lose $100 in 51% of instances. At the end of each month, we earn back 20% of our $20 winnings. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. As you see, the stake then has positive math expectation, however the dispersion is big for you to play this way rather seldom - every week, or every month.

I'd like to provide a short remark. I'm a little off-topic. One forum member declared that tournaments weren't fair. He said, "No normal person will ever be able to stake a single stake in the last 10 minutes." The amount is 3,5 times the prize amount ($100) in the case of maximum losing, so that you won't lose. What is the point?"

And really does it make sense? The situation is similar to the one with return on losing. The stake is in the black if the stake is taken home. The stake will be awarded a prize of $100 in the event that 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, laptop could lose $250 today, but we will win $350 in the future. If we continue playing every day the total amount we earn will be quite impressive , at 365*$44=$16000. We'll discover that stakes as high as $1900 are profitable for us after solving the simplest equation. website is essential to have many thousands of dollars in our accounts to play this game, however we don't have to blame casinos for being untruthful or inexperienced.


Let's get back to our bonuses. They're the top "free-loading" bonuses without any deposit. In recent times, we've been able to notice an increasing number of ads promising the possibility of up to $500 completely for free, and without deposit. The way to look at it is this You actually receive $500 when you sign up for a specific account and limited time for play (usually an hour). After an hour, you will receive only the amount of your gain, but still not more than $500. The bonus must be redeemed back in a real bank account. playing video games , you've played it at least 20 times on slot machines. It sounds great however, what is the real cost of the bonus? First, let's look at the first step requires you to be able to win $500. It is evident that the odds of winning $500 is 50% using an easy formula. But in reality, it's much less. To get the bonus back it is necessary to bet 10 000 dollars on slot machines. The payout rates of slot machines aren't well-known. They range from 95 to 95% and fluctuate between 90-98 percent for various types. If we choose an average slot until the end of the wager we'll have $500-10 000*0,05=$0 in our account. Not an excellent game... If we are lucky to select a slot that has large payouts, we can look forward to $500-10 000*0,02=$300. The likelihood of picking the slot that has the highest payout is 50%. However, you have been influenced by the opinions of other gamblers , as this probability will not exceed 10-20%. In this instance the bonus for depositing is generous of $300*0.5*0.5=$75. A lot less than $500 but not too bad, though we can find that even with most ideal suppositions, the final amount of the bonus has decreased seven-fold.

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

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