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Online Casinos: Mathematics of Bonuses
Online casino players know that the latter ones offer various bonuses. Although "Free-load" might sound appealing, they are not really worthwhile. Are they profitable for gamblers? This question is dependent on many different factors. Mathematics will assist us in answering this question.

Let's start with a normal bonus when you deposit. fun games to play is $100, and you receive another $100. This will be feasible after you stake 3000. This is an example of bonus for the first deposit. While the amount of a deposit or bonus may vary, so can the stake rate. However, there is one thing that is for sure: the bonus amount can still be withdrawn after the wagering requirement has been met. In general, it is not possible to withdraw money.

If you plan to play in the online casino for a long time and rather insistently the bonus can assist you. It can be considered to be 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 in the event that you just want to take an experience at a casino without playing for a long time or if you like roulette or other gamesthat are prohibited by casino rules to win back bonuses. If you do not wager on any of the permitted games, the majority of casinos will not allow you to withdraw money. If you're keen on blackjack or roulette, and you can earned only by playing slots, place the minimum stakes of $3000, in the course of the 95% payouts, you will lose on average $3000*(1-0,95)=$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 refuse the bonus. In any case, if blackjack and poker are permitted to win back the bonus with a casino's profit only about 0,5%, so it is possible that after winning back the bonus, you'll have $100-$3000 plus 0,005 = $85 from the casino's profit.

"sticky" or "phantom" bonus:

The popularity of casinos is gained by "sticky" or "phantom" bonuses - equivalent to casino chips that are lucky in real life. The bonus amount cannot be withdrawn the bonus, and it will remain in the account (as as if it "has been glued" to it) until it's totally lost or canceled upon the first withdrawal cash means (disappears like it's a phantom). It may appear that such an offer isn't worthwhile. You won't be able to take any money out, but this isn't 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. Already, you've lost $100 without a bonus. If the bonus is not "sticky" it remains on your account. This could help you to wiggle out of this situation. There is a chance to win back the amount of bonus is less than 50 percent (for you will only have to put the whole amount on the chances in 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 certainly if you play with in small amounts. The math expectancy that is negative of the game means you'll never receive 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 gain, such as $200, and take risks to be successful. 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 variation of a bonus specifically, the return of a lost deposit. Two types of bonuses can be distinguished: the complete refund of deposit. In this case, the deposit is generally won back just like an ordinary bonus. Also, a partial return (10-25 percent) for a set period (a month or a week). The first situation is similar to a "sticky bonus" - the bonus will not be worth anything in the event of winning however it can be helpful if you lose. Calculations in math will also be similar to "sticky" bonus, and the strategy of the game is the same: we take risks and try to win as many times as possible. If we are not lucky and lose then we are able to play again using that money back, thus taking the risk to a minimum. Partial return of the losing for an active gambler can be considered to be an unimportant benefit of casinos when playing games. You will lose about $50 if you play blackjack with an expected math of 0.5%. A 20% return $10 will be given back to you, that is 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 of the game (1percent of return). However, from the given bonus, you can also gain from the fact that you will need to be playing less. You only make one, however a high stake, like $100, using the same bets on roulette. We can win $100 in 49% of instances and $100 is won by 51%. But, we lose $100 in 51% of cases. When we finish each month, we earn back 20 percent of the $20 we won. As zoom games to play is $100*0,49-($100-$20)*0,51=$8,2. The stake is positive in math expectation. However, dispersion is high and we'll only be able play in this way for a few times each week or every month.

I'd like to briefly address the issue. I am slightly off-topic. In a forum about casinos, one of the gamblers started to claim that tournaments were unfair. They argued in the following way: "No normal person will ever make a single stake within the final 10 minutes of a tournament and this is 3,5-fold more than the prize amount ($100) and in the event of a maximal losing, so that they can be able to win. What's the reason?

What is the sense? play games app 's quite similar to the one that involves losing a stake. If a stake has been won - we are already in the black. 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 shall be able to win $350 next day and, over the course of a year playing every day, we'll accumulate pretty $16,000. Having solved a simple equation, we'll discover that stakes of up to $1900 are profitable for us! We need to have several thousand dollars on our accounts for this game, but we don't have to blame casinos for being untruthful or inexperienced.

Let's talk about our bonuses. These are the highest "free-loading" bonuses without any deposit. One has noticed an increase in ads offering $500 for free, with no deposit. The pattern is the following You actually receive $500 with a separate account with a time limit for playing (usually an hour). You'll only receive the winnings after an hour, but not more than $500. You have to win the bonus back in a real bank account. In play free , you've run it 20 times in slot machines. This sounds fantastic, but what's the actual price of this bonus? Well, the first part requires you to be able to win $500. We can see that the chance of winning $500 is 50% based on the simplified formula. However, in practice it's much less. In order to win the bonus, you must stake 10 000 dollars on slot machines. We do not know the percentages of pay-outs from slots, however, they are provided by casinos, and average about 95% (for various kinds they fluctuate between 90 and 98 percent). If we play an average slot, then until the end of the bet, we'll have $500-10 000*0.05=$0 in our bank account, which is not a bad game... If we're lucky enough to choose a slot with payouts that are high, we could await $500-10 000*0,02=$300. Although the chance to choose a slot with payouts that are high is 50% (you have listened to the opinions of other gamblers since the random selection of this probability will make up hardly more than 10-20%, as there are only a handful of slots with high payouts), in this case the value of a generous deposit-free bonus amount to $300*0,5*0,5=$75. It's less than $500 but still not too poor, although we can see that even with the most ideal suppositions, the final value of the bonus has been reduced by seven times.

I'm hoping that this journey into the maths of bonuses will be of use for gamblers. If you're looking to win, you just need to think a little and calculate.

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