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Online Casinos: The Mathematics of Bonuses
Online casino players are well aware that these bonuses are available at many casinos. While "Free-load" may seem attractive, they're not really worth the effort. Are they profitable for gamblers? The answer to this question depends on many factors. Mathematical calculations can assist us in answering this question.

Let's start with a typical bonus on deposit: you transfer $100 and receive $100 more that it is possible to get having put up $3000. This is an example of a bonus that you can get on your first deposit. The size of the bonus and deposit can differ in addition to the stake requirements However, one thing remains unchangeable - the amount of bonus is available for withdrawal after the wager is completed. Till this moment it is impossible to withdraw money generally.

It is considered as free money if you gamble online for a long duration and keep playing. 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)=$2000), after that the amount of bonus will be over. There are some complications. In particular, if your goal is simply to take a look at the casino without spending too much time in there, or you like roulette or other games which aren't permitted by bonus rules, you may not be able to gain access to the bonus. If you aren't betting on any of the permissible games, casinos are unlikely to allow you to withdraw money. You can win a bonus when you play roulette or blackjack, but only if you have the required stakes of 3000. If you're lucky enough to win 95% payouts that you'll lose an average of 3000$ (1-0,95) which is $150. The loss is $50 and you also forfeit the bonus. In this instance it's best not to take the bonus. If blackjack and poker are allowed to win back the bonus with a casino's profit only about 0.5%, you can expect that after reclaiming the bonus, you'll have $100-$3000, which is a total of 0,005 or $85 for.

"Sticky" and "phantom” bonuses

Casinos are increasingly gaining traction for "sticky" and "phantom bonuses. These bonuses are the equivalent to lucky chips in real casino. It isn't possible to withdraw the bonus amount. The bonus amount must be kept on the account, like it "has stuck". It may appear that such a bonus is not worth the effort. You will not be able to withdraw any money, but this is not true. If you win, there is really no point in the bonus, however in the event that you lose the money, it could be of use to you. Already, you've lost $100, without a bonus. Even if good games to play is not "sticky", $100 will still be in your account. This can help to get out of this situation. The chance of winning back the amount of bonus 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". In reality, if you are playing with small stakes, you'll eventually lose money because of the negative mathematical expectations in games. Moreover, the bonus is likely to prolong agony, and won't help you to win. 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 would like to earn, like $200, and take risks to win 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:

There is a seldom encountered variation of a bonus which is the return of lost. There can be singled out two options - either the complete return of the deposit that was lost in which case the money usually is to be paid back as with any other bonus or a portion (10-25 percentage) of the losing for a fixed time period (a week, a month). In the first scenario, the situation is practically identical to the case with a "sticky" bonus - if you win, there's no reason to get the bonus, however it can be helpful in the event of loss. Calculations in math will also be similar to the "sticky" bonus, and the strategy of the game is the same: we take risks, try to win as much as we can. You can play with the money we've won, even if we fail to succeed. Casinos with games offer some kind of compensation for losses for gamblers who are active. You'll lose about $50 playing blackjack with an average math expectation of 0.5%. If you earn 20% of the money, $10 will be given back to you, that is the loss you'll suffer is $40, which is equivalent to the increase in the math expectation up to 0,4% (ME with return = theoretical ME of the game * (1percent of return). There is still a chance to benefits from the bonus but you'll have to play less. You only make one, however very high stake, such as $100, with the same roulette stakes. In 49% of instances, we again win $100, and 51% of the time we lose $100, however at the close of the month, we get back our 20%, which is 20 dollars. 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 dispersion is big for we'll be able to play this way rather seldom - at least once per week or once per month.

Let me provide a short remark. I'm a little off-topic. On a casino forum one of the gamblers began to argue that tournaments are unfair. They argued by saying: "No normal person will ever stake a single penny within the last 10 minutes of a tournament that is 3,5 times greater than the prize amount ($100), in nomination of a maximal losing, in order to be able to win. What is the point?"

It is logical. This situation is like the one that has loss of money. If a stake is successful the stake is already in the black. If it is 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. We could lose $250 today, but we will win $350 next day. Over a year of playing every day and earning a total of 365, our earnings are quite amazing at 365*$44 = $16,000. We'll discover that stakes up to $1900 could be profitable for us if we solve an easy equation. We'll need thousands on our accounts for this game, but we don't have to blame casinos for being dishonest or foolish.

Let's talk about our bonuses. These are the highest "free-loading" bonuses without any deposit. Of late one has been able to notice increasing numbers of advertisements that promise the possibility of up to $500 completely free of charge, without any deposit. The basic idea is as follows You actually receive $500 with a separate account, and a limited amount of time to playing (usually an hour). You'll only receive the amount of your win after an hour, but no more than $500. You must win the bonus back on a real account. Most often, you've run it 20 times in slot machines. This sounds fantastic but what's the exact value of this bonus? The first part is that you need to win $500. It is evident that the odds of winning $500 is 50% based on the simplified formula. But in reality, it's much lower. In order to win the bonus, you must stake $10 000 on slots. The payout rates of slot machines aren't known. They average around 95%, but can vary between 90-98% for different types. If we play an average slot, then at the end of our bet, we'll have $500-10 000*0.05=$0 on our account, not an awful game... It is possible to expect $500-10 000*0.02=$300 in the event that we are lucky enough to locate a high-paying slot. Even though the likelihood to choose a slot with payouts that are high is 50 percent (you have heard the opinions of other gamblers since randomly, this chance will be less than 10-20%, as there are a few slots that pay out generously) In this instance, the value of a huge deposit free bonus amounts to $300*0,5*0,5=$75. A lot less than $500 but still not too bad, even though we see that even with the most ideal assumptions, the final amount of the bonus has diminished seven times.

I'm hoping that this journey into the maths of bonus will prove of use to gamblers - if you are looking to win, you just must think about it and make calculations.

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