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Online Casinos: The Mathematical Basis of Bonuses
Online casino players are aware that casinos that offer a range of bonuses. Although "Free-load" might sound appealing, they are not worth the effort. Are they lucrative for gamblers The answer to this question is contingent on a lot of conditions. Mathematics will assist us in answering this question.


Let's begin with a typical bonus for deposits. You transfer $100 and get another $100. This is possible after you stake $3000. It is an example of a bonus that you can get on your first deposit. The size of the deposit and bonus can be different and so can the required stake rates, but one thing remains in place - the amount of the bonus is available for withdrawal following the wager requirement. It generally is impossible to withdraw any funds.

This bonus can be considered free money when you play at the casino online for a lengthy period of time 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. In particular when your objective is to just take an overview of the casino, without spending a lot of time in there, or you like roulette or other games that are not permitted by bonus rules, you could be denied access to the bonus amount. In the majority of casinos there is no way to withdraw cash or simply return a deposit, in the event that a bet isn't made on games permitted in the casino. If you're a fan of blackjack or roulette, and a bonus is earned only by playing slot machines, you must make the required stakes of $3000 and in the 95% payouts, you will lose on average $3000*(1-0,95)=$150. The loss is $50 and you also lose the bonus. In this scenario it's better not to accept the bonus. If poker or blackjack will be able to recoup the bonus by earning a profit of 0.5%, it is possible that you'll receive $100-3000*0,005=$85 after you've redeemed the bonus.
"sticky" or "phantom" benefits:

Casinos are increasingly gaining traction due to "sticky" as well as "phantom bonuses. These bonuses are equivalent to the lucky chips found in a real casino. It's not possible to withdraw the bonus amount. The bonus has to be placed on the account as if it "has been shackled". It could appear that bonuses are not worth the effort. You will not be able to take any money out, but this is not true. If you are a winner, there is really no point in the bonus, but in the event that you lose, it may be of use to you. You have already lost $100 without a bonus. However, with a bonus even if it's one that is "sticky" one, the $100 remain on your account. This can aid you in escaping the situation. A possibility to win back the bonus in this case is a bit less than 50 percent (for that you only need 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". It is possible to lose slowly but sure if you only stake tiny amounts. The negative math expectation of games implies that you won't receive 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 important to determine the amount you would like to earn, like $200, and then take the risk 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:

A bonus that is rarely seen is the return of lost funds. There can be singled out two variations - the full refund of the deposit lost, at this the returned cash is typically paid back as with any other bonus, or a partial return (10-25 percent) of the losing for a fixed time period (a week or month). The first scenario is nearly identical to that of a "sticky bonus" - the bonus is useless when you win however, it is beneficial if you lose. Math calculations are similar to the "sticky" bonus and the strategy is the same: we take risks and try to win as much as we can. If we don't win and we have lost the game, we can continue to play with the that money back, thus minimizing the risk. A partial return on the loss for an active gambler can be considered to be an unimportant benefit of casinos in games. It is possible to lose about $50 playing blackjack with a math expectancy of 0.5 percent. You'll get back $10 if you make a loss of 20 dollars. This is equal to an increase in math expectancy of 0.4%. However, from the given bonus, you can also gain benefits, which means you will need to play less. With the same stakes in roulette, we make one, however it's an enormous stake. We can win $100 in 49% of the cases however $100 is won by 51%. However, we have to lose $100 in 51% of instances. 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 is positive in math probability. However, dispersion is large and we will only be able to play this way once every week or once a month.

I'll let myself make an unintentional remark that is slight deviation from the main issue. One of the forum members claimed that tournaments weren't fair. He stated, "No normal person will ever put a stake in in the last 10 minutes." This 3,5-fold exceeds the amount of prize ($100) in nomination of maximum losing, so as not to lose. What's the reason?

Does it really make sense? fun games to play is identical to that of return on losing. If a stake has won the stake is already in the black. The stake will be awarded a prize of $100 if it loses. So, the math expectancy of the above-mentioned stake amounting to $350 is: $350*0,49-($350-$100)*0,51=$44. We could be losing $250 right now, however we win $350 tomorrow and, over the course of a year playing every day, we'll accumulate pretty $16,000. After completing a simple equation, we'll find out that stakes of up to $1900 can be profitable for us! We need to have several thousand dollars on our accounts for this kind of game, but we can't blame the casinos for being untruthful or inexperienced.

Let's get back to our bonuses. They are among the most "free-loading" bonuses without any deposit. Recently, one has seen an increasing number of ads promising the possibility of up to $500 completely for free, and without any deposit. The pattern is the following You actually receive $500 when you sign up for a specific account with a time limit for playing (usually one hour). After an hour, you will receive just the amount of your gain, but still not greater than $500. The gain is transferred on a real account where you have to get it back as any other bonus, generally after having run it 20 times in slots. $500 for free sounds appealing but what's the real price of the reward? The first thing to consider is requires you to win $500. We can see that the chance of winning $500 is 50% using a simplified formula. In reality, it is much lower. To win the bonus back, you must stake $10 000 on slots. read here of the rate of payouts on slots, however, they are published by casinos and average about 95% (for various kinds they fluctuate about 90-98%). If we play an average slot, at the end of our wager we'll have $500-10 000*0,05=$0 in our account. Not a bad 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 select a slot with the highest payouts is 50% (you have listened to the opinions of other gamblers , since randomly, this chance is less than 10-20%, as there are only a handful of slots with high payouts), in this case the worth of a large deposit-free bonus amount to $300*0,5*0,5=$75. It's less than $500 but not too bad, though we can observe that even with the most optimal suppositions the final value of the bonus has diminished seven times.

I am hoping that this investigation into the maths of bonuses will prove useful to gamblers. If you're looking to win, all you need is to think and do calculations.

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