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Online Casinos: Mathematics of Bonuses
Casino players who play online are aware that these bonuses can be found in many casinos. Although "Free-load" may seem attractive, they're not really worthwhile. Are they profitable for gamblers? Answering this question depends on many factors. The answer to this question is possible with mathematics.

Let's begin with an ordinary bonus upon deposit: you make $100 and obtain $100 more that it is possible to obtain after having placed a bet of $3000. This is an example of bonus on the first deposit. The amount of bonus and deposit may differ, as well as the stake rate required however one thing is in place - the amount of the bonus can be withdrawn after the wager is completed. Till this moment it is impossible to withdraw funds, as a rule.

If you plan to be playing at an online casino for a lengthy time and rather insistently the bonus can help you, it can really be considered 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 instance, if your goal is to simply have a peek at the casino, without spending a lot of time there, or you like roulette or other games that are not permitted under bonus rules, you could be denied access to the bonus amount. If you don't wager in any of the permitted games, casinos are unlikely to let you withdraw cash. There is a chance to win a bonus when you play roulette or blackjack however only if you make the required 3000 stakes. In the 95% of all payouts, you'll lose an average of $3000* (1-0,95) equals $150. You will not only lose the bonus but also have to take out of your wallet $50. In this case it is better to decline the bonus. If you could win back the bonus by earning a profit of 0.5 percent, it's likely that you'll get between $100 and $3000, which is equal to $85 after you've earned back the bonus.
"sticky" or "phantom" bonus:

A growing amount of popularity in casinos is derived from "sticky" or "phantom" bonuses, which are equivalent to luck chips in real casinos. It isn't possible to withdraw the bonus amount. The bonus has to be placed on the account as if it "has stuck". At first sight it may appear as if there's no value in an offer - you'll never be able to withdraw money at all however this isn't true. It's not worth the cost if you win. If you lose, it might be useful. If you don't have a bonus, you've lost your $100 , and you're done. However, with a bonus even if it's a "sticky" one, you will find that $100 remain on your account, which can help you worm out of the circumstance. The probability of winning the bonus is less than half (for this you will only need to stake 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 small stakes, you'll slowly and surely lose due to the negative math expectancy in games, and the bonus is likely to prolong suffering, and won't aid you to 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 desired amount you wish to profit, for instance $200, and attempt 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:

One bonus that is seldom recognized is the possibility of returning money the money that was lost. Two types of bonuses could be distinguished: the full refund of deposit. At this point the deposit is generally returned as an ordinary bonus. Or a partial return (10-25 percent) over a fixed period (a week or a month). In the first scenario, the situation is practically identical to that of the "sticky" bonus. In the event that you win, there's no reason to get the bonus, however it is helpful in the event loss. Math calculations will be also analogous to "sticky" bonus and the strategy is the same - we take risks, try to win as many times as we can. It is possible to bet with the money that we've won, even if we don't succeed. Casinos in games can offer some kind of compensation for losses for active gamblers. If you are playing blackjack with math expectancy of 0,5%,, having made stakes on $10,000, you'll lose an average of $50. With 20% of return 10 cents will be returned to you. most played games 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 of the game * (1percent of return). But, from the bonus can also be derived benefits, which means you'll need to play less. With the same stakes in roulette, we place one, but it's the largest stake. We win $100 in 49% of instances however $100 is won by 51%. We lose $100 in 51% of instances. At the end of every month, we receive 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 is positive in math expectation. The dispersion however is high and we'll only be able play in this manner once each week or every month.

I'd like to briefly address the issue. This is a bit off topic. One of the forum members declared that tournaments weren't fair. He said, "No normal person will ever stake a single stake during the last 10 minutes." The amount is 3,5 times the prize amount ($100) in nomination of maximum loss, meaning that you won't lose. What's the purpose?

It makes sense. The situation is similar to the one with the return of losing. The stake is in the black if the stake has been won. 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. Yes, we may lose $250 today, but we'll win $350 tomorrow in the course of a year. playing every day, we'll accumulate pretty 16 000 dollars. We'll see that stakes of up to $1900 can be profitable for us after solving the simplest equation. Of course, for this kind of game, we'll need to have thousands of dollars on our accounts and we can't blame casinos for dishonesty or gamblers for being foolish.

Let's look back at our bonuses, specifically the highest "free-load" ones- without any deposit. Of late one has seen more and more advertisements promising up to $500 absolutely for free, and without deposit. You can get $500 on a special account, and only a certain amount of time to play (usually one hour). You will only get the amount you win after an hour, but no more than $500. You must win the bonus back in a real bank account. Usually, you have run it 20 times in slot machines. $500 for free sounds appealing however, what is the real price of the bonus? The first aspect is that you must win $500. By using a simple formula, we can determine that the probability of winning is 50 percent (in practice, it is likely to be even lower). In order to win the bonus You must be able to stake at least $10 000 on slots. The pay-out rates in slot machines are not known. They are generally around 95%, and can range from 90-98% for different types. If we choose an average slot, until the end of the bet, we'll have $500-10 000*0.05=$0 on our account, not a bad game... We can expect $500-10 000*0.02=$300 If we're fortunate enough to find a high-paying slot. The probability of choosing a slot with the highest payout is 50%. However, you have been influenced by the opinions of other gamblers , as the probability of winning will be between 10-20%. In this instance the bonus for depositing is generous of $300*0.5*0.5=$75. Even though play games for real money 's not $500, this is still an impressive amount. However, we are able to find that the bonus's final value has decreased sevenfold, even with the best possible estimates.


I'm hoping that this journey into the mathematics of bonuses will be useful for gamblers. If you are looking to be successful, you only need to think a little and calculate.

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