# Online casino s: Mathematics of Bonuses

Online casino players know that the latter ones offer various bonuses. “Free-load” looks attractive, however, are they really useful these bonuses? Are they profitable for situs poker qq bettors? The answer to this question depends on a lot of conditions. Mathematics will help us answer this question.

Let’s focus on an ordinary bonus on deposit: you transfer $100 and acquire $100 more, which it will be possible to get having secured $3000. It is a typical example of bonus on the first deposit. The sizes of a deposit and bonus can be different, as well as the required pole rates, but one thing remains unchangeable — the amount of the bonus is available for disengagement after the required gamble. Till this moment it is impossible to withdraw money, as a rule.

If you are going to play in the Online casino for a long time and rather insistently, this bonus will help you, it can really be regarded as free money. If you play pai gow poker with 95% pay-outs, an additional benefit will let you make typically extra 2000 buck of pegs ($100/(1-0, 95)=$2000), after that the amount of bonus will be over. But there might be complications, for example, if you simply want to have a look at a casino, without playing for a long time, if you prefer roulette or other games, a no-no by casinos’ rules for winning back bonuses. In the majority of casinos you won’t be allowed to withdraw money or will simply return a deposit, if a gamble is not made on the games allowed in the casino. If you are keen on roulette or blackjack, and a bonus can be won back only by playing pai gow poker, make the desired $3000 of pegs, in the course of 95% of pay-outs you will lose typically $3000*(1-0, 95)=$150. As you see, you not only lose the bonus but also take from your pocket $50, in this case it is best to not allow the bonus. Anyway, if blackjack and poker are allowed for winning back the bonus with a casino’s profit just about 0, 5%, so it can be expected that after winning back the bonus you will have $100-3000*0, 005=$85 of the casino’s money.

“sticky” or “phantom” bonuses:

More and more popularity in casinos is gained by “sticky” or “phantom” bonuses — the equivalent of lucky chips in real casinos. The amount of bonus is impossible to withdraw, it must remain on the account (as if it “has stuck” to it), until it is completely lost, or annulled on the first disengagement of cash means (disappears like a phantom). At first view it may seem that there is little sense in that bonus — you won’t get money anyway, but it’s not completely true. If you win, then there is really no point in the bonus, but if you have lost, it may be of use to you. Without a bonus you have lost your $100 and that is it, bye-bye. But with a bonus, even if it is a “sticky” one, $100 are still on your account, which can help you earthworm out of the situation. A possible chance to win back the bonus in this case is a bit less than 50% (for that you only have to pole the entire amount on the chances 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 pegs, you will slowly and surely lose because of the negative mathematics expectancy in games, and the bonus will only stretch agony, and won’t help you win. Clever bettors usually try to realize their bonuses quickly — somebody pegs the entire amount on chances, in the anticipate to double it (just imagine, you pole 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, in other words, a pole has positive mathematics expectancy for you $200*0, 49-$100*0, 51=$47), some people use progressive strategies of Martingale type. It is recommended to fix the required amount of your gain, for example $200, and try to win it, taking risks. If you have contributed a deposit in the amount of $100, obtained “sticky” $150 and decide to increase the size of the sum on your account up to $500 (that is to win $250), a probability to achieve your aim is (100+150)/500=50%, when it reaches this the required real value of the bonus for you is (100+150)/500*(500-150)-100=$75 (you can substitute it on your own figures, but, please, remember the fact that the formulations pick up for games with zero mathematics expectancy, in real games the results will be lower).

The money back bonus:

There is a don’t often encountered variant of a bonus, particularly return of losing. There might be singled out two variants — the entire return of the lost deposit, when it reaches this the returned money usually is to be won back as with an ordinary bonus, or a partially return (10-25%) of the losing over the fixed period (a week, a month). In the first case the situation is practically identical to the case with a “sticky” bonus — if we win, there is no point in the bonus, but it helps in case of losing. Mathematics data will be also analogous to the “sticky” bonus and the strategy of the game is similar — we risk, try to win if you can ,. If we are not lucky and we have lost, we can play with the help of the returned money, already reducing the risk. Partially return of the losing for an active gambler can be regarded as an simple good thing about casinos in games. If you play blackjack with mathematics expectancy — 0, 5%, then, having made pegs on $10 000, you will lose typically $50. With 20% of return $10 will be given back to you, that is you losing will cost you $40, which is equivalent to the increase in mathematics expectancy up to 0, 4% (ME with return=theoretical ME of the game * (1-% of return). However, from the given bonus can also be derived benefit, for that you need to play less. We make only one but a high pole, for example $100, on the same pegs in roulette. In 49% of cases again we win $100, and 51% — we lose $100, but at the end of the month we get back our 20% that is $20. As a result the effect is $100*0, 49-($100-$20)*0, 51=$8, 2. As you see, the pole then has positive mathematics expectancy, but distribution is big for we’ll be able to play this way rather don’t often — once a week or even every.

I will allow myself a short statement, slightly digressing from the main subject. On a casino forum one of the bettors started to claim that tournaments just weren’t fair, fighting it in the following way: “No normal person will ever make a single pole within the last 10 minutes of the contest, which 3, 5-fold outclasses the prize amount ($100), in nomination of a maximum losing, so as to win. What is the? inch

And really does it add up? The situation is much like the variant with return of losing. If a pole has won — we are already in the black. If it has lost — we’ll get a contest prize of $100. So, the mathematics expectancy of the above-mentioned pole amounting to $350 is: $350*0, 49-($350-$100)*0, 51=$44. Yes, organic meat lose $250 today, but will win $350 tomorrow, and over a year playing every day, we’ll accumulate pretty 365*$44=$16 000. Having fixed a simple equation, we’ll find out that pegs up to $1900 are profitable for us! Of course, for such a game we need to have thousands of dollars on our account, but we certainly can’t responsibility casinos for dishonesty or bettors for being unreasonable.

Let’s come back to our bonuses, to the most “free-load” ones- without any deposit. Recently you have gotten to notice more and more advertisements promising up to $500 absolutely free of charge, without any deposit. The pattern is the following — you really get $500 on a special account and limited time for play (usually an hour). After an hour you get only the amount of your gain, but still not more than $500. The gain is transferred on a real account where you must win it back, like any bonus, usually having run it 20 times in pai gow poker. $500 free -it sounds attractive, but what is the real price of the bonus? Well, the first part — you need to win $500. Using a things to consider formula, we can see that probability of winning is 50% (in practice, it is certainly even smaller). The second part — we win the bonus back, you need to pole $10 000 in pai gow poker. We don’t know the rates of pay-outs in pai gow poker, they are not published by casinos and make up typically about 95% (for various kinds they go up and down about 90-98%). If we get at an average position, then till the end of the gamble we’ll have $500-10 000*0, 05=$0 on our account, not a bad game… If we are lucky to choose a position with high pay-outs, we can await $500-10 000*0, 02=$300. Even though the probability to choose a position with high pay-outs is 50% (you have listened to the opinions of other bettors since by random choice this probability will make up hardly more than 10-20%, for there are few generous slots), in this case the value of a generous deposit free bonus amounts to $300*0, 5*0, 5=$75. Much less than $500, but still not too bad, though we can see that even with the most optimal suppositions the final amount of the bonus has decreased seven-fold.

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