Online Casinos: The Mathematics of Bonuses
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Online casino players know that these casinos offer a range of bonuses. Although "Free-load" may seem appealing, they are not worthwhile. Are they profitable for gamblers? The answer to this question will depend on a lot of conditions. Mathematical knowledge can aid us in answering this question.
Let's start with a normal bonus on deposit. The deposit is $100, and you receive another $100. This is possible after you stake $3000. This is an example of a bonus on the first deposit. Although the size of a bonus or deposit may differ and so do the stake rate. But one thing is certain: the bonus amount can still be withdrawn after the wagering requirement.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 are playing at the casino online for a prolonged period of time and you are consistent. 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 complications. In particular, if your goal 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 prohibited under bonus rules, you might be denied access to the bonus. If you don't wager on any of the permitted games, most casinos won't let you withdraw cash. If you're keen on blackjack or roulette and a bonus is won back only by playing slots, place the minimum stakes of $3000, in the course of 95% of pay-outs you'll lose $3000*(1-0,95)=$150. As you see, you are not just losing the bonus, but you also have to take out of your pocket $50, in the case of this, it's better to not accept the bonus. If poker or blackjack will be able to recoup the bonus by earning a profit of 0.5%, it is possible to expect that you'll receive $100-3000*0,005=$85 after you have won back the bonus.
"Sticky" as well as "phantombonus
More and more popularity in casinos is gained by "sticky" or "phantom" bonuses - equivalent to casino chips that are lucky in real life. The bonus amount cannot be taken out and must stay in the account (as when it "has been glued" to it), until it is entirely lost or is canceled after the first time you withdraw cash (disappears like a phantom). It may appear that such an offer isn't worthwhile. You won't be able to withdraw any money, however it's not the case. The bonus is not worth it if you are successful. But, if you fail, the bonus could prove useful. You have already lost $100, without a bonus. Even if the bonus is not "sticky" the $100 remains in your account. can i play a game will allow you get from this mess. The odds of winning the bonus is just half (for this, you'll only need to stake 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". If you only play low stakes, you'll slowly and surely lose due to the negative math expectation in games, and bonuses will only add suffering, and won't aid you to win. play games 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 profit, for instance $200, and attempt 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).
The cash back bonus:
The most common bonus noticed is the return of the money that was lost. It is possible to distinguish two variants - the complete refund of the deposit lost in which case the amount is usually returned as any other bonus or a part return (10-25%) of the amount lost for a fixed time period (a week or month). The first situation is identical to that of a "sticky bonus" The bonus is useless when you win however, it is beneficial when you lose. The "sticky bonus" mathematical calculation will be analogous. The method of play for the game is identical - we gamble to win as frequently as is possible. If we do not win and we have lost, we can play using that money back, thus minimizing the risk. Casinos that offer games may provide a partial return on losing to gamblers who have a high level of activity. It is possible to lose about $50 if you play blackjack with a math expectancy of 0.5 percent. You'll get back $10 even if you lose 20 dollars. This is the equivalent of an increase in math expectancy of 0.4%. You can still derive benefit from the bonus, but you will need to be playing less. There is only one bet, but very high stake, for example $100, with the same roulette stakes. We win $100 in 49% of the cases and $100 is taken home by 51% of players. However, we lose $100 in 51% of the cases. When we finish each month, we earn back 20 percent of our winnings from $20. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. As you see, the stake then has positive math expectation, however the its dispersion is huge, since we'll be able to play this way rather seldom - once a week or even every month.
I'd like to provide a short remark. I'm a little off-topic. One of the forum members claimed that tournaments weren't fair. He stated, "No normal person will ever be able to stake a single stake within the final 10 minutes." The amount is 3,5 times the prize amount ($100) in the nomination of the maximum loss, so that you won't lose. What is the point?"
And really does it make sense? This situation is identical to that of loss of money. The stake is in the black if the stake has been taken home. If it has 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 we will win $350 in the future. Over a year of playing each day and earning a total of 365, our earnings are quite amazing at 365*$44 = $16,000. After completing a simple equation, we'll find out that stakes as high as $1900 are profitable for us! Of course, in order to win at such a game we need to have many thousands of dollars in our accounts, but we certainly can't accuse casinos of dishonesty or gamblers for being naive.
Let's look back at our bonuses, to the most "free-load" ones- with no requirement for any deposit. There are increasing numbers of ads that promise $500 at no cost with no deposit. You get $500 for a special account, and a limited amount of time to play (usually 1 hour). After an hour, you will receive only the amount you winnings, but no greater than $500. You have to win the bonus back in a real bank account. In most cases, you've been able to play it for 20 times in slot machines. $500 for free sounds appealing however, what is the exact cost of the reward? Well, the first part - you need to be able to win $500. Using a simplified formula, we can determine that the probability of winning is 50% (in reality, it's definitely lower). In order to get the bonus back and you have to bet $10 000 in slots. The payout rates of slot machines aren't known. They range from 95 to 95% and fluctuate between 90-98% for various kinds of. If we play an average slot, then until the end of the bet, we'll have $500-10 000*0.05=$0 in our bank account, which is not a bad game... You can anticipate $500 to 000*0.02=$300 If we're fortunate enough to find a high-paying slot. Although the chance to choose a slot with high pay-outs is 50 percent (you have listened to the comments of other gamblers as randomly, this chance is less than 10-20% since there are a few slots that pay out generously) In this instance, the value of a generous deposit-free bonus amount to $300*0,5*0.5%=$75. Although it is less than $500, it's still an impressive amount. However, we can see that the bonus's final value has decreased sevenfold, even with the best estimates.
