Notes

Online Casinos: The Mathematics of Bonuses
Casino players online are aware that these bonuses are offered in many casinos. While "Free-load" might sound appealing, they are not worthwhile. Are they lucrative for gamblers This question is dependent on many different factors. This question can be answered by math.

Let's begin with the typical bonus on deposit. You deposit $100 and receive another $100. This is possible after you have staked $3000. It is an example of a bonus on your first deposit. While the amount of a bonus or deposit can vary, so can the stake rate. However, one thing is sure: the bonus amount can be taken out after the wagering requirement. As a rule, it is not possible to withdraw money.

If you intend to play at the online casino for a lengthy period of time, and you are persistent about it 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. But there can be complications, for example, if you want to simply take a look at a casino without having to play for long, if you prefer roulette or other games, prohibited by casino rules to win back bonuses. If you aren't betting on any of the permissible games, casinos are unlikely to allow you to withdraw money. If you're a fan of blackjack or roulette, and a bonus is won back only by playing slots, make the required $3000 of stakes during the 95% payouts, you'll lose $3000*(1-0,95)=$150. The loss is $50 and you also forfeit the bonus. In this scenario it's best not to take the bonus. In any case, if blackjack and poker can be used to win back the bonus, with a casino's profits of just 0,5%, so it can be expected that after reclaiming the bonus, you'll have $100-3000*0,005=$85 of the casino's money.
"sticky" or "phantom" bonus:

Casinos are becoming increasingly popular for "sticky" as well as "phantom bonuses. These bonuses are equivalent of lucky chips in a real casinos. The amount of the bonus cannot be taken out the bonus, and it will remain on the account (as if it "has been glued" to it), until it is completely lost, or annulled upon the first withdrawal cash means (disappears as if it were it's a phantom). It may at first appear that there is no sense in such an offer - you'll never be able to withdraw money at all however this isn't accurate. If you are a winner, there's no reason in the bonus, however even if you lose the money, it could be of use to you. Without a bonus , you've lost your $100 , and that's it, bye-bye. However, with a bonus even if it is a "sticky" one, you will find that $100 are still in your account, which could aid you in escaping the circumstance. The odds of winning the bonus is just half (for this, you'll only have to put the full amount in 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 surely if you stake tiny amounts. The negative math expectancy of games means that you will not win any bonuses. 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 important to determine the amount you would like to earn, like $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:

The most common bonus noticed is the return of lost funds. Two types of bonuses could be distinguished: the complete refund of deposit. The money is usually to be returned just as an normal bonus. Also, a partial return (10-25 percent) for a set period (a week or a month). In the first scenario, the situation is practically identical to that of a "sticky" bonus. If you win, there's no point in the bonus, however, it is helpful in the event of loss. In the second case, the "sticky bonus" mathematical calculation will be analogous. The strategy of the game is similar: we play and win as often as possible. We can still play with the money we've won, even if we fail to succeed. read more on the loss for an active gambler can be regarded as an insignificant benefit of casinos in games. If you are playing blackjack with math expectancy - 0,5%, after you have staked 10 000 dollars, you'll lose an average of $50. With 20% of return the amount of $10 is returned to you, which means that the amount your loss will be 40 dollars, which is equal to the increase in math expectancy 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 play less. We make only one but very high stake, like $100, with the same bets on roulette. We can win $100 in 49% of the cases and $100 is taken home by 51% of players. We lose $100 in 51% of the cases. At the end of every month, we receive back 20 percent of our winnings from $20. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. The stake has a positive math probability. However, dispersion is huge and we'll only be able play this way once each week or every month.

I will allow myself to make a brief remark, but slight deviation from the main subject. In a forum for casinos, one gambler began to claim that tournaments were not fair, arguing it as follows: "No normal person will ever stake a single penny within the final 10 minutes of the tournament that is 3,5 times greater than the amount of prize ($100) as a result of a loss that is as high as so that they can take home a prize. What's the issue?"

Does it really make sense? The scenario is identical to the scenario with return of losing. If a stake has won the stake is already in the black. The stake will be awarded a prize of $100 if the stake is lost. 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 win $350 in the future. In the course of a year of daily play, our total earnings will be pretty impressive at 365*$44=$16 000. If we can solve a basic calculation, we'll see that stakes up to $1900 are profitable for us! Of course, for such a game we need to have many thousands of dollars in our accounts, but we certainly can't be blamed for dishonesty by casinos or gamblers for being naive.

Let's revisit our bonuses, specifically the most "free-load" ones- without any deposit. One has noticed an increase in ads offering $500 for free, with no deposit. You get $500 for an account with a specific number of players, as well as only a certain amount of time to play (usually an hour). After an hour, you will receive only the amount of your gains, but not more than $500. The gain is transferred on a real account where you have to win it back, like any other bonus, generally after having run it 20 times in slots. $500 free -it sounds attractive however, what is the real price of the bonus? The first thing to consider is that you have to win $500. By using a simple formula, we can see that the probability of winning is 50% (in reality, it's definitely lower). In order to win the bonus back, you need to stake $10 000 in slots. We don't know the rates of payouts on slots, they are not released by casinos and make up on average about 95 percent (for various kinds they fluctuate around 90-98 percent). An average slot will give us between $500 and 000*0.05=$0. That's not an awful amount. We can expect $500-10 000*0.02=$300 if we're lucky enough to locate a high-paying slot. The chance of selecting a slot with high payouts is 50%. But, you've been influenced by the comments of other gamblers that this probability will not exceed 10-20%. In this instance, the generous deposit bonus of $300*0.5*0.5=$75. Although it is less than $500, it is an impressive amount. But, we can find that the bonus's final value has decreased by sevenfold even with the most accurate assumptions.


I'm hoping this look into the maths of bonuses can prove beneficial to gamblers. If you'd like to be successful, all you need is to think about and perform calculations.

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