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Online Casinos: The Mathematics of Bonuses
Online casino players know that the latter ones offer a range of bonuses. While "Free-load" may seem appealing, they're not really worth the effort. Are they profitable for gamblers? Answering this question is contingent on many factors. The answer to this question is possible with mathematics.

Let's begin with an ordinary bonus when you deposit $100 and receive $100 more that it is possible to receive after you have staked $3000. It is an example of a bonus you receive on your first deposit. While the amount of a bonus or deposit may differ, so can the stake rates. However, one thing is sure: the bonus amount is still able to be withdrawn following the wagering requirement has been met. In general, it is not possible to withdraw money.

This bonus can be considered free money when you gamble online for a lengthy period of time and keep playing. 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)=$2000), after that the amount of bonus will be over. There are a few pitfalls. In particular If your intention is to simply have a peek at the casino, without spending too much time there, or you are a fan of roulette or any other games that are prohibited by the bonus rules, then you may not be able to gain access to the bonus. If you do not wager on any of the permissible games, the majority of casinos will not allow withdrawals. Bonuses can be won by playing blackjack or roulette, but only if you make the required 3000 stakes. In the 95% payouts, you'll lose an average of 3000$ (1-0,95) which is $150. The loss is $50 and you also forfeit the bonus. In this instance it's best not to accept the bonus. In any case, if blackjack and poker can be used for winning back the bonus with a casino's profit only about 0,5%, so you can expect that once you have repaid the bonus you will have $100-$3000 plus 0,005 = $85 from the casino's profit.
"sticky" or "phantom" bonus:

A growing amount of popularity in casinos is due to "sticky" or "phantom" bonuses - similar to casino chips that are lucky in real life. It isn't possible to cash out the bonus. The bonus must be kept on the account, like it "has stuck". It might appear as if an offer isn't worthwhile. It isn't possible to take any money out, but this isn't the case. The bonus won't be worth the cost if you win. If you lose, it may prove useful. You've already lost $100 with no bonus. If the bonus was not "sticky" it remains on your account. This could help you to wiggle out of the situation. A possibility to win back the amount of bonus is a bit less than 50% (for you will only have to stake the entire amount on the chances 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 small amounts. The negative math expectancy of games implies that you'll never get any bonus. 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 advised to determine the amount you want to winnings, such as $200, and then try to win it, while taking risk. 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. Two types of bonuses could be distinguished: the complete refund of deposit. In this case, the money is usually to be returned as an ordinary bonus. Or a partial return (10-25 percent) over a time period (a week or a month). In the first case the scenario is essentially identical as with the "sticky" bonus - if we win, there's no reason to get the bonus, but it helps in case of losing. The "sticky bonus" math calculation will also be similar. The strategy of the game is similar: we play to win as frequently as we can. It is possible to gamble with the money we've won, even if we fail to take home the prize. The partial refund of losses gambler could be considered to be an unimportant benefit of casinos in games. You will lose an average of $50 when you play blackjack using an average math expectation of 0.5%. A 20% return 10 cents will be returned to you, which means that the amount the loss you'll suffer is $40, which is comparable to the increase in the math expectation up to 0,4% (ME with return=theoretical ME of the game (1percent of return). You can still derive benefits from the bonus but you'll have to play less. slot game make only one but a high stake, for example $100, with the same stakes in roulette. In 49% of cases again we win $100, and 51% - we lose $100, however at the end of the month we get back our 20%, which is 20 dollars. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. The stake has a positive math expectation. However, dispersion is high and we'll only be able to play in this way for a few times each week or every month.

I will allow myself a short remark, slightly digressing from the main issue. One forum member declared that tournaments weren't fair. He said, "No normal person will ever be able to stake a single stake during the last 10 minutes." The 3,5-fold increase is more than the amount of prize ($100) in the nomination of the maximum loss, so that you won't lose. What's the reason?

And really does it make sense? The scenario is very similar to the variant that involves losing a stake. If a stake has been won it is already in the black. The stake will be awarded a prize of $100 in the event that it is lost. 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 earn $350 tomorrow. Over a year of daily play, our total earnings will be quite amazing at 365*$44 = $16,000. Having solved a simple equation, we'll find out that stakes up to $1900 are profitable for us! We need to have thousands on our accounts for this kind of game, but we don't have to blame casinos for being untruthful or inexperienced.


Let's go back to our bonuses. They are among the most "free-loading" bonuses with no deposit. Recently, one has noticed an increasing number of ads promising the possibility of up to $500 completely for free, and without deposit. You can get $500 on an account that is unique, and you have a time limit to play (usually 1 hour). After an hour, you receive just the amount of your winnings, but no greater than $500. You must win the bonus back on a real account. In most cases, you've played it at least 20 times on slot machines. It sounds great but what's the exact price of the bonus? The first thing to consider is - you need to win $500. We can determine that the probability of winning $500 is 50% based on an easy formula. But in reality, it's much lower. In order to receive the bonus and you have to bet $10 000 in slots. The payout rates of slot machines aren't known. They average around 95%, and can range from 90-98 percent for various types. If we get at an average slot, until the end of the wager we'll have $500-10 000*0,05=$0 on our account, not a bad game... If we are lucky to select a slot that has payouts that are high, we could expect to win $500-10 000*0.02=$300. Even though the likelihood to select a slot with high pay-outs is 50 percent (you are probably familiar with the opinions of other gamblers since the random selection of this probability will make up hardly more than 10-20%, for there are only a handful of slots with high payouts) in this scenario, the worth of a large deposit-free bonus amount to $300*0.5%*0.5%=$75. While it's less than $500, it's still a good amount. However, we are able to find that the bonus's final value has dropped sevenfold even with the most accurate estimations.

I'm hoping this look into the mathematical realm of bonuses can prove beneficial for gamblers. If you want to be successful, all you need is to think and do calculations.

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