Notes

Online Casinos: The Mathematics of Bonuses
Casino players who play online know that the latter ones offer a range of bonuses. "Free-load" looks attractive, however, do they actually provide are they really worth it? Are they worth the money for gamblers? The answer to this question depends on a variety of factors. The answer to this question is possible with mathematics.

Let's begin with a typical bonus on deposit. You deposit $100 and get $100 more. This will be possible after you stake $3000. This is an example of a bonus you receive on your first deposit. Although the size of a deposit or bonus may vary as well as the stake rate. But one thing is certain: the bonus amount is still able to be withdrawn following the wagering requirement has been met. Till this moment it is impossible to withdraw cash generally.

If good games to play are going to play at the online casino for a long time and rather insistently, this bonus will help you, it can 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. In particular If your intention is to simply have an overview of the casino without spending a lot of time in there, or you are a fan of roulette or any other games that are prohibited under bonus rules, you could be denied access to the bonus. If you don't wager in any of the permitted games, casinos are unlikely to allow withdrawals. There is a chance to win a bonus by playing blackjack or roulette however only if you meet the minimum stakes of 3000. If you're lucky enough to win 95% of payouts the odds are of $3000* (1-0,95) equals $150. You will lose $50, and lose the bonus. In this scenario it's best not to accept the bonus. Anyway, if blackjack and poker can be used to claim back the bonus with a casino's earnings of only 0,5%, so it is possible that after reclaiming the bonus, you'll be left with $100-3000*0,005=$85 of the casino's money.
"sticky" or "phantom" benefits:

Casinos are increasingly gaining traction because of "sticky" as well as "phantom bonuses. These bonuses are equivalent to lucky chips in real casino. It's not possible to cash out the bonus. The bonus has to be kept on the account, as if it "has stuck". At first sight it may appear that there is no sense in such bonuses - you don't be able to withdraw money at all, but it's not completely correct. The bonus is not worth it if you are successful. However, if you fail, the bonus could be useful. If you don't have a bonus, you've lost $100, and then you're gone. If the bonus is not "sticky" it remains in your account. This could help you get out of the situation. The chance of winning back the bonus is just half (for this, you'll have to put the full amount on roulette). In order to maximize profits from "sticky" bonuses one needs to use the strategy "play-an-all-or-nothing game". You'll lose slowly and sure if you only stake tiny amounts. The negative math expectation of games means that you won't get 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. It is recommended to fix the desired amount you wish to gain, for example $200, and then try to win it, 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).

Cash back bonus:

There is a seldom encountered variation of a bonus namely return of losing. Two types of bonuses could be distinguished: the complete refund of deposit. In this case, the deposit is generally returned as an normal bonus. Or a partial return (10-25%) over a fixed period (a month or a week). In the second case, the situation is practically identical as with the "sticky" bonus - if we win, there's no reason to get the bonus, but it can be helpful in the event loss. In the second case, the "sticky bonus" math calculation will also be analogous. The principle of the game is similar: we play to win as frequently as we can. If we do not win and we have lost then we are able to play again using this money, thus taking the risk to a minimum. The partial refund of losses gambler could be considered to be an unimportant benefit of casinos in games. You will lose about $50 if you play blackjack with an average math expectation of 0.5%. If you earn 20% of the money, 10 cents will be returned to you, that is you losing will amount to 40 dollars, which is equivalent to the increase in the math expectation up to 0,4 percent (ME with return = theoretical ME of the game (1- % of return). But, from the bonus, you can also gain benefit, for that you need to be playing less. In the same way as in roulette, we play one, however it's an enormous stake. We can win $100 in 49% of instances however $100 is taken home by 51% of players. But, we have to lose $100 in 51% of cases. When we finish each month, we earn 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 math expectation, however the its dispersion is huge, since you to play this way only at least once per week or once a month.

Allow me to briefly address the issue. I'm a little off-topic. On a casino forum one of the gamblers started to claim that tournaments were unfair. They argued in the following way: "No normal person will ever stake a single penny in the final 10 minutes of the event that is 3,5 times greater than the prize ($100) as a result of a maximum loss, so that they can be able to win. What's the purpose?"

It is logical. This situation is like the one that has the return of losing. If a stake has won it is already in the black. If it is 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. We could lose $250 today, but we'll get $350 the next day and, over the course of a year playing each day, we'll build up $16,000. We'll discover that stakes of up to $1900 could be profitable after solving the simplest equation. We need to have many thousands of dollars in our accounts to play this game, but we shouldn't blame casinos for being untruthful or inexperienced.


Let's talk about our bonuses. These are the highest "free-loading" bonuses with no deposit. There are more and more ads promising $500 at no cost with no deposit. The pattern is the following - you really get $500 with a separate account with a time limit for playing (usually one hour). You'll only receive the amount you win after an hour, but not more than $500. You must win the bonus on a regular account. Usually, you have run it 20 times in slot machines. $500 free -it sounds attractive, but what is the exact cost of this bonus? The first part is that you need to get $500. Based on a simplified formula, we can determine that probability of winning is 50% (in the real world, it's likely to be even lower). The second part - we receive the bonus You must bet 10 000 dollars in slot machines. The pay-out rates in slot machines aren't known. trends are generally around 95%, and can range from 90-98 percent for various types. A typical slot can give us $500-10 000*0.05=$0. It's not an awful amount. If we happen to choose a slot with payouts that are high, we could expect to win $500-10 000*0.02=$300. The probability of choosing one with the highest payout is 50%. You've read the comments of other gamblers that this probability is not more than 10-20 10%. In this case the bonus for depositing is generous of $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 amount of the bonus has been reduced by seven times.

I am hoping that this investigation into the mathematical realm of bonuses will be useful to gamblers. If you're looking to succeed, all you have to do is to think and make calculations.

Here's my website: http://www.mac-guides-and-solutions.com/approaches-to-spin-the-roulette-wheel/