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Casino players who play online know that these casinos offer various bonuses. "Free-load" appears attractive, however, are they really useful such bonuses? Are they worth the money for gamblers? The answer to this question is contingent on many factors. Mathematics will help us answer this question.Let's look at an everyday bonus on deposit: you transfer $100 and receive $100 more, which it will be possible to receive after you have placed a bet of $3000. It is a typical instance of a bonus on the first deposit. The amount of bonus and deposit may differ in addition to the stake requirements However, one thing remains unchangeable - the amount of bonus is accessible for withdrawal following the wager requirement. It is currently impossible to withdraw money in the majority of cases.The bonus is free money when you are playing at the casino online for a long period of time and keep playing. 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)=$2000), after that the amount of bonus will be over. There are a few pitfalls. For instance, if your goal is to simply have a peek at the casino, without spending too much time in there, or you enjoy roulette or other games that are not permitted by the bonus rules, then you could be denied access to the bonus. In most casinos, there is no way to withdraw money or will simply return a deposit, when a wager isn't made on the games allowed at the casino. You can win a bonus by playing blackjack or roulette, but only if you have the required stakes of 3000. If you're lucky enough to win 95% of all payouts, you'll lose an average of 3000$ (1-0,95) equals $150. In other words, you do not just lose the bonus but also have to take out of your wallet $50. In the case of this, it's better to decline the bonus. If blackjack and poker are permitted to win back the bonus, with a casino's profit only about 0,5%, then you can expect that after winning back the bonus, you'll be left with $100-$3000, which is a total of 0,005 or $85 for."sticky" or "phantom" bonuses:Casinos are becoming more popular because of "sticky" as well as "phantom bonuses. These bonuses are the equivalent of lucky chips in a real casinos. The bonus amount cannot be taken out and must stay on the account (as when it "has stuck" to it) until it's entirely lost or is canceled upon the first withdrawal cash means (disappears like a phantom). It may appear that such an offer isn't worthwhile. You won't be able to take any money out, but this is not true. The bonus is not worth the cost if you win. However, if you lose, it might be useful. You've already lost $100 without a bonus. However, with a bonus even if it's one that is "sticky" one, the $100 are still in your account, which could assist you in getting out of the situation. https://diigo.com/0mh014 of winning back the bonus is around 50% (for that you only need 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". Really, if you play little stakes, you will slowly and surely lose because of the negative mathematical expectation in games, and the bonus is likely to prolong suffering, and won't aid 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 important to determine the amount you want to win, for instance $200, and take risks to win 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=$75 (you can substitute it for your own figures, but, please, take into account that the formulas are given for games with zero math expectancy, in real games the results will be lower).Cash back Bonus:<img width="409" src="http://i.ebayimg.com/00/s/MTUwMFgxMDg5/z/D-kAAOSwMKpUapx6/$_3.JPG?set_id=2">A bonus that is rarely recognized is the possibility of returning money lost. Two types of bonuses could be distinguished: the full return of the deposit. The cash is typically won back just like an normal bonus. Or a partial return (10-25%) for a set period (a week or a month). The first situation is identical to that of a "sticky bonus" which will not be worth anything in the event of winning however it can be helpful if you lose. In the second case, the "sticky bonus" calculation of math will be analogous. The method of play for the game is the same - we gamble and win as often as is possible. It is possible to bet with the money that we've earned, even if we do not take home the prize. Casinos with games offer a partial return on losing for gamblers who are active. It is possible to lose an average of $50 when you play blackjack using a math expectancy of 0.5%. A 20% return 10 cents will be returned to you. That means your loss will be 40 dollars, which is equal to the growth in the math expectation up to 0,4% (ME with return=theoretical ME the game * (1-% of return). But, from the bonus can also be derived benefit, for that you'll need to play less. On the same stakes as on roulette, we place one, but it is the largest stake. We can win $100 in 49% of cases and $100 is won by 51%. However, we have to lose $100 in 51% of the cases. When we finish 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. It is evident that the stake then has positive math probability, but the dispersion is big for we'll be able to play this way rather seldom - once a week or even once per month.I'll allow myself an unintentional remark that is somewhat diverging from the primary subject. On a casino forum one of the gamblers started to assert that tournaments were unfair. They argued as follows: "No normal person will ever make a single stake within the last 10 minutes of a tournament, which 3,5-fold surpasses the prize amount ($100), in nomination of a loss that is as high as so that they can take home a prize. What's the purpose?"It is logical. This situation is similar to the one with return on losing. We are in the black when a stake is taken home. 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 be able to win $350 next day, and over a year playing every day, we'll accumulate pretty $16,000. We'll discover that stakes of up to $1900 could be profitable for us after solving an easy equation. We need to have thousands on our accounts for this game, but we don't have to blame casinos for being untruthful or inexperienced.Let's revisit our bonus offers, especially the most "free-load" ones- without any deposit. Recently, one has seen more and more advertisements promising as much as $500 for free, and with no deposit. The basic idea is as follows - you really get $500 on a special account, and a limited amount of time to play (usually one hour). You'll only receive the winnings after one hour, but never more than $500. The money is transferred to an actual account, where you are required to win it back, like any other bonus, typically after when you have played it 20 times on slots. This sounds fantastic, but what's the actual cost of this bonus? First, let's look at the first step requires you to win $500. By using a simple formula, we can see the odds of winning are 50 percent (in reality, it's certainly even smaller). In order to get the bonus back, you need to stake at least $10 000 on slots. The pay-out rates in slot machines aren't well-known. They are generally around 95%, and can range from 90-98 percent for various types. If we choose an average slot, then at the end of our bet, we'll have $500-10 000*0.05=$0 on our account, not a bad game... If we happen to pick a slot with high pay-outs, we can look forward to $500-10 000*0,02=$300. The likelihood of picking one with high payouts is 50%. However, you have been influenced by the opinions of other gamblers as this probability is not more than 10-20 10%. In this case the bonus for depositing is generous of $300*0.5*0.5=$75. Although it is less than $500, this is still a good amount. But, we can observe that the bonus's total value has decreased by sevenfold even with the best assumptions.I'm sure this trip into the mathematics of bonuses will be useful to gamblers . If you're looking to win, you just need to think a little and do some calculations.