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Online Casinos: The Mathematics of Bonuses
Online casino players know that these casinos offer a range of bonuses. "Free-load" looks appealing, but do they actually provide such bonuses? Are they lucrative for gamblers The answer to this question is contingent on many factors. This question can be answered using math.

Let's start with a normal bonus on deposit. You transfer $100 and get another $100. This is possible after you have staked $3000. This is an example of a bonus on the first deposit. While the amount of a bonus or deposit may differ and so do the stake rate. But one thing is sure: the bonus amount can still be withdrawn after the wagering requirement. It generally is impossible to withdraw any funds.

If you intend to be playing at an online casino for a lengthy time and rather insistently you are a player, this bonus could help you, it can 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 a few pitfalls. For example when your objective is to simply have a peek at the casino, without spending a lot of time there, or if you enjoy roulette or other games that are not permitted by the bonus rules, then you may not be able to gain access to the bonus. If you do not wager in any of the permitted games, most casinos won't let you withdraw cash. Bonuses can be won by playing blackjack or roulette 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) equals $150. In other words, you do not just lose the bonus but also have to take out of your wallet $50. In this case it is better to decline the bonus. If blackjack or poker can win back the bonus with a casino profit of 0.5 percent, it's likely that you'll receive $100-3000*0,005=$85 after you've earned back the bonus.
"sticky" or "phantom" bonuses:

The popularity of casinos is due to "sticky" or "phantom" bonuses - equivalent to casino chips that are lucky in real life. The amount of bonus cannot be taken out the bonus, and it will remain in the account (as as if it "has stuck" to it), until it is totally lost or canceled upon the first withdrawal cash (disappears like a phantom). At first sight it may seem that there is little value in a bonus - you won't be able to withdraw money at all however this isn't accurate. If you are a winner, there's no reason in the bonus, but in the event that you lose the money, it could help you. You've already lost $100, without a bonus. But with a bonus, even if it is an "sticky" one, $100 are still in your account, which can help you worm out of the circumstance. The chance of winning back the bonus in this case is around 50 percent (for it is only necessary to put the whole amount on the chance of winning in 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 small stakes, you'll gradually and eventually lose because of the negative math expectations in games. Moreover, the bonus will only prolong agony, and won't 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 of your gain, for example $200, and try to win it by 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:

A bonus that is rarely recognized is the possibility of returning money lost funds. It can be distinguished into two variants - the complete return of the deposit that was lost in which case the cash is typically returned as normal bonuses or a part return (10-25%) of the amount lost for a fixed time period (a week or a month). The first scenario is almost the same as the "sticky bonus" The bonus is not worth it when you win however, it is beneficial in the event that you lose. Math calculations are identical to "sticky" bonus and the game's strategy is similar - we risk, try to win as much as we can. You can gamble with the money we've won, even if we don't succeed. Casinos with games offer a partial return on losing for active gamblers. You'll lose $50 on average if you play blackjack with a math expectancy of 0.5%. With 20% of return $10 will be given back to you, that is the loss you'll suffer is 40 dollars, which is equivalent to the growth in math expectancy to 0,4% (ME with return=theoretical ME of the game (1- % of return). You can still derive profit from the bonus but you will need to play less. In the same way as on roulette, we place one, however it's the largest stake. The majority of cases we again win $100, and 51% - we lose $100, however at the close of the month, we receive our 20% which is equal to $20. 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 probability, but the dispersion is big for you to play this way only at least once per week or once per month.

single player games 'll allow myself to make a brief remark, but slight deviation from the main issue. One of the forum members said that tournaments were unfair. He stated, "No normal person will ever be able to stake a single stake in the last 10 minutes." This 3,5-fold exceeds the prize amount ($100) in the case of maximum loss, meaning as not to lose. What's the reason?

It makes sense. This situation is like the one that has loss of money. We are in the black if the stake has been won. If it is lost, we'll be awarded a prize in a tournament 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 might lose $250 today but earn $350 next day. In the course of a year of playing every day and earning a total of 365, our earnings are quite impressive , at 365*$44=$16000. If we can solve a basic equation, we'll find out that stakes of up to $1900 are profitable for us! We need to have thousands on our accounts for this game, but we don't have to blame casinos for being dishonest or foolish.

Let's go back to our bonuses. They're the top "free-loading" bonuses without any deposit. You've seen an increase in ads offering $500 for free, with no deposit. You can get $500 on a special account, and you have a time limit to play (usually one hour). After an hour, you receive just the amount of your gain, but still not more than $500. The cash is transferred to a real account where you have to win it back, like any bonus, usually having played it at least 20 times through slot machines. The $500 bonus sounds tempting, but what is the exact cost of this bonus? The first thing to consider is is that you must get $500. Using a simplified formula, we can see that the probability of winning is 50% (in reality, it's definitely lower). The second part - we receive the bonus and you have to bet at least $10 000 on slots. website -out percentages of slot machines aren't known. They are generally around 95%, but can vary between 90-98% for various kinds of. The average slot gives us $500-10 000*0.05=$0. That's not a bad amount. If we are lucky to select a slot that has large payouts, we can await $500-10 000*0,02=$300. Although the chance to choose a slot with payouts that are high is 50% (you are probably familiar with the opinions of other gamblers , since by random choice this probability will be less than 10-20%, for there are only a handful of slots with high payouts), in this case the worth of a large deposit bonus is $300*0,5*0,5=$75. It's less than $500 but still not too poor, although we can find that even with most ideal assumptions, that the total amount of the bonus has diminished seven times.


I'm hoping that this journey into the mathematics of bonuses will be helpful to gamblers . If you're looking to win, you just have to think about it and do some calculations.

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