Online Casinos. Mathematics of Bonuses.Posted by Nick Niesen on October 26th, 2010 Online casino players know that the latter ones offer various casino bonuses. "Free-load" looks attractive, however, are they really useful these bonuses? Are they profitable for gamblers? The answer to this question depends on a lot of conditions. Mathematics will help us answer this question. Let's begin with an ordinary casino bonus on deposit: you transfer $100 and obtain $100 more, which it will be possible to get having staked $3000. It is a typical example of casino bonus on the first deposit. The sizes of a deposit and bonus can be different, as well as the required stake rates, but one thing remains unchangeable - the amount of the casino bonus is accessible for withdrawal after the required wager. Till this moment it is impossible to withdraw money, as a rule. If you are going to play in the online casino for a long time and rather insistently, this casino bonus will help you, it can really be considered free money. If you play casino slots with 95% pay-outs, a bonus will allow you to make on average extra 2000$ 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 simply want to have a look at a casino, without playing for a long time, if you prefer roulette or other casino games, forbidden by casinos' rules for winning back bonuses. In the majority of online casinos you won't be allowed to withdraw money or will simply return a deposit, if a wager is not made on the games allowed in the online casino. If you are keen on roulette or blackjack, and a bonus can be won back only by playing 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 bonus. Anyway, if blackjack and poker are allowed for winning back the bonus with a casino's profit only 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. The "sticky" or "phantom" bonuses: The cash back bonus: 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 person 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 casino game we need to have thousands of dollars on our 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 deposit. Of late one has been able to notice more and more casino 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 casino account where you must win it back, like any casino bonus, usually having run it 20 times in casino slots. $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 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 casino slots. We don't know the rates of pay-outs in casino slots, they are not published by online 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 casino 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 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 casino 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 casino bonus has decreased seven-fold. I hope, this excursion into mathematics domain of online casino bonuses will be of use to gamblers - if you want to win, you simply need to think a little and make calculations. Like it? Share it!More by this author |