Notes

Online Casinos: The Mathematics of Bonuses
Online casino players are well aware that these bonuses are available at many casinos. While "Free-load" might sound attractive, they're not worth the effort. Are they lucrative for gamblers Answering this question depends on a variety of factors. Mathematical calculations can help us answer this question.

Let's begin with the typical bonus for deposits. You deposit $100 and get $100 more. It is possible after you have staked $3000. It is an example of a bonus on your first deposit. Although the size of a bonus or deposit can vary as well as the stake rate. However, one thing is certain: the bonus can be taken out after the wagering requirement has been met. Till this moment it is impossible to withdraw cash generally.

If you plan 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 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)=$2000), after that the amount of bonus will be over. There are some complications. In particular when your objective is simply to take an overview of the casino without spending too much time there, or you are a fan of roulette or any other games that are not permitted under bonus rules, you could be denied access to the bonus amount. In player games will not be able to withdraw cash or simply refund a deposit when a wager isn't made on the games allowed at the casino. Bonuses can be won when you play roulette or blackjack, but only if you make the required 3000 stakes. If you're lucky enough to win 95% of all payouts, you'll lose an average of 3000$ (1-0,95) which is $150. In other words, you are not just losing the bonus, but also have to take out of your wallet $50. In the case of this, it's better to refuse the bonus. If poker or blackjack will be able to recoup the bonus, with a profit of 0.5%, it is possible that you'll get between $100 and $3000, which is equal to $85 after you've redeemed the bonus.
"sticky" or "phantom" benefits:

The popularity of casinos is derived from "sticky" or "phantom" bonuses - the equivalent of lucky chips in real casinos. It isn't possible to cash out the bonus. The bonus has to be placed on the account as if it "has stuck". At first sight it may seem that there is little sense in such a bonus - you won't get money anyway, but it's not completely accurate. If you win, then there is really no point in the bonus, but if you have lost it might help you. You've already lost $100, without a bonus. But with a bonus, even if it's an "sticky" one, $100 are still in your account. This can help you worm out of the problem. The chance of winning back the bonus is less than half (for this, you'll 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 eventually lose money because of the negative mathematical expectancy in games, and bonuses will only add suffering, and won't aid you to 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. Set the amount you would like to gain, such as $200, and take risks to make 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:

There is a seldom encountered variation of a bonus which is the return of lost. It is possible to distinguish two options - either the complete return of the deposit that was lost and the money usually is to be returned as an ordinary bonus or a part return (10-25 percentage) of the losing for a fixed time period (a week or month). In the first scenario, the scenario is essentially identical as with the "sticky" bonus - if we win, there is no need for the bonus, however it helps in case loss. Math calculations are identical to "sticky" bonus, and the strategy is similar - we risk and try to win as much as possible. You can play with the money we've earned, even if we don't succeed. Casinos in games can offer an opportunity to earn a portion of the loss for active gamblers. If you are playing blackjack with math expectancy - 0,5%, after you have staked $10 000, you will lose on average $50. You will receive $10 back if you make a loss of 20 dollars. This is equal to an increase in math expectancy of 0.4%. It is possible to still benefit from the bonus, but you'll have to play less. You only make one, however an extremely high stake, such as $100, with the same stakes in roulette. In 49% of cases we again win $100, and 51% of the time we lose $100, but at the close of the month, we receive our 20% that is $20. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. The stake has a positive mathematical expectation. The dispersion however is large and we will only be able play in this way for a few times each week or every month.

I'll let myself make a short remark, slightly digressing from the main issue. In a forum for casinos, one of the gamblers began to assert that tournaments were unfair. They argued in the following way: "No normal person will ever be able to make a single wager within the final 10 minutes of the tournament, which 3,5-fold surpasses the prize amount ($100), in nomination of a maximal losing, in order to win. What's the reason?

Does it really make sense? The scenario is identical to the scenario with return of losing. We are in the black when a stake is taken home. If it loses - 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. We could lose $250 today, but we will win $350 in the future. Over a year of daily play, our total earnings will be quite impressive , at 365*$44=$16000. Having solved a simple calculation, we'll see that stakes as high as $1900 can be profitable for us! Of course, in order to win at such a game we need to have many thousands of dollars in our accounts and we can't be blamed for dishonesty by casinos or gamblers for being foolish.


Let's go back to our bonuses. They're the top "free-loading" bonuses with no deposit. One has noticed an increase in ads offering $500 at no cost with no deposit. The pattern is the following You actually receive $500 when you sign up for a specific account and limited time for playing (usually an hour). After an hour you get only the amount of your gains, but not greater than $500. The money is transferred to an actual account, where you are required to win it back, 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 this bonus? Well, the first part requires you to get $500. We can see that the chance of winning $500 is 50% using a simplified formula. But in reality, it's much lower. The second part - we win the bonus back and you have to bet $10 000 in slots. The pay-out rates in slot machines aren't known. They average around 95%, but can vary between 90-98 percent for various types. If we choose an average slot, then till the end of the bet, we'll have $500-10 000*0.05=$0 on our account, not an awful game... You can anticipate $500 to 000*0.02=$300 If we're fortunate enough to find a high-paying slot. Although site web to select a slot with the highest payouts is 50 percent (you have heard the opinions of other gamblers since the random selection of this probability will be less than 10-20%, as there are a few slots that pay out generously) in this scenario, the value of a huge deposit free bonus amounts to $300*0,5*0.5%=$75. It's less than $500 but still not too bad, though we can observe that even with the most optimal suppositions that the total value of the bonus diminished seven times.

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

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