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Online Casinos: The Mathematical Basis of Bonuses
Online casino players are aware that the latter ones offer a range of bonuses. "Free-load" looks visit the site , however, do they actually provide are they really worth it? 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 look at an everyday bonus upon deposit: you make $100 and obtain $100 more and it's possible to receive after you have put up $3000. This is a common example of a bonus earned for the first deposit. While the amount of a bonus or deposit may differ and so do the stake rates. But there is one thing that is for certain: the bonus amount is still able to be withdrawn following the wagering requirement has been met. As a rule, it is impossible to withdraw any funds.

If you plan to play in the online casino for a long 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. There are a few pitfalls, for example, if you just want to take the chance to play at a casino, without playing for a long period of time or if you like roulette or other gamesthat are prohibited by casino rules for winning back bonus. If you do not wager on any of the allowed games, most casinos won't allow withdrawals. If you're keen on blackjack or roulette and a bonus can be earned only by playing slots, place the required stakes of $3000 during the 95% payouts, you'll lose an average of $3000*(1-0,95)=$150. As you see, you do not just lose the bonus, but will also be able to take from your account $50, in this scenario, it's best to decline the bonus. If blackjack or poker can win back the bonus, with a profit of 0.5 percent, it's possible to expect that you'll receive $100-3000*0,005=$85 after you have won back the bonus.
"Sticky" and "phantom" bonuses


More and more popularity in casinos is gained by "sticky" or "phantom" bonuses, which are equivalent to lucky chips in real casinos. It is not possible to cash out the bonus. The bonus has to be kept on the account, like it "has stuck". It may appear that such bonuses are not worthwhile. You will not be able to withdraw any money, but it's not the case. If you win, then there is really no point to the bonus. However, if you have lost, it may be useful to you. Without a bonus you have lost your $100 and then you're gone. Even if the bonus was not "sticky" the $100 will still be on your account. This can help you get out of the situation. The chance of winning back the amount of bonus is around 50 percent (for you will only have to stake the entire amount on the chance of winning in roulette). In business 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 eventually lose money because of the negative mathematical expectations in games. Moreover, the bonus is likely to prolong the pain, and will not help you gain. 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 wish to gain, such as $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:

It is a rare variant of a bonus, specifically, the return of a lost deposit. Two types of bonuses could be distinguished from the total return of the deposit. best games is generally returned as an ordinary bonus. Or a partial return (10-25 percent) over a time period (a month or a week). The first scenario is nearly similar to a "sticky bonus" - the bonus is not worth it if you win however, it is beneficial when you lose. Math calculations will be also similar to "sticky" bonus, and the strategy of the game is the same: we take risks trying to win as much as possible. If we don't win and we have lost then we are able to play again using that money back, thus decreasing the risk. Casinos that offer games may provide some kind of compensation for losses to gamblers who have a high level of activity. If you are playing blackjack with math expectancy - 0,5%,, having made stakes on $10 000, you will lose an average of $50. The payout is $10 when you make a loss of 20 dollars. This is equivalent to an increase in math expectancy of 0.4%. However, from the given bonus you will also get benefits, which means you'll need to play less. We make only one but very high stake, for example $100, on the same stakes in roulette. We can win $100 in 49% of cases however $100 is taken home by 51% of players. However, we lose $100 in 51% of instances. When we finish every month, we receive back 20% of our $20 winnings. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. The stake has a positive mathematical expectancy. However, dispersion is huge and we'll only be able to play in this manner once per week or once per month.

Let me provide a short remark. I'm a little off-topic. One of the forum members claimed that tournaments weren't fair. He stated, "No normal person will ever put a stake in in the final 10 minutes." This 3,5-fold exceeds the prize amount ($100) in nomination of maximum losing, so that you won't lose. What's the purpose?

And really does it make sense? The scenario is very similar to the variant with return of losing. The stake is in the black if a stake is won. 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. We could lose $250 today but earn $350 in the future. In the course of a year of playing each day, our total earnings are quite amazing at 365*$44 = $16,000. After completing a simple equation, we'll discover that stakes up to $1900 can be profitable for us! We need to have several thousand dollars on our accounts for this game, however we can't blame the casinos for being untruthful or inexperienced.

Let's revisit our bonuses, specifically the best "free-load" ones- 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 , with no cost and without deposit. You can get $500 on an account with a specific number of players, as well as only a certain amount of time to play (usually one hour). The only thing you will get is the amount of your win after an hour, but no more than $500. The money is transferred to an actual account, where you have to be able to win it back, just like any other bonus, typically after having played it at least 20 times on slots. $500 free -it sounds attractive, but what is the actual value of the reward? The first thing to consider is requires you to get $500. We can see that the chance of winning $500 is 50% based on an easy formula. But in reality, it is much lower. To win the bonus back it is necessary to bet at least $10 000 in slots. We do not know the percentages of pay-outs from slots, they are not released by casinos and are approximately 95% (for diverse types, they fluctuate about 90-98%). If we get at an average slot, till the end of the wager we'll have $500-10 000*0,05=$0 on our account, not an excellent game... If we are lucky to choose a slot with payouts that are high, we could await $500-10 000*0,02=$300. The probability of choosing one with the highest payout is 50%. You've read the comments of other gamblers that this probability is not more than 10-20 percent. In this case the deposit bonus is generous of $300*0.5*0.5=$75. A lot less than $500 however, it's still not poor, although we can observe that even with the most ideal suppositions, that the total amount of the bonus has been reduced by seven times.

I'm sure this trip into the maths of bonus will prove of use for gamblers. If you are looking to win, you just have to think about it and do some calculations.

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