Notes

Online Casinos: The Mathematics of Bonuses
Casino players who play online are aware that these bonuses are offered in many casinos. While "Free-load" might seem attractive, they're not really worthwhile. Are they profitable for gamblers? This question is dependent on many factors. The answer to this question is possible using math.

Let's start with a typical bonus upon deposit: you make $100, and then receive another $100 and it's possible to get having put up $3000. This is a common example of a bonus earned for the first deposit. Although the size of a bonus or deposit may differ and so do the stake rate. But one thing is sure: the bonus amount is still able to be withdrawn following the wagering requirement. In general, it is impossible to withdraw any money.

If you are going to play at the online casino for a long period of time, and you are persistent about it you are a player, this bonus could aid you, and it could really be considered free money. 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 some complications. For instance, if your goal is to just take a look at the casino without spending a lot of time there, or if you enjoy roulette or other games which aren't permitted under bonus rules, you could be denied access to the bonus. In most casinos there is no way to withdraw cash or simply return a deposit, when a wager isn't made on games permitted at the casino. If you are keen on blackjack or roulette, and a bonus can be returned only through playing slots, place the required $3000 of stakes, in the course of the 95% payouts, you will lose on average $3000*(1-0,95)=$150. As you see, you are not just losing the bonus, but you also have to take out of your account $50, in the case of this, it's better to not accept the bonus. If blackjack or poker will be able to recoup the bonus with a casino profit of 0.5 percent, it's possible to expect that you will get $100-3000*0,005=$85 after you've redeemed the bonus.
"sticky" or "phantom" bonuses:

Casinos are becoming more popular because of "sticky" and "phantom bonuses. These bonuses are the equivalent to lucky chips in real casino. It isn't possible to withdraw the bonus amount. The bonus amount must be kept on the account, as if it "has been shackled". It may at first appear as if there's no reason to get an offer - you'll never be able to withdraw money at all however this isn't true. It's not worth the cost if you win. However, if you fail, the bonus could prove useful. Without a bonus , you've lost your $100 and you're done. If the bonus was not "sticky" the $100 remains in your account. This will allow you to wiggle out of the situation. There is a chance to win back the bonus in this case is a bit less than 50 percent (for that you only need to put the whole amount on the chance of winning in roulette). In order to maximize profits from "sticky" bonuses one needs to use the strategy "play-an-all-or-nothing game". In reality, if you are playing with small stakes, you'll eventually lose money because of the negative mathematical expectancy in games, and the bonus will only prolong suffering, and won't aid you win. 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 important to determine the amount you would like to gain, such as $200, and be willing to take chances to be successful. 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:

A bonus that is rarely seen is the return of lost. There can be singled out two options - either the complete refund of the deposit lost and the cash is typically paid back as with an ordinary bonus or a portion (10-25 percentage) of the losing for a fixed time period (a week or month). In play the game , the situation is practically identical to the case with the "sticky" bonus - if we win, there is no point in the bonus, however it helps in case of losing. Math calculations will be also identical to "sticky" bonus and the strategy of the game is the same: we take risks, try to win as many times as we can. It is possible to play with the money you've earned even if we don't succeed. The partial refund of losses for an active gambler can be seen as a minor benefit of casinos in games. You'll lose about $50 when you play blackjack using an average math expectation of 0.5%. With 20% of return 10 cents will be returned to you, that is the loss you'll suffer is $40, which is comparable to the growth in math expectancy up to 0,4 percent (ME with return = theoretical ME of the game * (1-% of return). But, from the bonus you will also get benefit, for that you will need to play less. You only make one, however an extremely high stake, for example $100, using the same roulette stakes. The majority of cases again we win $100, and 51% of the time we lose $100. However, at the close of the month, we receive our 20% which is equal to $20. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. The stake has a positive mathematical probability. However, dispersion is large and we will only be able to play in this manner once per week or once per month.

Let me briefly address the issue. I'm a little off-topic. One forum member claimed that tournaments weren't fair. He stated, "No normal person will ever put a stake in during the final 10 minutes." The 3,5-fold increase is more than the prize amount ($100) in the case of the maximum loss, so that you won't lose. What's the purpose?"

It makes sense. It's very similar to the variant that involves losing a stake. If a stake has won it is already in the black. If it has lost - we'll be awarded a prize in a tournament of $100. So, the math expectancy of the above-mentioned stake amounting to $350 is: $350*0,49-($350-$100)*0,51=$44. We could be losing $250 right now, however we we'll be able to win $350 next day and, over the course of a year playing each day, we'll accumulate pretty 16 000 dollars. We'll discover that stakes as high as $1900 could be profitable for us if we solve an easy equation. Of course, to play this kind of game, we'll must have hundreds of dollars in our account, but we certainly can't be blamed for dishonesty by casinos or gamblers for being foolish.


Let's come back to our bonuses, to the most "free-load" ones- with no requirement for any deposit. There are an increase in ads offering $500 for free, without deposit. You get $500 for an account with a specific number of players, as well as only a certain amount of time to play (usually one hour). After an hour you get just the amount of your gain, but still not greater than $500. The money is transferred to an actual account, where you have to be able to win it back, just like any other bonus, typically after when you have played it 20 times in slot machines. $500 for free sounds appealing however, what is the actual value of the reward? The first thing to consider is requires you to be able to win $500. Based on a simplified formula, we will see that the probability of winning is 50 percent (in practice, it is certainly even smaller). To win the bonus back it is necessary to bet at least $10 000 in slots. The pay-out percentages of slot machines aren't well-known. They average around 95% and fluctuate between 90-98% for different types. If we get at an average slot, till the end of the bet, we'll have $500-10 000*0.05=$0 in our bank account, which is not an excellent game... If we happen to choose a slot with large payouts, we can expect to win $500-10 000*0.02=$300. The probability of choosing one with the highest payout is 50 percent. However, you have been influenced by the comments of other gamblers that this probability will not exceed 10-20%. In this instance, the generous deposit bonus of $300*0.5*0.5=$75. Much less than $500, but still not too bad, even though we see that even with the most ideal suppositions, the amount of the bonus has been reduced by seven times.

I'm hoping that this journey into the maths of bonuses will be helpful to gamblers . If you're looking to win, you simply must think about it and calculate.

Here's my website: https://charlesgquick14.edublogs.org/2021/08/04/try-blackjack-switch-the-best-cards-in-every-hand/