Online Casinos: The Mathematics of Bonuses
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Casino players online are aware that bonuses are available in a variety of casinos. "Free-load" looks appealing, but do they actually provide these bonuses? Are they worth the money for gamblers? Answering this question will depend on a variety of factors. The answer to this question is possible using math.
Let's begin with the typical bonus on deposit. You transfer $100 and get $100 more. It is possible after you have staked $3000. This is a common instance of a bonus on the first deposit. The size of the bonus and deposit may differ and so can the required stake rates, but one thing remains unchangeable : the amount of the bonus can be withdrawn after the wager is completed. As a rule, it is impossible to withdraw money.
If you intend to play in the online casino for a lengthy period of time, and you are persistent about it you are a player, this bonus could assist 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 such as if you simply want to have the chance to play at a casino, without having to play for long and you are a fan of roulette or any other game, forbidden by casinos' rules to win back bonuses. In most casinos, there is no way to withdraw money or will just return your deposit when a wager isn't placed on the games that are allowed at the casino. There is a chance to win a bonus when playing roulette or blackjack however only if you make the required 3000 stakes. In the 95% of all payouts that you'll lose an average of $3000* (1-0,95) equals $150. You lose $50 and also forfeit the bonus. In this scenario it's better not to accept the bonus. If blackjack or poker will be able to recoup the bonus with a casino profits 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 "phantom" bonuses
Casinos are becoming more popular due to "sticky" and "phantom bonuses. These bonuses are equivalent to lucky chips in real casino. The amount of bonus cannot be taken out, it must remain on the account (as if it "has been glued" to it) until it's entirely lost or is canceled on the first withdrawal of cash (disappears as if it were a phantom). It may appear that such a bonus is not worth the effort. It isn't possible to withdraw any money, however this is not true. It's not worth it if you win. However, if you fail, the bonus may be useful. You have already lost $100 with no bonus. If the bonus was not "sticky", $100 remains in your account. This could help you to wiggle out of the situation. The odds of winning the bonus is just half (for this, you'll only have to put the full amount of the bonus 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 low stakes, you'll gradually and eventually lose because of the negative math expectation in games, and the bonus is likely to prolong suffering, and won't aid 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. You should set the amount you wish to gain, such as $200, and be willing to take chances 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).
Cash back Bonus:
A bonus that is rarely noticed is the return of lost. Two types of bonuses can be distinguished: the complete return of the deposit. The money is usually to be won back just like an normal bonus. Or a partial return (10-25 percent) over a time period (a month or a week). In the second case, the scenario is essentially identical to the case with a "sticky" bonus. In the event that we win, there is no point in the bonus, however, it helps in case of losing. The "sticky bonus" calculation of math will be comparable. The method of play for the game is identical that we bet and win as often as is possible. If we are not lucky and we have lost the game, we can continue to play using this money, thus decreasing the risk. The partial refund of losses for a gambler who is active can be considered to be an unimportant benefit of casinos when playing games. You will lose about $50 when you play blackjack using an average math expectation of 0.5%. With 20% of return the amount of $10 is returned to you. That means your loss will be 40 dollars, which is comparable to the increase in math expectancy up to 0,4% (ME with return = theoretical ME of the game * (1percent of return). But, the bonus, you can also gain benefit, for that you'll need to be playing less. With the same stakes in roulette, we place one, but it's an enormous 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. The stake has a positive mathematical probability. But, the dispersion is large and we will only be able to play in this manner once each week or every month.
I will allow myself to make a brief remark, but somewhat diverging from the primary subject. One forum member declared that tournaments weren't fair. He stated, "No normal person will ever stake a single stake within the final 10 minutes." The amount is 3,5 times the prize amount ($100) in nomination of maximum losing, so as not to lose. What's the purpose?
What is the sense? This situation is like the one that has loss of money. We're in the black if a stake has been won. 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 may be losing $250 right now, however we shall get $350 the next day and, over the course of a year playing each day, we'll build up $16,000. Having solved a simple equation, we'll find out that stakes up to $1900 are profitable for us! We'll need several thousand dollars on our accounts for this game, but we shouldn't blame casinos for being shady or naive.
Let's revisit our bonuses, to the best "free-load" ones- with no requirement for any deposit. Recently, one has seen an increasing number of ads promising up to $500 absolutely free , with no cost and without deposit. You will receive $500 in exchange for an account that is unique, and only a certain amount of time to play (usually an hour). After apps , you receive only the amount you gain, but still not greater than $500. You must win the bonus back in a real bank account. In most cases, you've run it 20 times in slot machines. It sounds great but what's the exact cost of the bonus? First, let's look at the first step is that you must win $500. We can see that the odds of winning $500 is 50% based on the simplified formula. But in reality, it's much less. In order to win the bonus You must be able to stake at least $10 000 on slots. The pay-out percentages of slot machines aren't well-known. They range from 95 to 95%, but can vary between 90-98% for various kinds of. The average slot gives us between $500 and 000*0.05=$0. That's not an unreasonable amount. If we're lucky enough to choose a slot with large payouts, we can await $500-10 000*0,02=$300. The chance of selecting a slot with high payouts is 50%. But, fun player games heard the opinions of other gamblers as the probability of winning will be between 10-20 percent. In this instance the bonus for depositing is generous of $300*0.5*0.5=$75. Although it is less than $500, this is still an excellent amount. However, we can find that the bonus's final value has dropped sevenfold even with the best estimates.
