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Online Casinos: The Mathematical Basis of Bonuses
Casino players online are aware that bonuses are offered at many casinos. "Free-load" looks attractive, however, are they really useful such bonuses? Are they worth the money for gamblers? This question is dependent on many factors. The answer to this question is possible by math.


Let's begin with an ordinary bonus when you deposit $100 and obtain $100 more and it's possible to obtain after having staked $3000. It is an example of a bonus that you can get on your first deposit. Although the size of a bonus or deposit can vary, so can the stake rates. But there is one thing that is for certain: the bonus amount can be taken out after the wagering requirement. At present, it's impossible to withdraw cash, as a rule.

This bonus can be considered as free money if you are playing at the casino online for a long duration and you are consistent. 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. In particular If your intention is to just take a look at the casino without spending a lot of time there, or if you enjoy roulette or other games which aren't permitted by bonus rules, you might be denied access to the bonus. In most casinos you won't be allowed to withdraw cash or just return your deposit when a wager isn't made on the games allowed in the casino. Bonuses can be won when you play roulette or blackjack, but only if you meet the minimum stakes of 3000. If you're lucky enough to win 95% of all payouts, you'll lose an average of $3000* (1-0,95) equals $150. You will lose $50, and forfeit the bonus. In this instance, it is better not to take the bonus. If blackjack or poker could win back the bonus, with a profit of 0.5 percent, it's possible that you'll receive $100-3000*0,005=$85 after you have won back the bonus.
"sticky" or "phantom" benefits:

More and more popularity in casinos is gained by "sticky" or "phantom" bonuses, which are equivalent to lucky chips in real casinos. The bonus amount cannot be withdrawn and must stay in the account (as when it "has stuck" to it) until it's totally lost or canceled upon the first withdrawal cash means (disappears as if it were it's a phantom). It could appear that bonuses are not worthwhile. You won't be able to withdraw any money, however this isn't the case. The bonus won't be worth the cost if you win. If you lose, it may prove useful. Without play retro games have lost your $100 and then you're gone. If the bonus was not "sticky", $100 remains in your account. This will allow you to wiggle out of this situation. There is a chance to win back the bonus in this case is a bit less than 50 percent (for it is only necessary to stake the entire amount on the chance of winning in roulette). In order to maximize profits from "sticky" bonuses one needs to use the strategy "play-an-all-or-nothing game". You'll lose slowly and surely if you stake in small amounts. The negative math expectation of games means that you will not 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 recommended to fix the desired amount you wish to winnings, such as $200, and attempt to win it, while 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 type of bonus, specifically, the return of a lost deposit. Two types of bonuses can be distinguished: the full return of the 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 identical to that of a "sticky bonus" The bonus is not worth it if you win however it can be helpful when you lose. The "sticky bonus" calculation of math will be comparable. The strategy of the game is identical - we gamble, win as often as possible. If we don't win and lose the game, we can continue to play using this money, thus minimizing the risk. The partial refund of losses gambler could be regarded as an insignificant advantage of casinos in games. It is possible to lose an average of $50 playing blackjack with an expected math of 0.5 percent. A 20% return 10 cents will be returned to you, that is you losing will amount to 40 dollars, which is equivalent to an increase in the math expectation up to 0,4 percent (ME with return=theoretical ME of the game (1- % of return). You can still derive profit from the bonus however, you'll need to be playing less. In the same way as in roulette, we place one, however it's the largest stake. In 49% of the cases again we win $100, and 51% - we lose $100, however at the close of the month, we win back 20%, which is 20 dollars. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. As visit this site see, the stake has a positive math expectation, however the it's a big dispersion, as we'll be able to play this way rather seldom - once a week or even once per month.

I'll allow myself a short remark, somewhat diverging from the primary subject. In a forum about casinos, one of the gamblers started to argue that tournaments are unfair, and argued it as follows: "No normal person will ever be able to make a single wager within the final 10 minutes of the event and this is 3,5-fold more than the prize ($100) and in the event of a loss that is as high as so as to take home a prize. What is the point?"

What is the sense? It's like the one that has return on losing. If a stake has been won it is already in the black. If it loses - we'll win 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. We could lose $250 today but win $350 tomorrow. If we continue daily play, our total earnings are quite impressive at 365*$44=$16 000. We'll discover that stakes of up to $1900 could be profitable for us after solving an easy equation. Of course, for such a game , we'll must have thousands of dollars on our account and we can't be blamed for dishonesty by casinos or gamblers who are foolish.

Let's come back to our bonus offers, especially the best "free-load" ones, without any deposit. There are an increase in ads offering $500 for free, without deposit. You will receive $500 in exchange for a special account, and only a certain amount of time to play (usually one hour). The only thing you will get is the amount you win after an hour, but no over $500. You have to win the bonus back in a real bank account. In most cases, you've been able to play it for 20 times in slot machines. $500 for free sounds appealing however, what is the actual value of the reward? First, let's look at the first step requires you to be able to win $500. We can see that the probability of winning $500 is 50% using an easy formula. In reality, it's much lower. In order to receive the bonus, you need to stake at least $10 000 on slots. We do not know the percentages of pay-outs in slot machines, but they are published by casinos and are about 95% (for different types they vary about 90-98%). An average slot will give us $500-10 000*0.05=$0. find more 's not an unreasonable amount. It is possible to expect $500-10 000*0.02=$300 If we're fortunate enough to locate a high-paying slot. Even though the likelihood to choose a slot with the highest payouts is 50 percent (you are probably familiar with the opinions of other gamblers , since by random choice this probability will be less than 10-20%, as there are a few slots that pay out generously) In this instance, the value of a huge deposit bonus is $300*0.5%*0.5%=$75. A lot less than $500 however, it's still not bad, even though we find that even with most ideal assumptions, the value of the bonus been reduced by seven times.

I hope, this excursion into the maths of bonuses will be helpful to gamblers - if you are looking to be successful, you only must think about it and make calculations.

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