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Online Casinos: The Mathematical Logic of Bonuses
Casino players who play online know that these casinos provide a variety of bonuses. Although "Free-load" might sound appealing, they are not really worthwhile. Are they worth the money for gamblers? The answer to this question depends on a variety of factors. Mathematical calculations can assist us in answering this question.

Let's begin with a typical bonus on deposit. read more deposit $100 and get $100 more. This is feasible after you stake 3000. This is an example of a bonus that you can get on the first deposit. The size of the bonus and deposit can be different in addition to the required stake rates, but one thing remains unchangeable : the amount of the bonus can be withdrawn following the wager requirement. At present, it's impossible to withdraw money generally.

If you plan to play in the online casino for a long time and rather insistently, this bonus will help you, it can be considered as 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)=$2000), after that the amount of bonus will be over. There are a few pitfalls. For instance, if your goal is to just take an overview of the casino, without spending a lot of time in there, or you like roulette or other games that are not permitted by the bonus rules, then you may not be able to gain access to the bonus amount. In the majority of casinos you won't be allowed to withdraw money or will simply refund a deposit when a wager isn't made on the games allowed in the casino. You can win a bonus when playing roulette or blackjack, but only if you meet the minimum stakes of 3000. If you're lucky enough to win 95% payouts that you'll lose an average of 3000$ (1-0,95) which is $150. In other words, you not only lose the bonus, but will also be able to take from your account $50, in the case of this, it's better to decline the bonus. If you could win back the bonus with a casino profit of 0.5 percent, it's likely that you will get $100-3000*0,005=$85 after you have won back the bonus.
"Sticky" as well as "phantombonus

More and more popularity in casinos is due to "sticky" or "phantom" bonuses - similar to casino chips that are lucky in real life. It is not possible to withdraw the bonus amount. The bonus amount must be stored on the account like it "has stuck". It could appear that a bonus is not worth the effort. It isn't possible to withdraw any money, but it's not the case. The bonus won't be worth it if you win. If you lose, it might prove useful. You have already lost $100 with no bonus. Even if the bonus is not "sticky" the $100 will still be on your account. This will allow you to wiggle out of this situation. The chance of winning back the bonus is less than half (for this you will only have to bet the entire amount in 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 low stakes, you'll slowly and surely lose because of the negative math expectancy in games, and the bonus is likely to prolong suffering, and won't aid 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 recommended to fix the amount you want to profit, for instance $200, and attempt to win it by taking risks. 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 variant of a bonus, specifically, the return of a lost deposit. Two types of bonuses could be distinguished: the full return of the deposit. In this case, the money is usually to be returned just as an normal bonus. Or a partial return (10-25 percent) over a fixed period (a week or a month). In the second case, the situation is practically identical to that of a "sticky" bonus - if we win, there is no reason to get the bonus, however, it is helpful in the event of loss. Math calculations are similar to "sticky" bonus, and the strategy is similar - we risk trying to win as many times as possible. If we do not win and lose then we are able to play again with the the returned money, already minimizing the risk. The partial refund of losses for an active gambler can be regarded as an insignificant benefit of casinos in games. If you are playing blackjack with math expectancy of 0,5%, when you stake your stakes on $10 000, you will lose an average of $50. A 20% return the amount of $10 is returned to you. That means the loss you'll suffer is $40, which is equivalent to the increase in math expectancy to 0,4 percent (ME with return=theoretical ME of the game (1percent of return). However, from the given bonus can also be derived benefits, which means you'll need to play less. You only make one, however very high stake, for example $100, with the same bets on roulette. The majority of the cases we again win $100, and 51% - we lose $100, however at the end of the month we get back our 20% that is $20. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. As you see, the stake has a positive math probability, but the its dispersion is huge, since it to be played this way rather seldom - at least once per week or once a month.

I'll allow myself an unintentional remark that is slightly digressing from the main topic. In a forum about casinos, one gambler began to assert that tournaments were unfair, and argued it in the following way: "No normal person will ever be able to make a single wager in the final 10 minutes of the event and this is 3,5-fold more than the prize amount ($100) as a result of a maximum loss, so as to be able to win. What is the point?"

It makes sense. The situation is very similar to the variant that involves losing a stake. If a stake has won the stake is already in the black. If it is lost, we'll be awarded a prize in a tournament of $100. So, the math expectancy of the above-mentioned stake amounting to $350 is: $350*0,49-($350-$100)*0,51=$44. Sure, we could lose $250 today, but we will win $350 in the future. In the course of a year of daily play, our total earnings will be pretty amazing at 365*$44 = $16,000. It's clear that stakes of up to $1900 could be profitable after solving the simplest equation. We'll need thousands on our accounts for this game, but we don't have to blame casinos for being untruthful or inexperienced.

Let's go back to our bonuses. They're the top "free-loading" bonuses with no deposit. In recent times, we've been able to notice more and more advertisements promising up to $500 absolutely for free, and with no deposit. The basic idea is as follows you actually get $500 on a special account, and a limited amount of time to playing (usually one hour). After an hour you get just the amount of your gains, but not more than $500. The gain is transferred on an actual account, where you are required to be able to win it back, just like any other bonus, generally after having played it at least 20 times on slot machines. $500 free -it sounds attractive however, what is the actual value of the reward? First, let's look at the first step - you need to get $500. By using a simple formula, we will see the odds of winning are 50 percent (in the real world, it's definitely lower). To win the bonus back, you must stake at least $10 000 in slots. The payout rates of slot machines aren't known. They range from 95 to 95%, and can range from 90-98% for different types. The average slot gives us $500-10 000*0.05=$0. That's not an awful amount. If we happen to select a slot that has high pay-outs, we can await $500-10 000*0,02=$300. The likelihood of picking a slot with high payouts is 50 percent. You've read the opinions of other gamblers as this probability is not more than 10-20 percent. In this instance, the generous deposit bonus of $300*0.5*0.5=$75. A lot less than $500 however, it's still not bad, even though we see that even with the most optimal suppositions the final value of the bonus decreased seven-fold.

I'm hoping that this journey into mathematics domain of bonus will prove helpful for gamblers. If you're looking to be successful, you only must think about it and do some calculations.

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