Notes

Online Casinos: The Mathematics of Bonuses
Online casino players know that these casinos provide a variety of bonuses. "Free-load" is attractive, however, do they actually provide these bonuses? Are they profitable for gamblers? This question is dependent on a variety of factors. Mathematics will assist us in answering this question.

Let's begin with a typical bonus on deposit. You transfer $100 and get another $100. It is possible after you stake $3000. It is an example of a bonus that you can get on the first deposit. While the amount of a bonus or deposit can vary, so can the stake rate. But one thing is sure: the bonus can be taken out after the wagering requirement has been met. As a rule, it is impossible to withdraw any funds.

If you intend to play in the online casino for a long time and rather insistently the bonus can 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. But there can be complications such as if you want to simply take the chance to play at a casino, but not having to play for long, if you prefer roulette or other gamesthat are prohibited by casino rules for winning back bonus. If you don't wager in any of the permissible games, most casinos won't let you withdraw cash. There is a chance to win a bonus by playing blackjack or roulette however, only if have the required stakes of 3000. In the 95% of payouts, you'll lose an average of $3000* (1-0,95) = $150. In other words, you not only lose the bonus, but also have to take out of your account $50, in this scenario, it's best to not accept the bonus. If poker or blackjack will be able to recoup the bonus, with a profit of 0.5%, it is possible to expect that you will get $100-3000*0,005=$85 after you've earned back the bonus.
"Sticky" and "phantom" bonuses

A growing amount of popularity in casinos is due to "sticky" or "phantom" bonuses - the equivalent of lucky chips in real casinos. The bonus amount cannot be taken out the bonus, and it will remain in the account (as if it "has stuck" to it) until it's entirely lost or is canceled on the first withdrawal of cash (disappears like it's a phantom). It might appear as if bonuses are not worthwhile. You will not be able to withdraw any money, however it's not the case. The bonus won't be worth it if you are successful. However, if you fail, the bonus might be beneficial. Without a bonus , you've lost your $100 , and then you're gone. With a bonus, even if it is a "sticky" one, you will find that $100 are still in your account, which can help you worm out of the situation. There is a chance to win back the bonus in this case is less than 50% (for you will only have to bet the whole 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". In reality, if you are playing with small stakes, you'll eventually lose money because of the negative mathematical expectation in games, and bonuses will only add agony, and won't help you to win. our website 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 of your gain, for example $200, and try to win it by 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:

One bonus that is seldom noticed is the return of the money that was lost. Two types of bonuses could be distinguished: the full refund of deposit. At this point the deposit is generally returned just as an ordinary bonus. A partial return (10-25 percent) for a set period (a week or a month). The first scenario is nearly the same as the "sticky bonus" - the bonus will not be worth anything if you win, but helps if you lose. In the second case, the "sticky bonus" calculation of math will be similar. The principle of the game is the same - we gamble, win as often as possible. It is possible to play with the money you've earned even if we don't take home the prize. A partial return on the loss for a gambler who is active can be seen as a minor benefit of casinos in games. If you are playing blackjack with math expectancy of 0,5%, then, having made stakes on $10 000, you will lose an average of $50. A 20% return $10 will be given back to you, which means that the amount the loss you'll suffer is 40 dollars, which is equivalent to the growth in math expectancy to 0,4% (ME with return=theoretical ME the game * (1percent of return). However, from games news given bonus, you can also gain benefits, which means you'll need to play less. On the same stakes as in roulette, we make one, however it's an enormous stake. We can win $100 in 49% of instances, while $100 is taken home by 51% of players. But, we have to lose $100 in 51% of the cases. When we finish each month, we earn back 20% of our $20 winnings. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. The stake is positive in math probability. But, the dispersion is huge and we'll only be able play in this manner once per week or once per month.

Allow me to provide a short remark. I'm a little off-topic. On a casino forum one gambler began to assert that tournaments were unfair, and argued it in the following way: "No normal person will ever make a single stake within the final 10 minutes of the tournament, which 3,5-fold surpasses the prize amount ($100) as a result of a maximum loss, so that they can win. What's the point?

It makes sense. The scenario is very similar to the variant with return of losing. If a stake has won - we are already in the black. If site here 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. Sure, we could lose $250 today but earn $350 tomorrow. If we continue daily play and earning a total of 365, our earnings are quite amazing at 365*$44 = $16,000. If we can solve a basic equation, we'll discover that stakes as high as $1900 can be profitable for us! Of course, to play such a game we must have many thousands of dollars in our accounts however, we shouldn't accuse casinos of dishonesty or gamblers who are foolish.

Let's come back to our bonus offers, especially the best "free-load" ones, without any deposit. One has noticed an increase in ads offering $500 for free, with no deposit. You get $500 for a special account, and you have a time limit to play (usually 1 hour). You will only get the amount of your win after an hour, but not over $500. The cash is transferred to an actual account, where you have to get it back as any other bonus, typically after having played it at least 20 times on slots. This sounds fantastic but what's the exact value of the bonus? The first part is that you need to be able to win $500. We can see that the chance of winning $500 is 50% based on an easy formula. However, in practice it is much lower. The second part - we get the bonus back You must bet at least $10 000 on slots. The pay-out rates in slot machines are not known. They are generally around 95%, and can range from 90-98% for different types. A typical slot can give us between $500 and 000*0.05=$0. That's not a bad amount. It is possible to expect $500-10 000*0.02=$300 if we're lucky enough to find a high-paying slot. The likelihood of picking the slot that has the highest payout is 50 percent. You've heard the comments of other gamblers that this probability is not more than 10-20 percent. In this case, the generous deposit bonus of $300*0.5*0.5=$75. It's less than $500 but not too poor, although we can find that even with most optimal suppositions the final value of the bonus has been reduced by seven times.

I hope this exploration into the mathematical realm of bonuses will be useful for gamblers. If you want to win, all you need is to think and do calculations.


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