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Online Casinos: The Mathematical Basis of Bonuses
Online casino players are well aware that these bonuses can be found in many casinos. "Free-load" appears appealing, but are they really useful such bonuses? Are they worth the money for gamblers? This question is dependent on many different factors. Mathematical knowledge can help us answer this question.

Let' fun games to play online at an everyday bonus upon deposit: you make $100, and then receive another $100 and it's possible to get having put up $3000. This is a common instance of a bonus on the first deposit. While the amount of a deposit or bonus may vary and so do the stake rates. However, there is one thing that is for sure: the bonus amount can still be withdrawn after the wagering requirement has been met. At present, it's impossible to withdraw money, as a rule.

If you are going to be playing at an online casino for a lengthy period of time, and you are persistent about it, this bonus will aid you, and it could 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)=$2000), after that the amount of bonus will be over. There are a few pitfalls, for example, if you just want to take a look at a casino, without playing for a long period of time and you are a fan of roulette or other gamesthat are which are not permitted by the rules of casinos to win back bonuses. In most casinos, there is no way to withdraw funds or simply refund a deposit when a wager isn't placed on the games that are allowed at the casino. You can win a bonus when playing roulette or blackjack however only if you meet the minimum stakes of 3000. If you're lucky enough to win 95% payouts that you'll lose an average of 3000$ (1-0,95) which is $150. You will are not just losing the bonus, but you also have to take out of your pocket $50, in the case of this, it's better to decline the bonus. If poker or blackjack can 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" bonuses:

Casinos are increasingly gaining traction for "sticky" and "phantom bonuses. These bonuses are equivalent to lucky chips in real casino. It isn't possible to cash out the bonus. The bonus must be placed on the account like it "has stuck". At first sight it may appear as if there's no reason to get bonuses - you don't get money anyway, but it's not completely accurate. The bonus won't be worth it if you are successful. But, if you lose, it could be useful. You have already lost $100 without a bonus. If the bonus was not "sticky" the $100 will still be in your account. This can help to get out of the situation. The chance of winning back the amount of bonus is around 50 percent (for it is only necessary to put 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". It is possible to lose slowly but surely if you stake in small amounts. The math expectancy that is negative of games means that you'll never get 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. Set the amount you would like 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:

The most common bonus seen is the return of lost. It can be distinguished into two variations - the full return of the lost deposit, at this the returned cash is typically paid back as with normal bonuses or a portion (10-25 percentage) of the losing during the specified time (a week, a month). In the first case the scenario is essentially identical to that of the "sticky" bonus. If we win, there's no reason to get the bonus, but it can be helpful in the event loss. Calculations in math will also be similar to the "sticky" bonus, and the strategy is similar - we risk, try to win as many times as we can. If we do not win and lose then we are able to play again with the that money back, thus taking the risk to a minimum. Casinos with games offer some kind of compensation for losses for active gamblers. You will lose about $50 when you play blackjack using an expected math of 0.5%. If you earn 20% of the money, $10 will be given back to you. That means your loss will be $40, which is equivalent to the growth in math expectancy up to 0,4% (ME with return = theoretical ME of the game (1-% of return). You can still derive benefits from the bonus but you'll have to play less. You only make one, however a high stake, like $100, with the same stakes in roulette. We win $100 in 49% of the cases however $100 is won by 51%. However, we have to lose $100 in 51% of instances. At the end of each month, we get back 20% of our $20 winnings. As games to play at home is $100*0,49-($100-$20)*0,51=$8,2. The stake has a positive math probability. However, dispersion is huge and we'll only be able play this way once per week or once per month.

I'll let myself make an unintentional remark that is somewhat diverging from the primary issue. One forum member said that tournaments were unfair. He claimed, "No normal person will ever be able to stake a single stake within the last 10 minutes." The amount is 3,5 times the prize amount ($100) in the case of the maximum loss, so as not to lose. What's the point?

It makes sense. It's very similar to the variant that has a return on losing. We're in the black when a stake has been won. 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. Sure, we could lose $250 today but win $350 next day. If we continue daily play, our total earnings are quite amazing at 365*$44 = $16,000. Having solved a simple equation, we'll discover that stakes of up to $1900 are profitable for us! It is essential to have several thousand dollars on our accounts for this game, but we don't have to blame casinos for being shady or naive.

Let's look back at our bonus offers, especially the best "free-load" ones- without any deposit. Of late one has seen increasing numbers of advertisements that promise the possibility of up to $500 completely free , with no cost and without any deposit. You will receive $500 in exchange for an account that is unique, and you have a time limit to play (usually an hour). After an hour you get just the amount of your gains, but not more than $500. The cash is transferred to an actual account and you must win it back, like any bonus, usually when you have played it 20 times through slot machines. The $500 bonus sounds tempting but what's the actual value of the reward? Well, the first part requires you to win $500. We can determine that the chance of winning $500 is 50% using the simplified formula. In reality, it is much lower. To win the bonus back, you must stake 10 000 dollars on slot machines. The pay-out percentages of slot machines are not known. They average around 95% and fluctuate between 90-98 percent for various types. A typical slot can give us between $500 and 000*0.05=$0. It's not a bad amount. If we're lucky enough to choose a slot with large payouts, we can await $500-10 000*0,02=$300. Even though the probability to select a slot with payouts that are high is 50 percent (you have heard the opinions of other gamblers since by random choice this probability is less than 10-20%, for there are a few slots that pay out generously) in this scenario, the value of a generous deposit-free bonus amount to $300*0,5*0.5%=$75. A lot less than $500 however, it's still not bad, though we can observe that even with the most optimal suppositions the value of the bonus has diminished seven times.

I'm sure this trip into mathematics domain of bonuses will be helpful for gamblers. If you're looking to win, you just need to think a little and make calculations.


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