# Online Casinos: Mathematics of Bonuses

Casino players who play online know that the casinos offer a variety of bonuses. “Free-load” appears attractive but do they actually provide these bonuses? Can they be profitable to gamblers? The solution to the question is contingent on many factors. Mathematical calculations can help us answer this question.

Let’s start with a typical bonus when you deposit \$100 and receive \$100 more that it is possible to obtain after having placed a bet of \$3000. This is an example of a bonus that is credited to the initial deposit. The size of the bonus and deposit can differ and so can the stakes that are required however one thing is indefinite the amount of bonus – the sum that the bonus is available to withdraw after the necessary wager. At present, it’s impossible to withdraw funds, in general.

If you plan to be playing in the casinos online for a prolonged period and with a lot of determination the bonus can 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. However, there are some issues to be aware of such as if you just want to take an experience at a casino and not play for long periods of time or if you like roulette or other gamesthat are which are not permitted by the rules of casinos to win back bonuses. Visit:- https://www.vuabai99.com/

In the majority of casinos , you will not be permitted to withdraw funds or will return deposits when a bet is not placed on the games that are allowed at the casino. If you’re a fan of blackjack or roulette, and you can earned only by playing slot machines, you must make the necessary wager of \$3000 and in the case of 95% payouts, you’ll lose an average of \$3000*(1-0,95)=\$150. You will do not just lose the bonus, but also take from your pockets \$50, so in this instance it is best to decline the bonus. In any case, if blackjack and poker are permitted to win back the bonus, with the casino’s profits of just 0.5%, it is possible that once you have repaid the bonus, you’ll have \$100-\$3000 plus 0,005 = \$85 of the casino’s winnings.
“sticky” as well as “phantom” bonus:

The popularity of casinos is derived from “sticky” as well as “phantom” bonuses, which are the equivalent to luck chips in real casinos. The amount of the bonus cannot be withdrawn and must stay in the account (as as if it “has been glued” on it) until it’s totally lost or canceled upon the first cash withdrawal is (disappears as if it were it’s a phantom). It may at first appear that there is no value in an offer – you’ll never receive any money however this isn’t accurate. If you win, there’s no reason to the bonus, however even if you lose the money, it could be useful to you. If you don’t have a bonus, you’ve lost \$100, and that’s goodbye. However, with a bonus even if it’s one that is “sticky” bonus, the \$100 remain on your account, which could aid you in escaping the circumstance. The chance of winning back the bonus in this case is less than 50 percent (for that you’ll only have to bet the whole amount on the odds of roulette). In order to maximize profits from “sticky” bonuses one needs to use the strategy “play-an-all-or-nothing game”. If you only play small stakes, you’ll eventually lose money due to the negative math expectation in games as well as the bonus is only going to prolong your the pain, and will not help 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. It is suggested to set the desired amount you want to winnings, such as \$200, and then try to win itby 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).

The Cash Back Bonus:

It is not often seen variation of a bonus which is the return of lost. It is possible to distinguish two options – the full return of the lost deposit, and at this point the return of the money is usually to be redeemed as in a normal bonus or a return of a portion (10-25 percent) of the loss over the time period (a week or a month). In the first scenario the scenario is similar to the scenario that you receive the “sticky” bonus. If we win, there’s no need for the bonus, however it can be helpful in the event loss. Calculations in math will also be similar with the “sticky” bonuses, and the strategy for the game is the same – we take risks, and try to win as many times as we can. If we don’t win and lose the game, we can continue to play with the assistance of the return money, thus decreasing the risk. A partial return of the loss for an active gambler is an unimportant benefit of casinos when playing games. If you are playing blackjack with math expectancy of 0,5%, then after you have staked \$10,000, you’ll lose an average of \$50. If you earn 20% of the money, the amount of \$10 is returned to you, which means that the amount your loss will be \$40, which is equal to the rise in math expectation of up to 0,4% (ME with return = theoretical ME of the game* (1- % of return). But, from the offered bonus, there could be gained benefit, in that you will need to play less. There is only one bet, but an extremely high stake such as \$100 on the same roulette stakes. In the majority of the cases we also win \$100 and 51% of the time we lose \$100, however at the close of the month, we receive the 20%, which is \$20. As a result the effect is \$100*0,49-(\$100-\$20)*0,51=\$8,2. It is evident that the stake has a positive math expectation, however the it’s a big dispersion, as it to be played this way only every week, or every month.

I’ll allow myself to make a brief remark, but slight deviation from the principal topic. In a forum for casinos, one of the gamblers began to argue that tournaments are not fair and argued it in the following manner: “No normal person will ever be able to make a single wager in the final 10-minutes of the tournament, and it is 3,5-fold exceeds the prize money (\$100) and in the event of a maximum loss, in order to be able to win. What’s the purpose?”

Does it really make sense? The scenario is quite like the version with the return of losing. If a stake is successful it is already on the black. 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’ll be able to win \$350 next day, and in a year of playing every day, we’ll earn \$16,000. After completing a simple equation, we’ll discover that stakes as high as \$1900 can be profitable for us! Of course, to play this kind of game, we’ll must have thousands of dollars in our accounts however, we shouldn’t accuse casinos of dishonesty or gamblers for being naive.