The cash back bonus: There is a seldom encountered variant of a bonus, namely return of loosing. There can be singled out two variants – the complete return of the lost deposit, at this the returned money usually is to be won back like with an ordinary 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” bonus – if we win, there is no point in the bonus, but it helps in case of losing. Math calculations will be also analogous to the “sticky” 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 gambler can be regarded as an insignificant advantage of casinos in games. If you play blackjack 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 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 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 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 bonuses, to the most “free-load” ones- without any deposit. Of late one has been able 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 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 bonus back, you need to stake $10 000 in slots. We don’t know the rates of pay-outs in 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 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 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.

I hope, this excursion into mathematics domain of bonuses will be of use to gamblers - if you want to win, you simply need to think a little and make calculations.

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