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Online Casinos: Mathematics of Bonuses
Casino players online are aware that bonuses can be found at many casinos. While "Free-load" may seem appealing, they're not really worth the effort. Are they profitable for gamblers? Answering this question will depend on a variety of factors. The answer to this question is possible by math.

Let's begin with the typical bonus on deposit. The deposit is $100, and you get $100 more. This is feasible after you stake 3000. It is a typical example of bonus on the first deposit. The amount of bonus and deposit can be different, as well as the stake requirements However, one thing remains unchangeable - the amount of the bonus is accessible for withdrawal after the wager is completed. In general, it is impossible to withdraw any funds.


This bonus can be considered free money if you gamble online for a lengthy duration and are persistent. 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. For instance when your objective is simply to take an overview of the casino, without spending too much time there, or you are a fan of roulette or any other games that are not permitted by bonus rules, you might be denied access to the bonus amount. If you do not wager in any of the permissible games, the majority of casinos will not allow you to withdraw money. Bonuses can be won when playing roulette or blackjack, but only if you have the required stakes of 3000. If you're lucky enough to win 95% of all payouts, you'll lose an average of $3000* (1-0,95) which is $150. You will lose $50, and lose the bonus. In this case, it is better not to take the bonus. If poker or blackjack could win back the bonus with a casino profits of 0.5 percent, it's likely that you will get $100-3000*0,005=$85 after you've redeemed the bonus.
"Sticky" as well as "phantom" bonuses

Casinos are becoming more popular because of "sticky" and "phantom bonuses. These bonuses are the equivalent of lucky chips in a real casino. The amount of bonus is impossible to withdraw and must stay on the account (as when it "has been glued" to it) until it's completely lost, or annulled on the first withdrawal of cash means (disappears as if it were a phantom). It might appear as if a bonus is not worthwhile. It isn't possible to withdraw any money, but this isn't the case. If you win, then there's really no use in the bonus, but even if you lose the money, it could be of use to you. Already, visit url 've lost $100, without a bonus. Even if the bonus is not "sticky", $100 will still be in your account. This could help you get from this mess. A possibility to win back the amount of bonus is a bit less than 50 percent (for it is only necessary to stake the entire 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". Really, if playing video games play low stakes, you'll slowly and surely lose due to the negative math expectations in games. Moreover, the bonus is likely to prolong the pain, and will not help you 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. It is recommended to fix the amount you want to profit, for instance $200, and then try to win it, while taking chances. 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 type of bonus, specifically, the return of a lost deposit. Two types of bonuses can be distinguished: the complete return of the deposit. The cash is typically returned just as an ordinary bonus. Also, a partial return (10-25 percent) over a fixed period (a week or a month). In the first case the scenario is essentially identical to the case with a "sticky" bonus. In the event that we win, there's no point in the bonus, however it can be helpful in the event of losing. Math calculations will be also identical to the "sticky" bonus, and the strategy is the same - we take risks and try to win as much as possible. If we are not lucky and lose then we are able to play again with the help of that money back, thus minimizing the risk. Partial return of the losing for an active gambler can be regarded as an insignificant advantage of casinos in games. You'll lose an average of $50 when you play blackjack using an average math expectation of 0.5 percent. The payout is $10 when you lose 20 dollars. This is equal to an increase in math expectancy of 0.4%. But, the bonus you will also get benefit, for that you will need to play less. You only make one, however an extremely high stake, such as $100, on the same roulette stakes. We can win $100 in 49% of instances, while $100 is won by 51%. We lose $100 in 51% of the cases. When we finish every month, we receive back 20 percent of the $20 we won. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. The stake then has positive math expectancy, but dispersion is big for you to play in this manner very rarely - at least once per week or once a month.

I'll allow myself to make a brief remark, but slightly digressing from the main issue. In a forum about casinos, one of the gamblers began to claim that tournaments were not fair, arguing it by saying: "No normal person will ever stake a single penny within the final 10 minutes of the tournament, which 3,5-fold surpasses the prize amount ($100) as a result of a maximum loss, in order to take home a prize. What's the purpose?

It makes sense. The situation is similar to the one with loss of money. We're in the black when a stake is taken home. If it has lost - we'll win 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 might lose $250 today, but we will win $350 in the future. If we continue playing every day and earning a total of 365, our earnings will be quite amazing at 365*$44 = $16,000. If we can solve a basic equation, we'll discover that stakes up to $1900 are profitable for us! Of course, for this kind of game, we'll need to have hundreds of dollars in our accounts and we can't accuse casinos of dishonesty or gamblers for being naive.

Let's go back to our bonuses. These are the highest "free-loading" bonuses without any deposit. There are an increase in ads offering $500 free of cost, without deposit. You get $500 for an account with a specific number of players, as well as a limited amount of time to play (usually one hour). You will only get the amount you win after an hour, but not more than $500. You must win the bonus back in a real bank account. In most cases, you've been able to play it for 20 times in slot machines. The $500 bonus sounds tempting however, what is the actual value of the reward? The first part is that you have to be able to win $500. We can determine that the chance of winning $500 is 50% based on the simplified formula. However, in practice it is much lower. In order to win the bonus, you must stake 10 000 dollars on slot machines. We aren't aware of the rate of payouts on slot machines, but they are provided by casinos, and make up on average about 95 percent (for various kinds they fluctuate between 90 and 98 percent). If we get at an average slot, till the end of the wager , we'll be able to deposit $500-10 000*0,05=$ on our account, not an awful game... If we happen to select a slot that has large payouts, we can look forward to $500-10 000*0,02=$300. Even though the probability to pick a slot that has high pay-outs is 50 percent (you have listened to the comments of other gamblers as randomly, this chance is less than 10-20%, for there are few generous slots) In this instance, the value of a generous deposit-free bonus amount to $300*0,5*0,5=$75. Even though it's not $500, this is still an impressive amount. However, we are able to find that the bonus's final value has dropped sevenfold even with the most accurate estimates.

I'm sure this trip into mathematics domain of bonus will prove helpful to gamblers - if you're looking to win, you simply have to think about it and calculate.

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