Notes

Online Casinos: The Mathematics of Bonuses
Online casino players are aware that these casinos offer various bonuses. While "Free-load" might sound appealing, they are not really worth the effort. Are they profitable for gamblers? The answer to this question depends on a variety of factors. The answer to this question is possible using math.

Let's begin with a typical bonus for deposits. You transfer $100 and get another $100. It is possible after you have staked $3000. It is an example of a bonus you receive on the first deposit. The size of the bonus and deposit may be different in addition to the required stake rates, but one thing remains in place - the amount of the bonus is accessible for withdrawal after the required wager. As a rule, it is not possible to withdraw money.

If you plan to play in the online casino for a lengthy duration and with a lot of intensity the bonus can assist you. It can really be considered 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. However, there are some issues to be aware of, for example, if you want to simply take an experience at a casino, without playing for a long period of time and you are a fan of roulette or other gamesthat are which are not permitted by the rules of casinos to win back bonuses. If you aren't betting on any of the allowed games , casinos are unlikely to allow withdrawals. If you're a fan of blackjack or roulette and you can returned only through playing slots, make the required stakes of $3000, in the course of paying out 95% of the time you will lose on average $3000*(1-0,95)=$150. You will are not just losing the bonus, but also have to take out of your account $50, in the case of this, it's better to refuse the bonus. If blackjack and poker are allowed to claim back the bonus and the casino's earnings of only 0,5%, so it is possible that once you have repaid the bonus you will have $100-3000*0,005=$85 of the casino's money.
"Sticky" and "phantombonus


Casinos are becoming more popular for "sticky" and "phantom bonuses. These bonuses are equivalent to lucky chips in real casino. The amount of bonus cannot be withdrawn the bonus, and it will remain in the account (as as if it "has stuck" to it), until it is completely lost, or annulled upon the first withdrawal cash means (disappears like a phantom). It may at first seem that there is little reason to get a bonus - you won't get money anyway, but it's not completely true. It's not worth the cost if you win. However, if you fail, the bonus may be beneficial. Without a bonus , you've lost your $100 , and then you're gone. But with a bonus, even if it is one that is "sticky" one, the $100 are still on your account. This can help you worm out of the problem. The probability of winning the bonus is just half (for this, you'll only have to put the full amount on 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 little stakes, you will gradually and eventually lose because of the negative mathematical expectation in games, and bonuses will only add agony, and won't 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 important to determine the amount you would like to gain, such as $200, and then take the risk 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:

The most common bonus recognized is the possibility of returning money lost funds. It can be distinguished into two variations - the full return of the lost deposit in which case the cash is typically returned as an ordinary bonus or a portion (10-25 percent) of the loss for a fixed time period (a week or a month). In the second case, the situation is practically identical to that of a "sticky" bonus. In the event that you win, there's no point in the bonus, however it is helpful in the event loss. The "sticky bonus" mathematical calculation will be analogous. The strategy of the game is similar: we play and win as often as is possible. We can still bet with the money that we've won, even if we don't succeed. Partial return of the losing for a gambler who is active can be considered to be an unimportant benefit of casinos in games. It is possible to lose an average of $50 playing blackjack with an average math expectation of 0.5 percent. You'll get back $10 if you make a loss of 20 dollars. This is the equivalent of an increase in math expectancy of 0.4%. But, the bonus can also be derived from the fact that you need to be playing less. With the same stakes in roulette, we place one, however it's a large stake. We win $100 in 49% of cases and $100 is won by 51%. We lose $100 in 51% of the cases. When play online finish each month, we get 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 has a positive math expectancy, but dispersion is big for we'll be able to play in this manner very rarely - once a week or even once a month.

Allow me to make a brief remark. I'm a little off-topic. One forum member said that tournaments were unfair. He claimed, "No normal person will ever stake a single stake during the last 10 minutes." This 3,5-fold exceeds the amount of prize ($100) in the nomination of the maximum loss, so as not to lose. What's the issue?"

It makes sense. It's very similar to the variant that involves losing a stake. We're in the black if the stake is won. We'll be awarded a prize in a tournament of $100 if the stake is lost. So, the math expectancy of the above-mentioned stake amounting to $350 is: $350*0,49-($350-$100)*0,51=$44. Yes, we may be losing $250 right now, however we we'll be able to win $350 next day and, over the course of a year playing each day, we'll build up 365*$44=$16 000. After completing a simple equation, we'll discover that stakes of up to $1900 can be profitable for us! Of course, to play such a game we require thousands of dollars on our account however, we shouldn't accuse casinos of dishonesty or gamblers for being foolish.

Let's get back to our bonuses. They are among the most "free-loading" bonuses without any deposit. Recently, one has seen more and more advertisements promising as much as $500 for free, and without deposit. The pattern is the following you actually get $500 when you sign up for a specific account with a time limit for playing (usually one hour). The only thing you will get is the winnings after an hour, but no over $500. You must win the bonus on a regular account. Most often, you've played it at least 20 times on slot machines. $500 free -it sounds attractive but what's the real price of this bonus? Well, the first part - you need to get $500. Using a simplified formula, we will see that the probability of winning is 50 percent (in the real world, it's certainly even smaller). To win the bonus back You must be able to stake at least $10 000 on slots. The payout rates of slot machines aren't well-known. They range from 95 to 95%, and can range from 90-98 percent for various types. If we choose an average slot, then until the end of the wager we'll have $500-10 000*0,05=$0 in our bank account, which is not an excellent game... play free online games can anticipate $500 to 000*0.02=$300 in the event that we are lucky enough to find a high-paying slot. Even though the likelihood to pick a slot that has payouts that are high is 50% (you have heard the opinions of other gamblers , since the random selection of this probability will make up hardly more than 10-20%, for there are a few slots that pay out generously) In this instance, the value of a generous deposit bonus is $300*0.5%*0.5%=$75. While it's less than $500, this is still a good amount. But, we can observe that the bonus's total value has decreased sevenfold, even with the best possible estimates.

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

Website: http://www.kickbackpoker.net/