Notes

Online Casinos: Mathematics of Bonuses
Online casino players know that these casinos provide a variety of bonuses. Although "Free-load" may seem appealing, they are not worth the effort. Are they worth the money for gamblers? This question is dependent on a variety of factors. The answer to this question is possible by math.

Let's start with a normal bonus on deposit. You transfer $100 and receive another $100. It is possible after you have staked $3000. This is a common example of bonus for the first deposit. Although the size of a bonus or deposit can vary and so do the stake rates. But one thing is sure: the bonus can still be withdrawn after the wagering requirement. In general, it is not possible to withdraw any money.

The bonus is free money when you gamble online for a long 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)=$2000), after that the amount of bonus will be over. However, there are some issues to be aware of such as if you just want to take a look at a casino without having to play for long or if you like roulette or other games, which are not permitted by the rules of casinos to win back bonuses. If you don't wager in any of the allowed games, most casinos won't let you withdraw cash. Bonuses can be won by playing blackjack or roulette, but only if you have the required stakes of 3000. If you're lucky enough to win 95% of payouts, you'll lose an average of 3000$ (1-0,95) which is $150. You lose $50 and also lose the bonus. In this scenario it's better not to take the bonus. If blackjack or poker can win back the bonus, with a profit of 0.5 percent, it's likely that you'll receive $100-3000*0,005=$85 after you have won back the bonus.
"Sticky" as well as "phantombonus

The popularity of casinos is due to "sticky" or "phantom" bonuses, which are the equivalent of casino chips that are lucky in real life. It's not possible to cash out the bonus. The bonus has to be stored on the account as if it "has stuck". It may appear that such a bonus is not worthwhile. You won't be able to withdraw any money, however this isn't the case. It's not worth the cost if you win. However, if visit url lose, it could be useful. You have already lost $100 without a bonus. Even if the bonus was not "sticky" it will still be on your account. This can help you to wiggle from this mess. There is a chance to win back the bonus in this case is around 50% (for you will only have to bet 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". In reality, if you are playing with little stakes, you will slowly and surely lose because of the negative math expectation in games, and the bonus is likely to prolong the pain, and will not help you 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 suggested to set the desired amount you wish to gain, for example $200, and try to win it, while taking risks. 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:

One bonus that is seldom seen is the return of the money that was lost. Two types of bonuses can be distinguished: the full return of the deposit. At this point the deposit is generally returned just as an ordinary bonus. A partial return (10-25 percent) for a set period (a month or a week). In the first case the scenario is essentially identical to the case with the "sticky" bonus - if you win, there's no need for the bonus, but it helps in case loss. The "sticky bonus" mathematical calculation will be similar. The method of play for the game is the same: we play and win as often as possible. If we are not lucky and we have lost then we are able to play again with the the returned money, already decreasing the risk. play free games of losses for an active gambler can be regarded as an insignificant benefit of casinos in games. If you gamble on blackjack using the math expectation of 0,5%,, having made stakes on $10,000, you'll lose an average of $50. A 20% return $10 will be given back to you. That means you losing will amount to $40, which is equal to the growth in the math expectation up to 0,4% (ME with return=theoretical ME the game * (1percent of return). But, the bonus you will also get from the fact that you need to play less. You only make one, however very high stake, like $100, with the same bets on roulette. We win $100 in 49% of instances, while $100 is taken home by 51% of players. We have to lose $100 in 51% of the cases. At the end of every month, we receive back 20% of our $20 winnings. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. The stake has a positive mathematical probability. The dispersion however is large and we will only be able to play in this manner once per week or once per month.

I'll let myself make to make a brief remark, but somewhat diverging from the primary topic. In a forum for casinos, one gambler began to argue that tournaments are unfair. They argued as follows: "No normal person will ever make a single stake in the final 10 minutes of the tournament, which 3,5-fold surpasses the prize amount ($100) as a result of a maximal losing, in order to win. What's the purpose?

What is the sense? The scenario is identical to the scenario with return of losing. If a stake has won it is already in the black. We'll receive a tournament prize of $100 in the event that it loses. So, the math expectancy of the above-mentioned stake amounting to $350 is: $350*0,49-($350-$100)*0,51=$44. Yes, we may lose $250 today, but shall win $350 tomorrow in the course of a year. playing each day, we'll earn $16,000. It's clear that stakes up to $1900 can be profitable for us after solving an easy equation. It is essential to have several thousand dollars on our accounts for this game, however we shouldn't blame casinos for being dishonest or foolish.

Let's get back to our bonuses. They are among the most "free-loading" bonuses that do not require a deposit. There are increasing numbers of ads that promise $500 free of cost, with no deposit. You get $500 for a special account, and only a certain amount of time to play (usually 1 hour). The only thing you will get is the amount of your win after an hour, but no over $500. The cash is transferred to a real account where you must win it back, like any bonus, usually having played it at least 20 times on slot machines. It sounds wonderful but what's the exact value of the bonus? The first part is that you need to win $500. We can determine that the probability of winning $500 is 50% based on an easy formula. But in reality, it is much lower. If you want to get the bonus back, you need to stake $10 000 in slots. We do not know the percentages of pay-outs from slot machines, but they are provided by casinos, and average about 95% (for different types they vary between 90 and 98 percent). A typical slot can give us between $500 and 000*0.05=$0. This isn't a bad amount. If we are lucky to pick a slot with payouts that are high, we could expect to win $500-10 000*0.02=$300. Even though the probability to pick a slot that has payouts that are high is 50 percent (you have listened to the comments of other gamblers as the random selection of this probability is less than 10-20%, as there are a few slots that pay out generously), in this case the value of a generous deposit bonus is $300*0,5*0.5%=$75. While it's less than $500, it is a good amount. However, we are able to observe that the bonus's total value has dropped sevenfold even with the best estimations.

I hope this exploration into the mathematics realm of bonuses will be useful for gamblers. If you'd like to win, all you need is to think and do calculations.


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