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Online Casinos: The Mathematical Logic of Bonuses
Online casino players are well aware that these bonuses are offered in many casinos. "Free-load" looks appealing, but are they really worth are they really worth it? Are they profitable for gamblers? The answer to this question depends on many different factors. This question can be answered with mathematics.

Let's begin with a typical bonus for deposits. You deposit $100 and get another $100. It is possible after you have staked $3000. It is a typical example of a bonus earned on the first deposit. The amount of bonus or deposit may differ as well as the stake rate. But one thing is certain: the bonus amount is still able to be withdrawn following the wagering requirement has been met. Till this moment it is impossible to withdraw cash in the majority of cases.

If you plan to be playing at an online casino for a lengthy time and rather insistently, this bonus will 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. There are some complications. For example, if your goal is to just take a peek at the casino without spending a lot of time in there, or you like roulette or other games which aren't permitted under bonus rules, you may not be able to gain access to the bonus. If you aren't betting on any of the permitted games, most casinos won't allow you to withdraw money. If you are keen on blackjack or roulette and a bonus can be won back only by playing slots, place the required $3000 of stakes and in paying out 95% of the time you'll lose an average of $3000*(1-0,95)=$150. As you see, you are not just losing the bonus but will also be able to take from your wallet $50. In this scenario, it's best to refuse the bonus. Anyway, if blackjack and poker are allowed to win back the bonus with a casino's profits of just 0.5%, it is possible that after winning back the bonus you will have $100-$3000, which is a total of 0,005 or $85 for.
"sticky" or "phantom" bonuses:

Casinos are increasingly gaining traction due to "sticky" as well as "phantom bonuses. http://www.inkfilepicker.com/find-a-suitable-online-casino/ are equivalent of lucky chips in a real casinos. The amount of bonus is impossible to withdraw and must stay in the account (as when it "has stuck" to it), until it is completely lost, or annulled upon the first withdrawal cash (disappears as if it were an illusion). It may at first appear that there is no sense in such a bonus - you won't get money anyway however, this isn't true. It's not worth it if you win. But, if you lose, it might be useful. You have already lost $100 with no bonus. But with a bonus, even if it is one that is "sticky" one, the $100 are still on your account. This can help you worm out of the circumstance. The chance of winning back the bonus is just half (for this, you'll only have to put the full amount of the bonus in 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 low stakes, you'll gradually and eventually lose because of the negative math expectation in games, and the bonus is likely to prolong agony, and won't help you gain. play games app 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 want to win, for instance $200, and take risks to be successful. 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 specifically, the return of a lost deposit. It is possible to distinguish two variations - the full refund of the deposit lost and the amount is usually won back like with any other bonus or a part return (10-25%) of the losing during the specified time (a week or month). The first scenario is almost the same as the "sticky bonus" - the bonus will not be worth anything when you win, but helps in the event that you lose. In the second case, the "sticky bonus" mathematical calculation will be comparable. The method of play for the game is the same that we bet and win as often as we can. If we are not lucky and lose then we are able to play again using this money, thus taking the risk to a minimum. Casinos with games offer an opportunity to earn a portion of the loss for gamblers who are active. You'll lose an average of $50 when you play blackjack using an average math expectation of 0.5%. If you earn 20% of the money, the amount of $10 is returned to you. That means your loss will be 40 dollars, which is equivalent to an increase in math expectancy up to 0,4% (ME with return=theoretical ME of the game (1percent of return). You can still derive benefit from the bonus, but you'll have to be playing less. You only make one, however an extremely high stake, for example $100, on the same roulette stakes. In 49% of the cases we also win $100 and 51% of the time 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 is positive in math expectation. The dispersion however is huge and we'll only be able play in this manner once each week or every month.

I'd like to briefly address the issue. I'm a little off-topic. One of the forum participants claimed that tournaments weren't fair. He claimed, "No normal person will ever stake a single stake in the last 10 minutes." The amount is 3,5 times the amount of prize ($100) in the nomination of the maximum loss, so it's impossible to lose. What's the issue?"

It makes sense. The situation is quite similar to the one that involves losing a stake. The stake is in the black if a stake is taken home. If it is lost, we'll get a tournament prize 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 in the future. In the course of a year of playing every day the total amount we earn will be pretty amazing at 365*$44 = $16,000. We'll see that stakes up to $1900 are profitable for us after solving the simplest equation. We need to have many thousands of dollars in our accounts to play this game, however we shouldn't blame casinos for being dishonest or foolish.

Let's talk about our bonuses. They're the top "free-loading" bonuses that do not require a deposit. You've seen more and more ads promising $500 at no cost without deposit. The way to look at it is this You actually receive $500 on a special account, and a limited amount of time to playing (usually one hour). After an hour, you will receive just the amount of your gain, but still not greater than $500. The cash is transferred to a real account where you must win it back, like any bonus, usually having run it 20 times through slot machines. This sounds fantastic however, what is the real value of the bonus? The first thing to consider is that you have to get $500. By using a simple formula, we will see that probability of winning is 50% (in practice, it is likely to be even lower). To win the bonus back You must be able to stake at least at least $10 000 in slots. We aren't aware of the rate of payouts on slots, however, they are provided by casinos, and average approximately 95% (for different types they vary between 90 and 98 percent). If we play an average slot until the end of the wager , we'll be able to deposit $500-10 000*0,05=$ on our account, not a bad game... It is possible to expect $500-10 000*0.02=$300 if we're lucky enough to locate a high-paying slot. The probability of choosing one with high payouts is 50 percent. But, you've heard the opinions of other gamblers , as the probability of winning will be between 10-20 percent. In this instance, the generous deposit bonus of $300*0.5*0.5=$75. A lot less than $500 however, it's still not bad, though we can observe that even with the most ideal assumptions, the value of the bonus been reduced by seven times.

I'm hoping this look into the mathematical realm of bonuses will be useful to gamblers. If you want to win, all you need is to think and make calculations.

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