Notes

Online Casinos: The Mathematics of Bonuses
Online casino players are aware that these casinos provide a variety of bonuses. "Free-load" appears appealing, but do they actually provide are they really worth it? Are best games for gamblers The answer to this question depends on a variety of factors. This question can be answered with mathematics.

Let's begin with the typical bonus on deposit. click here for more is $100, and you get another $100. This will be feasible after you stake 3000. This is an instance of a bonus for the first deposit. Although the size of a bonus or deposit can vary as well as the stake rate. But one thing is sure: the bonus amount is still able to be withdrawn following the wagering requirement has been met. In general, it is impossible to withdraw any funds.

If you plan 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 help you, it can be considered to be 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 a few pitfalls in the event that you just want to take a look at a casino without playing for a long time or if you like roulette or other games, which are not permitted by the rules of casinos for winning back bonuses. If player games do not wager in any of the permissible games, most casinos won't allow withdrawals. If you're a fan of blackjack or roulette, and you can returned only through playing slot machines, you must make the required stakes of $3000 and in paying out 95% of the time you will lose on average $3000*(1-0,95)=$150. You will lose $50, and lose the bonus. In this case, it is better not to take the bonus. If blackjack or poker can win back the bonus with a casino profits of 0.5 percent, it's possible that you'll receive $100-3000*0,005=$85 after you've redeemed the bonus.
"sticky" or "phantom" bonuses:

A growing amount of popularity in casinos is gained by "sticky" or "phantom" bonuses - the equivalent of casino chips that are lucky in real life. It isn't possible to cash out the bonus. The bonus has to be placed on the account as if it "has stuck". It may at first appear that there is no reason to get a bonus - you won't be able to withdraw money at all however this isn't accurate. If you are a winner, there is really no point in the bonus, however in the event that you lose it might be of use to you. Without a bonus you have lost your $100 and you're done. However, with a bonus even if it's an "sticky" one, $100 are still on your account, which could aid you in escaping the problem. A possibility to win back the bonus in this case is less than 50% (for you will only have to bet the whole amount on the chances in roulette). In order to maximize profits from "sticky" bonuses one 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 games, and the bonus will only prolong suffering, and won't aid you to 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. Set the amount you wish to win, for instance $200, and take risks 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:

It is a rare variation of a bonus namely return of losing. There can be singled out two variants - the complete return of the lost deposit and the money usually is to be paid back as with normal bonuses or a portion (10-25 percent) of the loss during the specified time (a week, a month). In the first scenario, the scenario is essentially identical to that of the "sticky" bonus. If we win, there is no reason to get the bonus, however it helps in case of losing. In the second case, the "sticky bonus" math calculation will also be analogous. website of play for the game is identical that we bet and win as often as we can. If we are not lucky and we have lost the game, we can continue to play with the help of the returned money, already decreasing the risk. The partial refund of losses for a gambler who is active can be seen as a minor benefit of casinos in games. If you play blackjack with math expectancy - 0,5%, after you have staked $10 000, you will lose an average of $50. The payout is $10 if you make a loss of 20 dollars. This is equivalent to an increase in math expectancy of 0.4 percent. However, from the given bonus you will also get from the fact that you need to play less. You only make one, however a high stake, for example $100, on the same roulette stakes. In 49% of cases again we win $100, and 51% - 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. The stake has a positive math expectation. The dispersion however is huge and we'll only be able play this way once each week or every month.

I will allow myself an unintentional remark that is somewhat diverging from the primary subject. In a forum for casinos, one of the gamblers began to claim that tournaments were not fair, arguing it as follows: "No normal person will ever be able to make a single wager within the final 10 minutes of the event and this is 3,5-fold more than the amount of prize ($100) as a result of a maximal losing, so as to be able to win. What's the reason?

Does it really make sense? The situation is identical to that of return on losing. The stake is in the black if the stake is taken home. If it loses - we'll win 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. Sure, we could lose $250 today, but shall win $350 tomorrow in the course of a year. playing each day, we'll earn 365*$44=$16 000. Having solved a simple calculation, we'll see that stakes up to $1900 can be profitable for us! Of course, for this kind of game, we'll must have many thousands of dollars in our accounts and we can't be blamed for dishonesty by casinos or gamblers for being naive.

Let's look back at our bonus offers, especially the highest "free-load" ones- with no requirement for any deposit. Of late one has seen more and more advertisements promising as much as $500 free , with no cost and without any deposit. You get $500 for a special account, and a limited amount of time to play (usually an hour). You will only get the amount of your win after one hour, but never more than $500. You have to win the bonus on a regular account. Most often, you've run it 20 times in slot machines. It sounds wonderful but what's the exact cost of the bonus? The first thing to consider is that you need to get $500. Based on a simplified formula, we will see that probability of winning is 50% (in practice, it is definitely lower). If you want to receive the bonus You must bet at least $10 000 on slots. The payout rates of slot machines aren't well-known. They range from 95 to 95%, and can range from 90-98 percent for various types. If we play an average slot, till the end of the wager , we'll be able to deposit $500-10 000*0,05=$ on our account, not an awful game... You can anticipate $500 to 000*0.02=$300 If we're fortunate enough to locate a high-paying slot. The likelihood of picking a slot with high payouts is 50 percent. You've read the comments of other gamblers that this probability will not exceed 10-20 percent. In this case, the generous deposit bonus of $300*0.5*0.5=$75. Although it is less than $500, it is an excellent amount. But, we can find that the bonus's final value has decreased sevenfold, even with the most accurate assumptions.

I'm sure this trip into the maths of bonus will prove of use to gamblers . If you want to win, you just have to think about it and do some calculations.

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