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Online Casinos: Mathematics of Bonuses
Online casino players know that casinos that offer various bonuses. "Free-load" looks appealing, but are they really useful these bonuses? Are they lucrative for gamblers This question is dependent on a variety of factors. Mathematics will aid us in answering this question.

Let's begin with a typical bonus when you deposit. The deposit is $100, and you get another $100. It is possible after you stake $3000. It is an example of a bonus on your first deposit. Although the size of a bonus or deposit may differ, so can the stake rates. But one thing is sure: the bonus amount is still able to be withdrawn following the wagering requirement has been met. Till this moment it is impossible to withdraw money generally.

This bonus can be considered free money when you play at the casino online for a lengthy duration and are persistent. 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)=$2000), after that the amount of bonus will be over. However, there are some issues to be aware of such as if you want to simply take a look at a casino, without playing for a long period of time, if you prefer roulette or any other game, forbidden by casinos' rules for winning back bonus. If you aren't betting in any of the allowed games, casinos are unlikely to let you withdraw cash. There is a chance to win a bonus when playing roulette or blackjack however only if you meet the minimum stakes of 3000. In the 95% of payouts that you'll lose an average of 3000$ (1-0,95) which is $150. You will are not just losing the bonus, but will also be able to take from your account $50, in this scenario, it's best to not accept the bonus. If blackjack and poker are permitted to claim back the bonus with a casino's profits of just 0,5%, then it is possible that after winning back the bonus, you'll have $100-$3000, which is a total of 0,005 or $85 for.
"sticky" or "phantom" bonus:

Casinos are becoming increasingly popular because of "sticky" as well as "phantom bonuses. best games to play are equivalent to the lucky chips found in a real casinos. It isn't possible to withdraw the bonus amount. The bonus has to be kept on the account, as if it "has been shackled". It could appear that an offer isn't worthwhile. You will not be able to withdraw any money, but it's not the case. If you win, then there is really no point in the bonus, but if you have lost, it may be useful to you. You've already lost $100 with no bonus. With a bonus, even if it's one that is "sticky" one, the $100 are still in your account, which can help you worm out of the situation. The odds of winning the bonus is just half (for this, you'll only need to stake the full amount in roulette). In order to maximize profits from "sticky" bonuses one needs to use the strategy "play-an-all-or-nothing game". You will lose slowly and certainly if you play with in small amounts. The negative math expectation of the game means you'll never get any bonus. 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. You should set the amount you wish to earn, like $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).

The cash back bonus:

There is a seldom encountered type of bonus, which is the return of lost. There can be singled out two variants - the complete return of the lost deposit, at this the returned amount is usually paid back as with normal bonuses, or a partial return (10-25 percentage) of the losing over the fixed period (a week or month). play games is identical to that of a "sticky bonus" - the bonus is useless if you win however, it is beneficial when you lose. Math calculations will be also identical to "sticky" bonus and the strategy is the same - we take risks trying to win as much as possible. We can still gamble with the money you've earned even if we fail to succeed. Casinos with games offer a partial return on losing for active gamblers. You'll lose an average of $50 when you play blackjack using an expected math of 0.5 percent. The payout is $10 when you lose 20 dollars. This is equal to the math expectancy increase of 0.4 percent. It is possible to still benefits from the bonus however, you'll need to play less. We make only one but very high stake, like $100, with the same stakes in roulette. The majority of the cases again we win $100, and 51% of the time we lose $100. However, at the close of the month, we receive our 20%, which is 20 dollars. 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 expectation, however the dispersion is big for you to play this way rather seldom - at least once per week or every month.

Let me briefly address the issue. I am slightly off-topic. One forum member said that tournaments were unfair. He claimed, "No normal person will ever stake a single stake within the last 10 minutes." The amount is 3,5 times the amount of prize ($100) in the nomination of maximum loss, meaning as not to lose. What's the purpose?

And really does it make sense? The scenario is very similar to the variant that has a return on losing. If a stake is successful the stake is already in the black. We'll be awarded a prize in a tournament of $100 if it fails to win. 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 shall get $350 the next day in the course of a year. playing each day, we'll earn 365*$44=$16 000. We'll discover that stakes as high as $1900 could be profitable for us if we solve a simple equation. Of course, for such a game we require thousands of dollars on our accounts and we can't blame casinos for dishonesty or gamblers for being naive.

Let's revisit our bonus offers, especially the most "free-load" ones- with no requirement for any deposit. You've seen more and more ads promising $500 at no cost with no deposit. You get $500 for a special account, and a limited amount of time to play (usually 1 hour). After an hour you get only the amount you gains, but not more than $500. fun player games must win the bonus back on a real account. Most often, you've run it 20 times in slot machines. The $500 bonus sounds tempting but what's the exact cost of the bonus? The first thing to consider is - you need to get $500. Using a simplified formula, we will see that the probability of winning is 50 percent (in the real world, it's definitely lower). The second part - we receive the bonus and you have to bet 10 000 dollars in slot machines. The pay-out percentages of slot machines are not known. They are generally around 95%, and can range from 90-98 percent for various types. An average slot will give us between $500 and 000*0.05=$0. That's not a bad amount. If we're lucky enough to choose a slot with payouts that are high, we could look forward to $500-10 000*0,02=$300. The chance of selecting one with high payouts is 50 percent. But, you've heard the opinions of other gamblers , as the probability of winning will be between 10-20 10%. In this case, the generous deposit bonus of $300*0.5*0.5=$75. Much less than $500, however, it's still not bad, though we can see that even with the most ideal assumptions, the final amount of the bonus has diminished seven times.


I'm hoping that this journey into the mathematics of bonus will prove useful to gamblers . If you are looking to be successful, you only have to think about it and do some calculations.

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