Notes

Online Casinos: The Mathematical Logic of Bonuses
Casino players who play online are aware that these bonuses are available in many casinos. "Free-load" appears attractive, however, are they really worth these bonuses? Are they lucrative for gamblers Answering this question depends on a variety of factors. This question can be answered by math.

Let's begin with the typical bonus for deposits. read here deposit $100 and get another $100. This is feasible after you stake 3000. This is an example of bonus for the first deposit. Although the size of a deposit or bonus may vary, so can the stake rate. But one thing is sure: the bonus can still be withdrawn after the wagering requirement has been met. In general, it is not possible to withdraw any money.


It is considered free money if you are playing at the casino online for a long period of time and are persistent. 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)=$2000), after that the amount of bonus will be over. But there can be complications, for example, if you want to simply take the chance to play at a casino without having to play for long and you are a fan of roulette or other games, which are not permitted by the rules of casinos to win back bonuses. In most casinos, you will not be able to withdraw cash or simply refund a deposit if a wager is not made on the games allowed at the casino. There is a chance to win a bonus by playing blackjack or roulette however, only if meet the minimum stakes of 3000. In the 95% payouts that you'll lose an average of 3000$ (1-0,95) = $150. You lose $50 and also lose the bonus. In this scenario it's better not to accept the bonus. If poker or blackjack could win back the bonus with a casino profit of 0.5%, it is possible that you will get $100-3000*0,005=$85 after you've earned back the bonus.
"Sticky" click here as "phantom" bonuses

More and more popularity in casinos is gained by "sticky" or "phantom" bonuses - similar to luck chips in real casinos. The amount of the bonus cannot be withdrawn the bonus, and it will remain in the account (as if it "has stuck" to it) until it's totally lost or canceled after the first time you withdraw cash (disappears like it's a phantom). On first glance, it might appear as if there's no sense in such a bonus - you won't be able to withdraw money at all, but it's not completely correct. The bonus won't be worth the cost if you win. However, if you lose, it could be beneficial. Already, you've lost $100 with no bonus. However, with a bonus even if it's an "sticky" one, $100 remain on your account, which could assist you in getting out of the situation. The odds of winning the bonus is less than half (for this you will only need to stake 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". If you only play little stakes, you will eventually lose money because of the negative mathematical expectations in games. Moreover, the bonus is likely to prolong agony, and won't help you to 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. Set the amount you would like to win, for instance $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 recognized is the possibility of returning money lost. Two types of bonuses can be distinguished: the complete refund of deposit. The money is usually to be won back just like an ordinary bonus. Or a partial return (10-25%) over a fixed period (a week or a month). The first situation is identical to that of a "sticky bonus" The bonus is useless if you win, but helps when you lose. In the second case, the "sticky bonus" mathematical calculation will be comparable. The principle of the game is similar that we bet to win as frequently as possible. It is possible to play with the money we've won, even if we don't succeed. A partial return on the loss gambler could be considered to be an unimportant benefit of casinos when playing games. It is possible to lose $50 on average when you play blackjack using a math expectancy of 0.5%. You'll get back $10 even if you make a loss of 20 dollars. This is equivalent to the math expectancy rise of 0.4 percent. However, from the given bonus, you can also gain from the fact that you will need to play less. In the same way as on roulette, we play one, but it is an enormous stake. We win $100 in 49% of instances, while $100 is won by 51%. However, we lose $100 in 51% of the cases. When we finish each month, we get back 20% of our $20 winnings. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. It is evident that the stake is then positive in math expectancy, but dispersion is big for it to be played in this manner very rarely - once a week or even once per month.

I'll let myself make an unintentional remark that is slight deviation from the main issue. In a forum for casinos, one of the gamblers began to assert that tournaments were unfair. They argued as follows: "No normal person will ever be able to make a single wager within the last 10 minutes of the event, which 3,5-fold surpasses the prize amount ($100) and in the event of a maximal losing, so that they can take home a prize. What's the point?

And really does it make sense? It's quite similar to the one with return of losing. We are in the black if the stake is won. If it is lost, we'll get 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. web site could lose $250 today, but we will win $350 next day. Over a year of playing every day and earning a total of 365, our earnings will be pretty impressive , at 365*$44=$16000. If we can solve a basic equation, we'll discover that stakes of up to $1900 are profitable for us! It is essential to have thousands on our accounts for this game, but we shouldn't blame casinos for being untruthful or inexperienced.

Let's come back to our bonuses, specifically the highest "free-load" ones, without any deposit. One has noticed more and more ads promising $500 for free, with no deposit. The way to look at it is this You actually receive $500 on a special account and limited time for play (usually one hour). After an hour, you will receive just the amount of your gain, but still not greater than $500. The bonus must be redeemed back in a real bank account. Most often, you've been able to play it for 20 times in slot machines. It sounds wonderful however, what is the real price of this bonus? The first thing to consider is requires you to win $500. We can determine that the chance of winning $500 is 50% using the simplified formula. But in reality, it is much lower. The second part - we win the bonus back and you have to bet at least $10 000 on slots. We aren't aware of the rate of pay-outs in slots, they are not published by casinos and make up on average approximately 95 percent (for different types they vary about 90-98%). An average slot will give us $500-10 000*0.05=$0. It's not an unreasonable amount. We can expect $500-10 000*0.02=$300 if we're lucky enough to land a lucrative slot. The chance of selecting one with high payouts is 50 percent. However, you have been influenced by the comments of other gamblers that the probability of winning will be between 10-20%. In this case the bonus for depositing is generous of $300*0.5*0.5=$75. A lot less than $500 but still not too poor, although we can observe that even with the most optimal suppositions the value of the bonus has decreased seven-fold.

I'm hoping this look into the mathematical realm of bonuses will be useful for gamblers. If you'd like to succeed, all you have to do is to think about and perform calculations.

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