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Online Casinos: The Mathematics of Bonuses
Online casino players know that casinos that provide a variety of bonuses. While "Free-load" might sound appealing, they are not worth the effort. Are they profitable for gamblers? Answering this question is contingent on many factors. Mathematics will aid us in answering this question.

Let's begin with an ordinary bonus when you deposit $100, and then receive another $100 that it is possible to get having staked $3000. This is an example of a bonus on the first deposit. While the amount of a bonus or deposit can vary as well as the stake rate. However, one thing is sure: the bonus can still be withdrawn after the wagering requirement. It generally is impossible to withdraw any funds.

If you are going to play at the online casino for a long duration and with a lot of intensity you are a player, this bonus could aid you, and it could be considered as 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. In particular If your intention is to just take a peek at the casino, without spending a lot of time there, or you enjoy roulette or other games that are not permitted by bonus rules, you could be denied access to the bonus. If over at this website don't wager on any of the permissible games, most casinos won't let you withdraw cash. If you're a fan of blackjack or roulette, and a bonus can be won back only by playing slots, place the required $3000 of stakes, in the course of paying out 95% of the time you will lose on average $3000*(1-0,95)=$150. You will lose $50, and lose the bonus. In this scenario, it is better not to take the bonus. If blackjack and poker can be used to claim back the bonus with a casino's profits of just 0.5%, it can be expected that once you have repaid the bonus you will have $100-$3000 plus 0,005 = $85 from the casino's profit.
"sticky" or "phantom" bonus:

The popularity of casinos is due to "sticky" or "phantom" bonuses, which are similar to lucky chips in real casinos. It isn't possible to withdraw the bonus amount. The bonus must be stored on the account like it "has stuck". It may at first appear as if there's no sense in such an offer - you'll never get money anyway however, this isn't accurate. It's not worth it if you are successful. But, if you lose, it may be useful. Without a bonus you have lost $100, and then you're gone. If the bonus was not "sticky", $100 will still be in your account. This could help to get from this mess. There is a chance to win back the bonus in this case is a bit less than 50 percent (for it is only necessary 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". If blog here play low stakes, you'll slowly and surely lose because of the negative mathematical expectancy in games, and bonuses will only add 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 advised to determine the desired amount you wish to gain, for example $200, and try to win it, while 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).

The cash back bonus:

There is a seldom encountered variation of a bonus specifically, the return of a lost deposit. There can be singled out two options - either the complete return of the deposit that was lost in which case the cash is typically paid back as with normal bonuses or a part return (10-25 percentage) of the losing for a fixed time period (a week or month). The first scenario is almost the same as the "sticky bonus" which will not be worth anything in the event of winning, but helps in the event that you lose. Math calculations are similar to the "sticky" bonus and the strategy is the same: we take risks trying to win as many times as we can. It is possible to gamble with the money we've earned, even if we fail to win. The partial refund of losses gambler could be regarded as an insignificant benefit of casinos when playing games. If you play blackjack with the math expectation of 0,5%, when you stake your stakes on $10,000, you'll lose an average of $50. A 20% return 10 cents will be returned to you. That means you losing will amount to $40, which is comparable to an increase in math expectancy up to 0,4 percent (ME with return=theoretical ME of the game * (1percent of return). It is possible to still benefit from the bonus, however, you'll need to play less. You only make one, however a high stake, like $100, with the same stakes in roulette. The majority of instances, we again win $100, and 51% of the time we lose $100. However, at the time the month is over, we receive our 20%, which is 20 dollars. 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 expectation, however the it's a big dispersion, as you to play in this manner very rarely - once a week or even once a month.

I will allow myself to make a brief remark, but somewhat diverging from the primary issue. On a casino forum one of the gamblers started to argue that tournaments are not fair, arguing it in the following way: "No normal person will ever stake a single penny within the last 10 minutes of the event and this is 3,5-fold more than the prize ($100) as a result of a maximal losing, so that they can win. What's the point?

It makes sense. It's identical to that of return on losing. The stake is in the black if a stake has been taken home. If games to play has lost - 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. Yes, we may be losing $250 right now, however we shall be able to win $350 next day, and over a year playing each day, we'll accumulate pretty 16 000 dollars. Having solved a simple calculation, we'll see that stakes as high as $1900 can be profitable for us! Of course, for such a game we require many thousands of dollars in our account, but we certainly can't accuse casinos of dishonesty or gamblers who are foolish.


Let's revisit our bonuses, specifically the highest "free-load" ones- without any deposit. Recently, one has noticed an increasing number of ads promising the possibility of up to $500 completely free of charge, without deposit. You can get $500 on an account that is unique, and only a certain amount of time to play (usually one hour). The only thing you will get is the winnings after an hour, but not over $500. 1 player games is transferred on a real account where you are required to get it back as any other bonus, typically after when you have played it 20 times through slot machines. $500 free -it sounds attractive but what's the actual value of this bonus? The first thing to consider is is that you must win $500. Based on a simplified formula, we will see the odds of winning are 50% (in the real world, it's certainly even smaller). In order to get the bonus back You must bet at least $10 000 on slots. The pay-out percentages of slot machines are not known. They range from 95 to 95% and fluctuate between 90-98 percent for various types. A typical slot can give us between $500 and 000*0.05=$0. This isn't an unreasonable amount. You can anticipate $500 to 000*0.02=$300 in the event that we are lucky enough to locate a high-paying slot. Even though the likelihood to select a slot with high pay-outs is 50% (you have listened to the comments of other gamblers as the random selection of this probability will make up hardly more than 10-20% since there are few generous slots) In this instance, the worth of a large deposit bonus is $300*0,5*0.5%=$75. A lot less than $500 but not too bad, even though we see that even with the most optimal suppositions the final value of the bonus been reduced by seven times.

I hope, this excursion into mathematics domain of bonuses will be useful for gamblers. If you want to win, you simply need to think a little and calculate.

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