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Online Casinos: The Mathematical Logic of Bonuses
Online casino players know that the latter ones offer a range of bonuses. "Free-load" is appealing, but are they really worth these bonuses? Are they lucrative for gamblers Answering this question is contingent on a lot of conditions. This question can be answered by math.

Let's start with a typical bonus on deposit: you transfer $100 and obtain $100 more, which it will be possible to receive after you have staked $3000. It is an example of a bonus that you can get on your first deposit. While the amount of a deposit or bonus may vary as well as the stake rates. But there is one thing that is for certain: the bonus can be taken out after the wagering requirement. It generally is not possible to withdraw money.

If you are going to play in the online casino for a lengthy time and rather insistently the bonus can help you, it can be considered to be 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)=$2000), after that the amount of bonus will be over. There are some complications. For example when your objective is to just take an overview of the casino without spending a lot of time there, or you like roulette or other games that are prohibited by the bonus rules, then you might be denied access to the bonus amount. If you do not wager on any of the permitted games, most casinos won't allow you to withdraw money. You can win a bonus by playing blackjack or roulette, but only if you meet the minimum stakes of 3000. If you're lucky enough to win 95% payouts that you'll lose an average of 3000$ (1-0,95) equals $150. The loss is $50 and you also forfeit the bonus. In this scenario it's better not to take the bonus. If blackjack and poker are allowed to claim back the bonus and the casino's profit only about 0,5%, then it can be expected that once you have repaid the bonus you will have $100-3000*0,005=$85 of the casino's money.

"sticky" or "phantom" bonuses:

Casinos are becoming increasingly popular because of "sticky" and "phantom bonuses. These bonuses are equivalent of lucky chips in a real casinos. The amount of the bonus cannot be taken out and must stay in the account (as when it "has been glued" to it) until it's totally lost or canceled upon the first withdrawal cash means (disappears like a phantom). It could appear that an offer isn't worthwhile. You will not be able to take any money out, but this isn't the case. If you are a winner, there's no reason to the bonus. However, if you have lost the money, it could be useful to you. You've already lost $100, without a bonus. If the bonus is not "sticky", $100 will still be on your account. This will allow to get from this mess. The chance of winning back the bonus is a bit less than 50 percent (for that you only need to put 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". It is possible to lose slowly but surely if you stake small amounts. The negative math expectation of games implies that you'll never receive any bonuses. 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 important to determine the amount you want to gain, such as $200, and be willing to take chances to make it. 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:

A bonus that is rarely recognized is the possibility of returning money lost funds. It can be distinguished into two options - either the complete refund of the deposit lost in which case the amount is usually returned as an ordinary bonus or a part return (10-25 percentage) of the losing over the fixed period (a week or a month). The first situation is identical to that of a "sticky bonus" - the bonus will not be worth anything in the event of winning, but helps if you lose. Math calculations will be also identical to the "sticky" bonus, and the strategy of the game is similar - we risk trying to win as much as we can. It is possible to bet with the money that we've earned, even if we fail to take home the prize. Partial return of the losing for an active gambler can be regarded as an insignificant benefit of casinos in games. If you play blackjack with math expectancy of 0,5%, then, having made stakes on $10 000, you will lose on average $50. With 20% of return the amount of $10 is returned to you. That means your loss will be 40 dollars, which is equal to an increase in math expectancy to 0,4 percent (ME with return=theoretical ME the game (1- % of return). However, from the given bonus you will also get benefits, which means you'll need to play less. In the same way as on roulette, we make one, but it's an enormous stake. We can win $100 in 49% of the cases and $100 is taken home by 51% of players. We have to lose $100 in 51% of instances. At the end of each month, we get back 20 percent of our winnings from $20. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. The stake has a positive mathematical expectancy. But, the dispersion is huge and we'll only be able to play this way once every week or once a month.

I'll let myself make a short remark, slightly digressing from the main topic. In a forum for casinos, one gambler 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 the event and this is 3,5-fold more than the amount of prize ($100), in nomination of a loss that is as high as so as to take home a prize. What's the reason?

It is logical. This situation is similar to the one with loss of money. We are in the black if a stake is won. We'll be awarded a prize in a tournament of $100 if it is lost. So, the math expectancy of the above-mentioned stake amounting to $350 is: $350*0,49-($350-$100)*0,51=$44. Yes, we might lose $250 today, but we will win $350 in the future. Over a year of playing each day and earning a total of 365, our earnings will be quite impressive , at 365*$44=$16000. Having solved a simple equation, we'll discover that stakes as high as $1900 can be profitable for us! play video 'll need several thousand dollars on our accounts for this kind of game, but we don't have to blame casinos for being untruthful or inexperienced.

Let's get back to our bonuses. They're the top "free-loading" bonuses with no deposit. In recent times, we've seen more and more advertisements promising the possibility of up to $500 completely for free, and with no deposit. The pattern is the following You actually receive $500 on a special account, and a limited amount of time to play (usually one hour). You'll only receive the winnings after an hour, but no over $500. The bonus must be redeemed back in a real bank account. In most cases, you've been able to play it for 20 times in slot machines. This sounds fantastic but what's the exact cost of the bonus? The first aspect is that you have to get $500. Based on a simplified formula, we can see the odds of winning are 50% (in the real world, it's likely to be even lower). In order to win the bonus, you must stake $10 000 on slots. We do not know the percentages of pay-outs from slots, they are not released by casinos and average around 95% (for different types they vary around 90-98 percent). If we play an average slot until the end of the wager we'll have $500-10 000*0,05=$0 in our bank account, which is not a bad game... We can expect $500-10 000*0.02=$300 if we're lucky enough to locate a high-paying slot. The chance of selecting the slot that has the highest payout is 50%. You've heard the opinions of other gamblers as the probability of winning will be between 10-20 10%. In free games to play , the generous deposit bonus of $300*0.5*0.5=$75. It's less than $500 but still not too poor, although we can see that even with the most optimal suppositions the final value of the bonus diminished seven times.

I hope this exploration into the mathematical realm of bonuses can prove beneficial for gamblers. If you're looking to be successful, all you need is to think and do calculations.

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