Notes

Online Casinos: Mathematics of Bonuses
Players of online casinos know that they offer a variety of bonuses. "Free-load" looks attractive, but do they actually provide these bonuses? Are they profitable for gamblers? This is a question that depends on a myriad of aspects. Mathematical calculations can help us answer this question.

Begin with a standard bonus: You deposit $100 and receive $100 more. You can get this bonus by wagering $3000. This is a common example of a bonus for the first deposit. Although the size of the bonus and deposit will vary, so too will the stake requirement however, one thing remains constant the bonus amount can be withdrawn after the wagering requirement is fulfilled. It is currently impossible to withdraw cash, as a rule.

If go to the website intend to play in the online casino for a long time and rather insistently, this bonus will aid you, and it could 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. There are a few pitfalls, for example, if you simply want to have an experience at a casino, without playing for a long time or if you like roulette or any other game, prohibited by casino rules for winning back bonuses. In the majority of casinos you won't be allowed to withdraw cash or simply return a deposit, in the event that a bet isn't placed on the games that are allowed at the casino. In the event that you prefer roulette or blackjack and the bonus is only available through slot machines, you must make the required stakes of $3000. If the payout percentage is 95%, then when it's made, you will lose the average of $3000*(1-0.95)=$150. You will not only lose your bonus, but also be required to pay $50 out of your pockets. If this is the case it's recommended to turn down the bonus. Anyway, if blackjack and poker are permitted to return the bonus and an average of 0,5%, then you can expect that if you win back the bonus you'll be left with $100-3000*0,005=$85 of the casino's money.
Bonuses that are "sticky" and "phantoms":

More and more popularity in casinos is attributed to "sticky" or "phantom" bonuses - the equivalent of lucky chips in real casinos. The bonus amount cannot be taken out and must stay in the account (as if it "has been glued" to it) until it's completely lost, or annulled after the first time you withdraw cash (disappears as if it's an illusion). At first sight it may seem like there's no reason to get bonuses - you don't be able to withdraw money at all but that's not entirely correct. If you are a winner, there's really no use in the bonus, however if you have lost the money, it could be useful to you. Without a bonus you have lost your $100 and that's it. play games app -bye. However, with a bonus even if it's a "sticky" one, the $100 remain on your account, which could assist you in getting out of the situation. In this situation the odds of winning the money back is less than 50%. (For this, you'll have to wager the whole amount at 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 at small stakes, you'll lose quickly and steadily since the math of games is negative. The bonus won't help you 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 amount you wish to winnings, such as $200, and then try to win it, taking risks. 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:

Return of Loss is a very rare type of casino bonus. There are two variants - the complete return of the lost deposit in which case the cash is usually paid back as with an ordinary bonus, or a fractional return (10-25 percentage) of the loss during the specified time (a week or month). In the second case, the situation is practically identical to the case with the "sticky" bonus. If we win, there's no need for the bonus, however it can be helpful in the event of losing. The math calculations are similar to a "sticky" Bonus, and the strategy is similar - we attempt to win the most money possible. If play games on zoom are not lucky and we lose then we are able to play again with the that money back, taking the risk to a minimum. The partial refund of losses for a gambler who is active could be considered to be an unimportant benefit of casinos when playing games. If you play blackjack with math expectancy - 0,5%, then, having made stakes on 10 000 dollars, you'll lose $50 on average. You'll get 10 dollars back if you earn 20 percent return. That means you will lose 40 dollars. The math expectancy increases to 0,4 percent. This isn't the sole benefit. There is also benefits by playing smaller. You only make one bet, but very high stake, such as $100, with the same stakes in roulette. In 49% of cases again we win $100, and 51% of the time we lose $100, but at the end of the month we get back our 20% that's $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 probability, but the it's a big dispersion, as you to play this way rather seldom - every week, or once a month.

I'll allow myself to make a brief remark, but somewhat diverging from the primary topic. On a casino forum, one of the gamblers began to assert that tournaments were unfair, and argued it by saying: "No normal person will ever be able to make a single wager in the final 10 minutes of a tournament that is 3,5-fold higher than the amount of prize ($100) as a result of a maximal losing, in order to win. What is the point?"

And really does it make sense? It is similar to a variant that pays back the stake. We are in the black if stake is won. If we lose, we will be awarded a $100 prize in the tournament. So, the math expectancy of the above-mentioned stake amounting to $350 is: $350*0,49-($350-$100)*0,51=$44. It is possible to lose $250, however, we'll get $350 on the next day. Over a year of playing each day, we could accumulate $16,000. If check my site solve a basic mathematical equation, we can realize that stakes as high as to $1900 could be profitable. Of course, in order to win at such a game we require thousands of dollars in our accounts and we can't be blamed for the dishonesty of casinos or gamblers who are foolish.

Let's look back at our bonuses, specifically the most "free-load" ones- with no requirement for any deposit. In recent years, more more ads have been seen promising $500 free of charge without a deposit. The pattern is the following - you really get $500 on a special account with a limited amount of time to play (usually an hour). After an hour, you will receive only the amount of your gains, but not greater than $500. The money is deposited into a real account where you have to win it back as with any bonus typically after having played it through 20 times on slots. What is the true value of $500 worth of free bonus money? In the first place, you must be able to win $500. We can calculate the probability of winning with a simple formula. In actual practice, this is less. The second part: To recoup the bonus, you have to place a bet of at least $10 000 on slots. The casino does not disclose the payout rates for slots. They average 95% but can range from 90-98 percent. The payout will be $500-10000 if we play an average slot. Not a bad game. If we select one with high payouts, then we can expect $500-10 000*0.02=$300. Although the chance of choosing one that pays effectively is just 50% (you've heard from other gamblers, since this chance of random selection is likely to be less than 10%-20 percent), in this case the worth of the deposit-free bonus is $300*0.50*0.50=$75. zoom games to play than $500, but not a bad deal however we can observe that even if we use the most optimal suppositions the final amount of the bonus has decreased by sevenfold.


I'm hoping that this journey into the mathematics of bonus will prove of use to gamblers - if you're looking to win, you simply must think a bit and do some calculations.

Arthur Prudent is the developer of the casino bonus mathematics web site, which covers gambling news. offers reviews on casinos, Poker rooms, bingos, Sports Betting bonuses promotions and more.



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