Online casino players know that the latter ones offer various casino bonuses. Sign up casino bonuses, no deposit casino bonuses or even High Rollers casino bonuses look attractive, however, are they really useful these casino bonuses? Are they profitable for casino players? The answer to this question depends on a lot of conditions. Mathematics will help us answer this question.
Let's begin with an ordinary deposit casino bonus: you transfer $100 and obtain $100 casino bonus more, which it will be possible to get having staked $3000. It is a typical example of casino bonus on the first deposit. The sizes of a casino deposit and casino bonus can be different, as well as the required stake rates, but one thing remains unchangeable - the amount of the casino bonus is accessible for withdrawal after the required wager. Till this moment it is impossible to withdraw money, as a rule.
If you are going to play in the online casino for a long time and rather insistently, this casino bonus will help you, it can really be considered free casino money. If you play casino slots with 95% pay-outs, a casino bonus will allow you to make on average extra 2000$ of stakes ($100/(1-0,95)=$2000), after that the amount of casino bonus will be over. But there can be complications, for example, if you simply want to have a look at an online casino, without playing for a long time, if you prefer roulette or other games, forbidden by casinos' rules for winning back casino bonuses.
In the majority of online casinos you won't be allowed to withdraw free casino money or will simply return a deposit, if a wager is not made on the casino games allowed in the casino. If you are keen on roulette or black jack, and a casino bonus can be won back only by playing casino slots, make the required $3000 of stakes, in the course of 95% of pay-outs you will lose on average $3000*(1-0,95)=$150. As you see, you not only lose the casino bonus but also take out of your pocket $50, in this case it is better to refuse the casino bonus. Anyway, if black jack and online poker are allowed for winning back the casino bonus with a casino's profit only about 0,5%, so it can be expected that after winning back the casino bonus you will have $100-3000*0,005=$85 of the casino's money.
The "sticky" or "phantom" casino bonuses:
More and more popularity in casinos is gained by "sticky" or "phantom" casino bonuses - the equivalent of lucky casino chips in real casinos. The amount of casino 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 withdrawal of casino cash means (disappears like a phantom). At first sight it may seem that there is little sense in such a casino bonus - you won't get money anyway, but it's not completely true. If you win, then there is really no point in the casino bonus, but if you have lost, it may be of use to you. Without a casino bonus you have lost your $100 and that's it, bye-bye. But with a casino bonus, even if it is a "sticky" one, $100 are still on your casino account, which can help you worm out of the situation. A possibility to win back the casino bonus in this case is a bit less than 50% (for that you only need to stake the entire amount on the chances in roulette).
In order to maximize profits from "sticky" casino bonuses a casino player needs to use the strategy "play-an-all-or-nothing game". Really, if you play little stakes, you will slowly and surely lose because of the negative math expectancy in casino games, and the casino bonus will only prolong agony, and won't help you win. Clever casino players usually try to realize their casino 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 casino 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 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 plan to enlarge the sum on your casino 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 casino 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 casino games with zero math expectancy, in real casino games the results will be lower).
The cash back casino bonus:
There is a seldom encountered variant of a casino bonus, namely return of loosing. There can be singled out two variants - the complete return of the lost casino deposit, at this the returned money usually is to be won back like with an ordinary casino bonus, or a partial return (10-25%) of the loosing over the fixed period (a week, a month). In the first case the situation is practically identical to the case with a "sticky" casino bonus - if we win, there is no point in the casino bonus, but it helps in case of losing. Math calculations will be also analogous to the "sticky" casino bonus and the strategy of the game is similar - we risk, try to win as much as possible. If we are not lucky and we have lost, we can play with the help of the returned money, already minimizing the risk. Partial return of the losing for an active casino player can be regarded as an insignificant advantage of casinos in games.
If you play black jack with math expectancy - 0,5%, then, having made stakes on $10 000, you will lose on average $50. With 20% of return $10 will be given back to you, that is you losing will amount to $40, which is equivalent to the increase in math expectancy up to 0,4% (ME with return=theoretical ME of the game * (1-% of return). However, from the given casino bonus can also be derived benefit, for that you need to play less. We make only one but a high stake, for example $100, on the same stakes 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 stake then has positive math expectancy, but dispersion is big for we'll be able to play this way rather seldom - once a week or even once a month.
I will allow myself a short remark, slightly digressing from the main subject. On a casino forum one of the gamblers started to claim that tournaments were not fair, arguing it in the following way: "No normal casino player will ever make a single stake within the last 10 minutes of the tournament, which 3,5-fold surpasses the prize amount ($100), in nomination of a maximal losing, so as to win. What is the point?"
And really does it make sense? The situation is very similar to the variant with return of losing. If a stake has won - we are already in the black. If it has 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. Yes, we may lose $250 today, but shall win $350 tomorrow, and over a year playing every day, we'll accumulate pretty 365*$44=$16 000. Having solved a simple equation, we'll find out that stakes up to $1900 are profitable for us! Of course, for such a game we need to have thousands of dollars on our casino account, but we certainly can't blame casinos for dishonesty or gamblers for being foolish.
Let's come back to our casino bonuses, to the most "free-load" ones- without any casino deposit. Of late one has been able to notice more and more advertisements promising up to $500 casino bonus absolutely free of charge, without any deposit. The pattern is the following - you really get $500 on a special casino account and limited time for play in th casino (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 casino account where you must win it back, like any casino bonus, usually having run it 20 times in casino slots. $500 free casino money - it sounds attractive, but what is the real price of the casino bonus? Well, the first part - you need to win $500.
Using a simplified formula, we can see that probability of winning is 50% (in practice, it is certainly even smaller). The second part - we win the casino bonus back, you need to stake $10 000 in slots. We don’t know the rates of pay-outs in casino slots, they are not published by casinos and make up on average about 95% (for various kinds they fluctuate about 90-98%). If we get at an average slot, then till the end of the wager we'll have $500-10 000*0,05=$0 on our account , not a bad game... If we are lucky to choose a casino slot with high pay-outs, we can await $500-10 000*0,02=$300. Even though the probability to choose a casino slot with high pay-outs is 50% (you have listened to the opinions of other gamblers 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 casino 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.
I hope, this excursion into mathematics domain of bonuses (online casinos free money) will be of use to gamblers - if you want to win, you simply need to think a little and make calculations. |