I'm hoping this look into the mathematics realm of bonuses will be useful for gamblers. If you'd like to win, all you need is to think about and perform calculations.
Let's begin with the typical bonus on deposit. You transfer $100 and get $100 more. It is possible after you have staked $3000. This is a common instance of a bonus on the first deposit. The size of the bonus and deposit may differ and so can the required stake rates, but one thing remains unchangeable : the amount of the bonus can be withdrawn after the wager is completed. As a rule, it is impossible to withdraw money.
If you intend to play in the online casino for a lengthy period of time, and you are persistent about it you are a player, this bonus could assist 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 such as if you simply want to have the chance to play at a casino, without having to play for long and you are a fan of roulette or any other game, forbidden by casinos' rules to win back bonuses. In most casinos, there is no way to withdraw money or will just return your deposit when a wager isn't placed on the games that are allowed at the casino. There is a chance to win a bonus when playing roulette or blackjack however only if you make the required 3000 stakes. In the 95% of all payouts that you'll lose an average of $3000* (1-0,95) equals $150. You lose $50 and also forfeit the bonus. In this scenario it's better not to accept the bonus. If blackjack or poker will be able to recoup the bonus with a casino profits 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 "phantom" bonuses
Casinos are becoming more popular due to "sticky" and "phantom bonuses. These bonuses are equivalent to lucky chips in real casino. The amount of bonus cannot be taken out, it must remain on the account (as if it "has been glued" to it) until it's entirely lost or is canceled on the first withdrawal of cash (disappears as if it were a phantom). It may appear that such a bonus is not worth the effort. It isn't possible to withdraw any money, however this is not true. It's not worth it if you win. However, if you fail, the bonus may be useful. You have already lost $100 with no bonus. If the bonus was not "sticky", $100 remains in your account. This could help you to wiggle out of the situation. The odds of winning the bonus is just half (for this, you'll only have to put the full amount of the bonus 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 low stakes, you'll gradually and eventually lose because of the negative math expectation in games, and the bonus is likely to prolong suffering, and won't aid 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. You should set the amount you wish to gain, such as $200, and be willing to take chances 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).
Cash back Bonus:
A bonus that is rarely noticed is the return of lost. Two types of bonuses can be distinguished: the complete return of the deposit. The money is usually to be won back just like an normal bonus. Or a partial return (10-25 percent) over a time period (a month or a week). In the second case, the scenario is essentially identical to the case with a "sticky" bonus. In the event that we win, there is no point in the bonus, however, it helps in case of losing. The "sticky bonus" calculation of math will be comparable. The method of play for the game is identical that we bet and win as often as is possible. If we are not lucky and we have lost the game, we can continue to play using this money, thus decreasing the risk. The partial refund of losses for a gambler who is active can be considered to be an unimportant benefit of casinos when playing games. You will lose about $50 when you play blackjack using an average math expectation of 0.5%. With 20% of return the amount of $10 is returned to you. That means your loss will be 40 dollars, which is comparable to the increase in math expectancy up to 0,4% (ME with return = theoretical ME of the game * (1percent of return). But, the bonus, you can also gain benefit, for that you'll need to be playing less. With the same stakes in roulette, we place one, but it's an enormous 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. The stake has a positive mathematical probability. But, the dispersion is large and we will only be able to play in this manner once each week or every month.
I will allow myself to make a brief remark, but somewhat diverging from the primary subject. One forum member declared that tournaments weren't fair. He stated, "No normal person will ever stake a single stake within the final 10 minutes." The amount is 3,5 times the prize amount ($100) in nomination of maximum losing, so as not to lose. What's the purpose?
What is the sense? This situation is like the one that has loss of money. We're in the black if a stake has been won. 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 may be losing $250 right now, however we shall get $350 the next day and, over the course of a year playing each day, we'll build up $16,000. Having solved a simple equation, we'll find out that stakes up to $1900 are profitable for us! We'll need several thousand dollars on our accounts for this game, but we shouldn't blame casinos for being shady or naive.
Let's revisit our bonuses, to the best "free-load" ones- with no requirement for any deposit. Recently, one has seen an increasing number of ads promising up to $500 absolutely free , with no cost and without deposit. You will receive $500 in exchange for an account that is unique, and only a certain amount of time to play (usually an hour). After apps , you receive only the amount you gain, but still not greater than $500. You must win the bonus back in a real bank account. In most cases, you've run it 20 times in slot machines. It sounds great but what's the exact cost of the bonus? First, let's look at the first step is that you must win $500. We can see that the odds of winning $500 is 50% based on the simplified formula. But in reality, it's much less. In order to win the bonus You must be able to stake at least $10 000 on slots. The pay-out percentages of slot machines aren't well-known. They range from 95 to 95%, but can vary between 90-98% for various kinds of. The average slot gives us between $500 and 000*0.05=$0. That's not an unreasonable amount. If we're lucky enough to choose a slot with large payouts, we can await $500-10 000*0,02=$300. The chance of selecting a slot with high payouts is 50%. But, fun player games heard the opinions of other gamblers as the probability of winning will be between 10-20 percent. In this instance the bonus for depositing is generous of $300*0.5*0.5=$75. Although it is less than $500, this is still an excellent amount. However, we can find that the bonus's final value has dropped sevenfold even with the best estimates.
I'm hoping this look into the mathematics realm of bonuses will be useful for gamblers. If you'd like to win, all you need is to think about and perform calculations.
