Notes

Online Casinos: Mathematics of Bonuses
Online casino players know that the latter ones provide a variety of bonuses. "Free-load" is appealing, but are they really worth such bonuses? Are they worth the money for gamblers? The answer to this question is contingent on a variety of factors. Mathematical calculations can assist us in answering this question.

Let's look at an everyday bonus when you deposit $100 and obtain $100 more and it's possible to obtain after having put up $3000. business is an example of a bonus earned on your first deposit. Although the size of a bonus or deposit may differ and so do the stake rates. However, there is one thing that is for sure: the bonus can still be withdrawn after the wagering requirement. It is currently impossible to withdraw funds, as a rule.

If you are going to play at the online casino for a long duration and with a lot of intensity the bonus can 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)=$2000), after that the amount of bonus will be over. There are a few pitfalls. For instance when your objective is to simply have an overview of the casino without spending a lot of time there, or you are a fan of roulette or any other games that are not permitted by bonus rules, you could be denied access to the bonus. If you don't wager on any of the allowed games, most casinos won't allow withdrawals. Bonuses can be won by playing blackjack or roulette however only if you make the required 3000 stakes. In the 95% of all payouts the odds are of 3000$ (1-0,95) equals $150. You will do not just lose the bonus but will also be able to take from your wallet $50. In this case it is better to decline the bonus. If blackjack and poker are permitted to win back the bonus, with a casino's profits of just 0.5%, you can expect that once you have repaid the bonus, you'll have $100-3000*0,005=$85 of the casino's money.

"Sticky" and "phantom" bonuses

more information and more popularity in casinos is derived from "sticky" or "phantom" bonuses, which are similar to lucky chips in real casinos. computer 's not possible to cash out the bonus. The bonus has to be placed on the account like it "has been shackled". It may at first appear as if there's no reason to get a bonus - you won't be able to withdraw money at all however this isn't true. It's not worth it if you win. If you fail, the bonus may prove useful. You've already lost $100 without a bonus. With a bonus, even if it is one that is "sticky" one, you will find that $100 remain on your account. This can assist you in getting out of the problem. The probability of winning the bonus is less than 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". Really, if you play little stakes, you will gradually and eventually lose due to the negative math expectations in games. Moreover, the bonus will only prolong agony, and won't help 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 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).

Cash back Bonus:

The most common bonus noticed is the return of lost funds. Two kinds of bonuses can be distinguished: the full return of the deposit. At this point the cash is typically returned just as an ordinary bonus. Also, a partial return (10-25%) over a time period (a week or a month). The first scenario is nearly identical to that of the "sticky bonus" - the bonus will not be worth anything if you win, but helps if you lose. Calculations in math will also be analogous to the "sticky" bonus, and the game's strategy is similar - we risk and try to win as many times as we can. If we don't win and we have lost, we can play using this money, thus decreasing the risk. The partial refund of losses gambler could be considered to be an unimportant benefit of casinos in games. If you gamble on blackjack using the math expectation of 0,5%, after you have staked $10 000, you will lose an average of $50. If you earn 20% of the money, 10 cents will be returned to you, which means that the amount the loss you'll suffer is $40, which is equal to the increase in math expectancy to 0,4 percent (ME with return=theoretical ME the game * (1-% of return). However, from the given bonus you will also get benefits, which means you will need to be playing less. On the same stakes as on roulette, we play one, but it's an enormous stake. In 49% of the cases again we win $100, and 51% of the time we lose $100. However, at the close of the month, we receive our 20% that is $20. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. The stake has a positive mathematical probability. However, dispersion is huge and we'll only be able to play this way once per week or once per month.

Allow me to briefly address the issue. I'm a little off-topic. On a casino forum one gambler began to argue that tournaments are 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 prize ($100), in nomination of a maximal losing, so as to be able to win. What's the point?

It is logical. The situation is very similar to the variant that has a return on losing. We are in the black if the stake is 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. Sure, we could be losing $250 right now, however we shall be able to win $350 next day, and over a year playing each day, we'll earn 365*$44=$16 000. It's clear that stakes as high as $1900 could be profitable for us if we solve an easy equation. Of course, for such a game , we'll must have hundreds of dollars in our account and we can't blame casinos for dishonesty or gamblers for being foolish.

Let's revisit our bonuses, to the most "free-load" ones- with no requirement for any deposit. In recent times, we've noticed an increasing number of ads promising up to $500 absolutely free , with no cost and without any deposit. You can get $500 on 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 winnings, but no greater than $500. The bonus must be redeemed back on a real account. Usually, you have played it at least 20 times on slot machines. $500 free -it sounds attractive, but what is the real price of this bonus? The first thing to consider is that you must get $500. By using a simple formula, we can see that probability of winning is 50% (in the real world, it's certainly even smaller). To get the bonus back You must be able to stake at least $10 000 on slots. We don't know the rates of pay-outs from slots, however, they are published by casinos and average approximately 95% (for various kinds they fluctuate around 90-98 percent). If we play an average slot, then at the end of our bet, we'll have $500-10 000*0.05=$0 on our account, not an excellent game... If we're lucky enough to select a slot that has large payouts, we can expect to win $500-10 000*0.02=$300. Although the chance to pick a slot that has high pay-outs is 50% (you have heard the opinions of other gamblers , since by random choice this probability will be less than 10-20%, as there are a few slots that pay out generously) In this instance, the worth of a large deposit bonus is $300*0.5%*0.5%=$75. Although it is less than $500, this is still an excellent amount. However, we are able to see that the bonus's final value has decreased by sevenfold even with the best possible estimates.

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

Website: http://zapitano.com/