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Online Casinos: Mathematics of Bonuses
Online casino players know that casinos that offer various bonuses. While "Free-load" might seem appealing, they are not really worth the effort. Are they worth the money for gamblers? The answer to this question depends on many factors. Mathematics will assist us in answering this question.

Let's start with a typical bonus on deposit: you transfer $100, and then receive another $100, which it will be possible to get having put up $3000. This is a common instance of a bonus on the first deposit. Although the size of a bonus or deposit may differ, so can the stake rate. However, one thing is sure: the bonus amount is still able to be withdrawn following the wagering requirement. As a rule, it is not possible to withdraw money.

If you plan to play in the online casino for a long time and rather insistently you are a player, this bonus could assist 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 complexities. For example If your intention is to simply have a look at the casino without spending a lot of time there, or you like roulette or other games that are prohibited under bonus rules, you might be denied access to the bonus. If you aren't betting in any of the allowed games, most casinos won't allow withdrawals. If you're keen on blackjack or roulette, and you can returned only through playing slots, make the minimum stakes of $3000 and in paying out 95% of the time you'll lose $3000*(1-0,95)=$150. You lose $50 and also forfeit the bonus. In this instance it's best not to accept the bonus. If blackjack or poker can win back the bonus by earning a profit of 0.5 percent, it's possible that you'll receive $100-3000*0,005=$85 after you've redeemed the bonus.
"sticky" or "phantom" benefits:

Casinos are becoming more popular for "sticky" as well as "phantom bonuses. These bonuses are equivalent of lucky chips in a real casino. The amount of bonus cannot be taken out and must stay on the account (as when it "has stuck" to it), until it is totally lost or canceled upon the first withdrawal cash (disappears as if it were an illusion). On first glance, it might appear that there is no reason to get a bonus - you won't get money anyway however this isn't accurate. The bonus is not worth it if you are successful. If you fail, the bonus may prove useful. Without a bonus you have lost $100, and then you're gone. However, with a bonus even if it is one that is "sticky" one, $100 are still on your account. This can assist you in getting out of the circumstance. The odds of winning the bonus is less than half (for this, you'll have to bet the entire amount in 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 small stakes, you'll gradually and eventually lose because of the negative mathematical expectations in games. Moreover, bonuses will only add the pain, and will not help you gain. 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 of your gain, for example $200, and then try to win it by taking chances. 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:

It is a rare type of bonus, which is the return of lost. There can be singled out technology - either the complete refund of the deposit lost, at this the returned money usually is to be paid back as with an ordinary bonus or a portion (10-25%) of the amount lost over the fixed period (a week or month). The first scenario is nearly similar to a "sticky bonus" The bonus is not worth it in the event of winning, but helps if you lose. Math calculations are analogous to the "sticky" bonus, and the game's strategy is the same - we take risks trying to win as many times as possible. It is possible to gamble with the money we've won, even if we fail to win. Casinos in games can offer some kind of compensation for losses to gamblers who have a high level of activity. You will lose $50 on average if you play blackjack with a math expectancy of 0.5 percent. You will receive $10 back when you lose 20 dollars. This is the equivalent of an increase in math expectancy of 0.4%. But, the bonus you will also get benefits, which means you'll need to play less. You only make one, however a high stake, such as $100, with the same stakes in roulette. We win $100 in 49% of cases and $100 is won by 51%. But, we lose $100 in 51% of instances. When we finish each month, we get back 20 percent of the $20 we won. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. As you see, the stake is then positive in math probability, but the dispersion is big for it to be played this way rather seldom - once a week or even once per month.

Let me briefly address the issue. This is a bit off topic. One of the forum participants claimed that tournaments weren't fair. He said, "No normal person will ever be able to stake a single stake during the last 10 minutes." The 3,5-fold increase is more than the amount of prize ($100) in the case of maximum losing, so as not to lose. What's the purpose?"

It makes sense. The situation is identical to the scenario that involves losing a stake. The stake is in the black if the stake is taken home. If it loses - 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. We could lose $250 today, but we will win $350 in the future. If we continue daily play and earning a total of 365, our earnings are quite amazing at 365*$44 = $16,000. Having solved a simple equation, we'll find out that stakes up to $1900 are profitable for us! Of course, in order to win at such a game , we'll require thousands of dollars on our account however, we shouldn't be blamed for dishonesty by casinos or gamblers for being foolish.

Let's look back at our bonus offers, especially the most "free-load" ones, without any deposit. Recently, one has been able to notice an increasing number of ads promising the possibility of up to $500 completely free , with no cost and with no deposit. You will receive $500 in exchange for a special account, and you have a time limit to play (usually 1 hour). After an hour you get just the amount of your winnings, but no more than $500. You must win the bonus back in a real bank account. Most often, you've been able to play it for 20 times in slot machines. It sounds wonderful but what's the exact value of the bonus? The first aspect is that you need to get $500. We can determine that the odds of winning $500 is 50% using an easy formula. In reality, it is much lower. To win the bonus back it is necessary to bet $10 000 on slots. We don't know the rates of pay-outs in slot machines, but they are released by casinos and are about 95 percent (for various kinds they fluctuate between 90 and 98 percent). If we play an average slot, until the end of the wager , we'll be able to deposit $500-10 000*0,05=$ in our account. Not an awful game... You can anticipate $500 to 000*0.02=$300 in the event that we are lucky enough to locate a high-paying slot. The likelihood of picking a slot with the highest payout is 50 percent. You've heard the comments of other gamblers that the probability of winning will be between 10-20 percent. In this case the bonus for depositing is generous of $300*0.5*0.5=$75. While it's less than $500, it is a good amount. However, we can see that the bonus's final value has dropped sevenfold even with the most accurate assumptions.


I hope this exploration into the mathematical realm of bonuses will prove useful to gamblers. If you want to succeed, all you have to do is to think and do calculations.

Read More: http://www.thepollspace.com/internet-casino-software-vs-casino-title/