Online Casinos: The Mathematical Logic of Bonuses

· 6 min read
Online Casinos: The Mathematical Logic of Bonuses

Casino players who play online are aware that these bonuses are available at many casinos. While "Free-load" might seem appealing, they're not really worthwhile. Are they profitable for gamblers? The answer to this question depends on many factors. This question can be answered with mathematics.

Let's begin with the typical bonus for deposits. The deposit is $100, and you get another $100. This is possible after you stake $3000. It is a typical instance of a bonus on the first deposit. The amount of bonus or deposit may differ and so do the stake rate. However, one thing is certain: the bonus can still be withdrawn after the wagering requirement. In general, it is not possible to withdraw any funds.

The bonus is free money if you are playing at the casino online for a lengthy period of time and are persistent. 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 in the event that you want to simply take the chance to play at a casino, without having to play for long or if you like roulette or other games, prohibited by casino rules for winning back bonus. If you do not wager in any of the permitted games, casinos are unlikely to allow you to withdraw money. If you're keen on blackjack or roulette, and a bonus is earned only by playing slots, place the required stakes of $3000, in the course of 95% of pay-outs you will lose on average $3000*(1-0,95)=$150. You will lose $50, and lose the bonus. In this instance, it is better not to accept the bonus. Anyway, if blackjack and poker are allowed to claim back the bonus, with a casino's profits of just 0,5%, then it can be expected that after winning back the bonus you will have $100-$3000 plus 0,005 = $85 from the casino's profit.
"Sticky" and "phantom" bonuses

The popularity of casinos is due to "sticky" or "phantom" bonuses - equivalent to luck chips in real casinos.  play free online games 's not possible to cash out the bonus. The bonus amount must be kept on the account, like it "has been shackled". At first sight it may seem that there is little reason to get a bonus - you won't receive any money however this isn't true. If you win, then there's no reason to the bonus. However, even if you lose, it may be useful to you. Without a bonus you have lost your $100 and you're done. Even if the bonus is not "sticky" the $100 remains in your account. This will allow to get out of this situation. There is a chance to win back the amount of bonus is around 50 percent (for that you only need to put the whole amount on the odds of roulette). In order to maximize profits from "sticky" bonuses one needs to use the strategy "play-an-all-or-nothing game". It is possible to lose slowly but certainly if you play with tiny amounts. The negative math expectation of the game means you'll never win any bonus. 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. It is advised to determine the amount you want to gain, for example $200, and attempt to win it by taking chances. 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:


It is a rare variant of a bonus, namely return of losing. Two types of bonuses can be distinguished: the complete refund of deposit. At this point the deposit is generally won back just like an ordinary bonus. A partial return (10-25 percent) over a fixed period (a month or a week). In the first scenario, the situation is practically identical as with the "sticky" bonus. In the event that we win, there is no point in the bonus, however, it helps in case of loss. The "sticky bonus" mathematical calculation will be comparable. The method of play for the game is identical - we gamble to win as frequently as we can. If  playing video games  are not lucky and we have lost, we can play with the help of this money, thus minimizing the risk. The partial refund of losses gambler could be considered to be an unimportant advantage of casinos in games. If  visit website  are playing blackjack with math expectancy - 0,5%, when you stake your stakes on 10 000 dollars, you'll lose an average of $50. You'll get back $10 when you lose $20. This is the equivalent of the math expectancy rise of 0.4%. It is possible to still benefits from the bonus however, you'll need to be playing less. On the same stakes as on roulette, we place one, but it is an enormous stake. The majority of the cases again we win $100, and 51% of the time we lose $100, however at the time the month is over, we receive our 20% which is equal to $20. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. As you see, the stake is then positive in math expectation, however the it's a big dispersion, as you to play in this manner very rarely - at least once per week or once per month.

I'd like to provide a short remark. I am slightly off-topic. One of the forum members said that tournaments were unfair. He said, "No normal person will ever put a stake in during the last 10 minutes." This 3,5-fold exceeds the amount of prize ($100) in nomination of maximum loss, meaning it's impossible to lose. What's the purpose?

And really does it make sense? It's identical to the scenario that has a return on losing. We are in the black when a stake has been won. We'll be awarded a prize in a tournament of $100 in the event that it loses. So,  video games  of the above-mentioned stake amounting to $350 is: $350*0,49-($350-$100)*0,51=$44. Sure, we could lose $250 today, but we'll win $350 tomorrow, and over a year playing every day, we'll accumulate pretty 365*$44=$16 000. After completing a simple calculation, we'll see that stakes as high as $1900 are profitable for us! We'll need thousands on our accounts for this game, but we can't blame the casinos for being dishonest or foolish.

Let's go back to our bonuses. They are among the most "free-loading" bonuses without any deposit. You've seen more and more ads promising $500 free of cost, with no deposit. You can get $500 on a special account, and only a certain amount of time to play (usually one hour). After an hour, you will receive just the amount of your gains, but not more than $500. You must win the bonus on a regular account. Most often, you've run it 20 times in slot machines. This sounds fantastic but what's the exact price of this bonus? Well, the first part - you need to be able to win $500. By using a simple formula, we can determine the odds of winning are 50 percent (in reality, it's definitely lower). To get the bonus back, you must stake at least $10 000 in slots. We aren't aware of the rate of payouts on slots, they are not published by casinos and make up on average about 95 percent (for various kinds they fluctuate around 90-98 percent). An average slot will give us $500-10 000*0.05=$0. That's not an unreasonable amount. It is possible to expect $500-10 000*0.02=$300 if we're lucky enough to find a high-paying slot. Even though the probability to pick a slot that has the highest payouts is 50% (you have listened to the comments of other gamblers as by random choice this probability will make up hardly more than 10-20% since there are a few slots that pay out generously) In this instance, the value of a generous deposit-free bonus amount to $300*0,5*0,5=$75. Even though it's not $500, this is still a good amount. However, we are able to see that the bonus's final value has decreased sevenfold, even with the best possible estimates.

I'm hoping this look into the mathematics realm of bonuses can prove beneficial for gamblers. If you'd like to succeed, all you have to do is to think and do calculations.