I am hoping that this investigation into the maths of bonuses can prove beneficial for gamblers. If you'd like to win, all you need is to think about and perform calculations.
Let's start with a normal bonus on deposit. The deposit is $100, and you receive another $100. This is possible after you stake $3000. This is an example of a bonus on the first deposit. Although the size of a bonus or deposit may differ and so do the stake rate. But one thing is certain: the bonus amount 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 are playing at the casino online for a prolonged period of time and you are consistent. 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 complications. In particular, if your goal 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 prohibited under bonus rules, you might be denied access to the bonus. If you don't wager on any of the permitted games, most casinos won't let you withdraw cash. If you're keen on blackjack or roulette and a bonus is won back only by playing slots, place the minimum stakes of $3000, in the course of 95% of pay-outs you'll lose $3000*(1-0,95)=$150. As you see, you are not just losing the bonus, but you also have to take out of your pocket $50, in the case of this, it's better to not accept the bonus. If poker or blackjack will be able to recoup the bonus by earning a profit of 0.5%, it is possible to expect that you'll receive $100-3000*0,005=$85 after you have won back the bonus.
"Sticky" as well as "phantombonus
More and more popularity in casinos is gained by "sticky" or "phantom" bonuses - equivalent to casino chips that are lucky in real life. The bonus amount cannot be taken out and must stay in the account (as when it "has been glued" to it), until it is entirely lost or is canceled after the first time you withdraw cash (disappears like a phantom). It may appear that such an offer isn't worthwhile. You won't be able to withdraw any money, however it's not the case. The bonus is not worth it if you are successful. But, if you fail, the bonus could prove useful. You have already lost $100, without a bonus. Even if the bonus is not "sticky" the $100 remains in your account. can i play a game will allow you get from this mess. The odds of winning the bonus is just half (for this, you'll only need to stake 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". If you only play low stakes, you'll slowly and surely lose due to the negative math expectation in games, and bonuses will only add suffering, and won't aid you to win. play games 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 profit, for instance $200, and attempt 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).
The cash back bonus:
The most common bonus noticed is the return of the money that was lost. It is possible to distinguish two variants - the complete refund of the deposit lost in which case the amount is usually returned as any other bonus or a part return (10-25%) of the amount lost for a fixed time period (a week or month). The first situation is identical to that of a "sticky bonus" The bonus is useless when you win however, it is beneficial when you lose. The "sticky bonus" mathematical calculation will be analogous. The method of play for the game is identical - we gamble to win as frequently as is possible. If we do not win and we have lost, we can play using that money back, thus minimizing the risk. Casinos that offer games may provide a partial return on losing to gamblers who have a high level of activity. It is possible to lose about $50 if you play blackjack with a math expectancy of 0.5 percent. You'll get back $10 even if you lose 20 dollars. This is the equivalent of an increase in math expectancy of 0.4%. You can still derive benefit from the bonus, but you will need to be playing less. There is only one bet, but very high stake, for example $100, with the same roulette stakes. We win $100 in 49% of the cases and $100 is taken home by 51% of players. However, we lose $100 in 51% of the cases. When we finish each month, we earn back 20 percent of our winnings from $20. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. As you see, the stake then has positive math expectation, however the its dispersion is huge, since we'll be able to play this way rather seldom - once a week or even every month.
I'd like to provide a short remark. I'm a little off-topic. One of the forum members claimed that tournaments weren't fair. He stated, "No normal person will ever be able to stake a single stake within the final 10 minutes." The amount is 3,5 times the prize amount ($100) in the nomination of the maximum loss, so that you won't lose. What is the point?"
And really does it make sense? This situation is identical to that of loss of money. The stake is in the black if the stake has been taken home. If it has 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 we will win $350 in the future. Over a year of playing each day and earning a total of 365, our earnings are quite amazing at 365*$44 = $16,000. After completing a simple equation, we'll find out that stakes as high as $1900 are profitable for us! Of course, in order to win at such a game we need to have many thousands of dollars in our accounts, but we certainly can't accuse casinos of dishonesty or gamblers for being naive.
Let's look back at our bonuses, to the most "free-load" ones- with no requirement for any deposit. There are increasing numbers of ads that promise $500 at no cost with no deposit. You get $500 for a special account, and a limited amount of time to play (usually 1 hour). After an hour, you will receive only the amount you winnings, but no greater than $500. You have to win the bonus back in a real bank account. In most cases, you've been able to play it for 20 times in slot machines. $500 for free sounds appealing however, what is the exact cost of the reward? Well, the first part - you need to be able to win $500. Using a simplified formula, we can determine that the probability of winning is 50% (in reality, it's definitely lower). In order to get the bonus back and you have to bet $10 000 in slots. The payout rates of slot machines aren't known. They range from 95 to 95% and fluctuate between 90-98% for various kinds of. If we play an average slot, then until the end of the bet, we'll have $500-10 000*0.05=$0 in our bank account, which is not a bad game... You can anticipate $500 to 000*0.02=$300 If we're fortunate enough to find a high-paying slot. Although the chance to choose a slot with high pay-outs is 50 percent (you have listened to the comments of other gamblers as randomly, this chance is less than 10-20% since there are a few slots that pay out generously) In this instance, the value of a generous deposit-free bonus amount to $300*0,5*0.5%=$75. Although it is less than $500, it's still an impressive amount. However, we can see that the bonus's final value has decreased sevenfold, even with the best estimates.
I am hoping that this investigation into the maths of bonuses can prove beneficial for gamblers. If you'd like to win, all you need is to think about and perform calculations.
