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Online Casinos: The Mathematics of Bonuses
free games to play now know that these casinos offer various bonuses. Although "Free-load" might seem appealing, they are not worth the effort. Are they profitable for gamblers? This question is dependent on many different factors. Mathematics will help us answer this question.


Let's start with a normal bonus on deposit. You deposit $100 and get another $100. This is feasible after you stake 3000. It is a typical instance of a bonus on the first deposit. Although the size of a bonus or deposit may differ and so do the stake rates. However, one thing is certain: the bonus amount can be taken out after the wagering requirement has been met. It generally is impossible to withdraw money.

If you are going to play in the online casino for a lengthy period of time, and you are persistent about it, this bonus will help you, it can be considered to be 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 some complications. For instance If your intention is to just take a peek at the casino, without spending too much time there, or if you are a fan of roulette or any other games that are not permitted under bonus rules, you could be denied access to the bonus amount. In most casinos, you will not be able to withdraw money or will simply return a deposit, if a wager is not placed on the games that are allowed in the casino. If you're a fan of blackjack or roulette and a bonus is won back only by playing slots, place the required $3000 of stakes, in the course of 95% of pay-outs you'll lose an average of $3000*(1-0,95)=$150. You will lose $50, and lose the bonus. In this scenario it's better not to accept the bonus. Anyway, if blackjack and poker are allowed to claim back the bonus, with a casino's earnings of only 0.5%, it is possible that once you have repaid the bonus, you'll be left with $100-$3000 plus 0,005 = $85 from the casino's profit.
"Sticky" and "phantom” bonuses

play games for money are increasingly gaining traction for "sticky" and "phantom bonuses. These bonuses are equivalent of lucky chips in a real casinos. The bonus amount is impossible to withdraw, it must remain in the account (as when it "has been glued" to it), until it is entirely lost or is canceled upon the first withdrawal cash (disappears like it's a phantom). On first glance, it might appear as if there's no value in an offer - you'll never be able to withdraw money at all however this isn't accurate. If you win, there's no reason to the bonus. However, in the event that you lose the money, it could be useful to you. You've already lost $100 with no bonus. Even if the bonus is not "sticky" it will still be on your account. This can help you to wiggle out of this situation. The chance of winning back the amount you received is less than half (for this, you'll have to put the full amount of the bonus in roulette). In order to maximize profits from "sticky" bonuses one needs to use the strategy "play-an-all-or-nothing game". You'll lose slowly and surely if you stake tiny amounts. The negative math expectation of games means that you will not receive any bonuses. more info here 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 desired amount you wish to gain, for example $200, and attempt to win it, 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 not often seen variant of a bonus, namely return of losing. It can be distinguished into two options - either the complete refund of the deposit lost, at this the returned money usually is to be paid back as with an ordinary bonus, or a partial return (10-25%) of the amount lost for a fixed time period (a week, a month). In the first case the scenario is essentially identical to the case with the "sticky" bonus - if you win, there's no need for the bonus, however it can be helpful in the event of losing. In the second case, the "sticky bonus" calculation of math will be comparable. The strategy of the game is similar: we play to win as frequently as we can. If we don't win and lose the game, we can continue to play using this money, thus decreasing the risk. Casinos with games offer some kind of compensation for losses for active gamblers. You'll lose $50 on average when you play blackjack using an average math expectation of 0.5 percent. With 20% of return $10 will be given back to you. That means you losing will amount to $40, which is equivalent to the growth in the math expectation up to 0,4% (ME with return=theoretical ME of the game (1-% of return). But, from the bonus you will also get from the fact that you need to play less. In the same way as on roulette, we play one, but it is an enormous stake. In 49% of instances, we again win $100, and 51% - we lose $100, but at the close of the month, we receive our 20%, which is 20 dollars. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. The stake then has positive math expectation, however the it's a big dispersion, as we'll be able to play in this manner very rarely - every week, or every month.

I'll let myself make an unintentional remark that is slight deviation from the main issue. In a forum about casinos, one of the gamblers 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, which 3,5-fold surpasses the prize ($100), in nomination of a maximum loss, in order to take home a prize. What's the point?

It makes sense. The situation is like the one that has the return of losing. If a stake is successful it is already in the black. If it has 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. Yes, we might lose $250 today, but we will win $350 in the future. Over a year of daily play, our total earnings are quite impressive , at 365*$44=$16000. After completing a simple equation, we'll discover that stakes up to $1900 can be profitable for us! Of course, in order to win at such a game , we'll need to have hundreds of dollars in our account and we can't accuse casinos of dishonesty or gamblers who are foolish.

Let's come back to our bonuses, specifically the best "free-load" ones, without any deposit. Of over here has been able to notice more and more advertisements promising as much as $500 free of charge, without any deposit. The way to look at it is this - you really get $500 with a separate account, and a limited amount of time to playing (usually one hour). After an hour you get just the amount of your winnings, but no more than $500. The gain is transferred on an actual account and you must win it back, like any other bonus, typically after having played it at least 20 times through slot machines. $500 free -it sounds attractive however, what is the real price of the reward? Well, the first part is that you must win $500. Using a simplified formula, we can see that the probability of winning is 50% (in practice, it is likely to be even lower). The second part - we win the bonus back You must bet $10 000 in slots. We don't know the rates of payouts on slot machines, but they are provided by casinos, and average about 95% (for different types they vary 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 pick a slot with high pay-outs, we can expect to win $500-10 000*0.02=$300. Even though the probability to choose a slot with high pay-outs is 50 percent (you have listened to the comments of other gamblers as the random selection of this probability will be less than 10-20%, as there are few generous slots) In this instance, the worth of a large deposit free bonus amounts to $300*0,5*0.5%=$75. It's less than $500 but not too bad, though we can find that even with most ideal suppositions, the final value of the bonus diminished seven times.

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

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