Notes

Online Casinos: The Mathematics of Bonuses
Casino players online are aware that these bonuses are offered in many casinos. "Free-load" appears blog here , but are they really worth such bonuses? Are they lucrative for gamblers The answer to this question is contingent on a variety of factors. This question can be answered using math.

Let's begin with the typical bonus on deposit. The deposit is $100, and you get $100 more. This will be possible after you have staked $3000. This is an instance of a bonus for the first deposit. The amount of deposit or bonus may vary and so do the stake rate. But one thing is certain: the bonus can still be withdrawn after the wagering requirement has been met. It generally is impossible to withdraw any funds.

If you are going to play at the online casino for a lengthy duration and with a lot of intensity you are a player, this bonus could assist you. It can be considered to be 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)=$2000), after that the amount of bonus will be over. There are some complications. In particular If your intention is to simply have an overview of the casino, without spending a lot of time there, or if you enjoy roulette or other games which aren't permitted by the bonus rules, then you could be denied access to the bonus. If you aren't betting in any of the allowed games, most casinos won't let you withdraw cash. You can win a bonus when you play roulette or blackjack, but only if you make the required 3000 stakes. If you're lucky enough to win 95% of payouts that you'll lose an average of 3000$ (1-0,95) which is $150. As you see, you do not just lose the bonus, but will also be able to take from your account $50, in this scenario, it's best to refuse the bonus. In any case, if blackjack and poker can be used to claim back the bonus and the casino's profits of just 0,5%, then you can expect that after reclaiming the bonus, you'll have $100-$3000 plus 0,005 = $85 from the casino's profit.
"sticky" or "phantom" benefits:

Casinos are increasingly gaining traction due to "sticky" as well as "phantom bonuses. These bonuses are equivalent to the lucky chips found in a real casinos. It's not possible to withdraw the bonus amount. The bonus must be placed on the account as if it "has been shackled". It might appear as if an offer isn't worthwhile. You will not be able to take any money out, but this isn't the case. It's not worth it if you win. However, if you lose, it could be useful. You have already lost $100 without a bonus. However, with a bonus even if it is an "sticky" one, $100 are still on your account, which can aid you in escaping the circumstance. There is a chance to win back the bonus is around 50 percent (for that you only need to put the whole amount on the chance of winning 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 little stakes, you will slowly and surely lose because of the negative math expectation in games, and the bonus will only prolong agony, and won't help you gain. 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 winnings, such as $200, and try to win it by taking risk. 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. There can be singled out two options - either the complete refund of the deposit lost, at this the returned amount is usually won back like with normal bonuses, or a partial return (10-25 percent) of the losing for a fixed time period (a week, a month). The first scenario is almost identical to that of a "sticky bonus" The bonus is not worth it if you win however it can be helpful when you lose. In the second case, the "sticky bonus" math calculation will also be comparable. play games for real money of the game is the same: we play to win as frequently as possible. If we don't win and lose then we are able to play again using that money back, thus minimizing the risk. Casinos in games can offer an opportunity to earn a portion of the loss for active gamblers. If you are playing blackjack with math expectancy of 0,5%, then, having made stakes on $10,000, you'll lose an average of $50. You'll get back $10 when you make a loss of $20. This is the equivalent of the math expectancy increase of 0.4%. It is possible to still profit from the bonus but you'll have to play less. We make only one but a high stake, for example $100, on the same roulette stakes. In 49% of cases we again win $100, and 51% of the time we lose $100, but at the time the month is over, we receive our 20%, which is 20 dollars. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. As you see, the stake is then positive in math expectancy, but its dispersion is huge, since you to play this way only once a week or even every month.


I will allow myself a short remark, somewhat diverging from the primary subject. In a forum for casinos, one gambler began to claim that tournaments were unfair. They argued in the following way: "No normal person will ever stake a single penny within the last 10 minutes of a tournament that is 3,5 times greater than the prize ($100), in nomination of a loss that is as high as so as to be able to win. What's the purpose?

And really does it make sense? It's quite similar to the one that has a return on losing. We are in the black if a stake has been won. If it loses - 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. Sure, we could lose $250 today but win $350 tomorrow. Over a year of daily play and earning a total of 365, our earnings will be quite impressive at 365*$44=$16 000. After completing free play online , we'll see that stakes as high as $1900 can be profitable for us! We'll need thousands on our accounts for this game, however we can't blame the casinos for being dishonest or foolish.

Let's revisit our bonus offers, especially the highest "free-load" ones, without any deposit. In recent times, we've noticed an increasing number of ads promising up to $500 absolutely free of charge, without deposit. The way to look at it is this You actually receive $500 with a separate account and limited time for playing (usually an hour). After an hour, you receive just the amount of your gains, but not more than $500. You must win the bonus back on a real account. In most cases, you've run it 20 times in slot machines. This sounds fantastic, but what's the actual cost of the bonus? The first aspect is that you must be able to win $500. We can determine that the chance of winning $500 is 50% based on a simplified formula. In reality, it is much lower. go to my blog - we win the bonus back You must bet 10 000 dollars in slot machines. We aren't aware of the rate of pay-outs in slots, they are not released by casinos and make up on average approximately 95 percent (for various kinds they fluctuate about 90-98%). If we play an average slot, until the end of the bet, we'll have $500-10 000*0.05=$0 on our account, not an excellent game... If we happen to pick a slot with large payouts, we can look forward to $500-10 000*0,02=$300. Even though the probability to select a slot with payouts that are high is 50% (you have heard the opinions of other gamblers since the random selection of this probability will be less than 10-20% since there are a few slots that pay out generously) in this scenario, the value of a generous deposit bonus is $300*0.5%*0.5%=$75. Although it is less than $500, it is an impressive amount. But, we can observe that the bonus's total value has decreased sevenfold, even with the most accurate assumptions.

I'm hoping that this journey into mathematics domain of bonus will prove helpful to gamblers . If you want to win, you just need to think a little and do some calculations.

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