Notes

Online Casinos: Mathematics of Bonuses
Casino players online are aware that bonuses are offered in many casinos. "Free-load" is appealing, but are they really useful are they really worth it? Are they lucrative for gamblers The answer to this question is contingent on many factors. Mathematics will assist us in answering this question.

Let's begin with the typical bonus for deposits. You transfer $100 and get $100 more. This will be feasible after you stake 3000. It is a typical instance of a bonus on the first deposit. fun games to play online of the bonus and deposit may be different in addition to the stake requirements however one thing is unchangeable : the amount of the bonus can be withdrawn after the required wager. In general, it is not possible to withdraw any funds.

The bonus is free money when you are playing at the casino online for a long 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)=$2000), after that the amount of bonus will be over. There are a few pitfalls in the event that you want to simply take a look at a casino without playing for a long period of time and you are a fan of roulette or other games, forbidden by casinos' rules for winning back bonuses. In most casinos you won't be allowed to withdraw funds or just return your deposit in the event that a bet isn't placed on the games that are allowed in the casino. You can win a bonus when playing roulette or blackjack, but only if you meet the minimum stakes of 3000. If you're lucky enough to win 95% of all payouts that you'll lose an average of 3000$ (1-0,95) which is $150. As you see, you do not just lose the bonus, but you also have to take out of your account $50, in this scenario, it's best to refuse the bonus. If poker or blackjack will be able to recoup the bonus by earning a profit of 0.5%, it is likely that you'll get between $100 and $3000, which is equal to $85 after you've earned back the bonus.
"sticky" or "phantom" bonuses:

A growing amount of popularity in casinos is due to "sticky" or "phantom" bonuses, which are similar to lucky chips in real casinos. It isn't possible to cash out the bonus. The bonus must be placed on the account as if it "has been shackled". It may at first appear that there is no sense in such an offer - you'll never be able to withdraw money at all however this isn't accurate. It's not worth it if you are successful. However, if you lose, it could be useful. Already, you've lost $100, without a bonus. Even if the bonus is not "sticky" the $100 will still be in your account. This can help you to wiggle out of the situation. The chance of winning back the bonus in this case is around 50% (for that you only need to bet 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". If you only play small stakes, you'll slowly and surely lose because of the negative math expectancy in games, and the bonus is likely to prolong the pain, and will not help 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. It is important to determine the amount you wish to earn, like $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:


The most common bonus seen is the return of lost. It is possible to distinguish two variations - the full refund of the deposit lost in which case the cash is typically paid back as with normal bonuses or a portion (10-25%) of the loss over the fixed period (a week, a month). In the second case, the situation is practically identical to the case with a "sticky" bonus. If we win, there is no point in the bonus, however it can be helpful in the event loss. Math calculations will be also similar to the "sticky" bonus, and the strategy is the same: we take risks and try to win as much as we can. We can still bet with the money that we've won, even if we don't take home the prize. Casinos that offer games may provide an opportunity to earn a portion of the loss to gamblers who have a high level of activity. If you play blackjack with math expectancy - 0,5%,, having made stakes on $10,000, you'll lose on average $50. You'll get back $10 even if you make a loss of 20 dollars. This is the equivalent of the math expectancy rise of 0.4%. But, the bonus, you can also gain benefits, which means you'll need to play less. You only make one, however an extremely high stake, like $100, with the same bets on roulette. The majority of cases we also win $100 and 51% of the time we lose $100, but at the end of the month we get back our 20%, which is 20 dollars. As http://www.firstlinux.com/juegoscasino/ is $100*0,49-($100-$20)*0,51=$8,2. It is evident that the stake has a positive math expectation, however the its dispersion is huge, since it to be played this way only at least once per week or every month.

Let me make a brief remark. I am slightly off-topic. One of the forum members declared that tournaments weren't fair. He stated, "No normal person will ever put a stake in in the last 10 minutes." The amount is 3,5 times the prize amount ($100) in nomination of maximum losing, so it's impossible to lose. What's the purpose?"

It makes sense. The situation is like the one that has return on 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. We could lose $250 today, but get $350 the next day and, over the course of a year playing every day, we'll earn 16 000 dollars. We'll discover that stakes up to $1900 are profitable for us if we solve an easy equation. We need to have thousands on our accounts for this kind of game, but we can't blame the casinos for being shady or naive.

Let's come back to our bonus offers, especially the highest "free-load" ones- without any deposit. In recent times, we've been able to notice an increasing number of ads promising the possibility of up to $500 completely free of charge, without deposit. The pattern is the following You actually receive $500 on a special account with a time limit for play (usually one hour). The only thing you will get is the amount you win after one hour, but never more than $500. The bonus must be redeemed back in a real bank account. Usually, you have been able to play it for 20 times in slot machines. It sounds wonderful, but what's the actual price of the bonus? The first part is that you have to win $500. Based on a simplified formula, we can determine the odds of winning are 50 percent (in the real world, it's certainly even smaller). If you want to get the bonus back, you need to stake $10 000 in slots. We aren't aware of the rate of pay-outs in slots, they are not released by casinos and make up on average about 95% (for different types they vary between 90 and 98 percent). If we get at an average slot, then until the end of the bet, we'll have $500-10 000*0.05=$0 in our bank account, which is not a bad game... We can expect $500-10 000*0.02=$300 in the event that we are lucky enough to locate a high-paying slot. The chance of selecting the slot that has high payouts is 50%. You've been influenced by the comments of other gamblers that this probability will not exceed 10-20%. In this instance the deposit bonus is generous of $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 that the total value of the bonus has decreased seven-fold.

I hope, this excursion into the mathematics of bonuses will be of use for gamblers. If you're looking to be successful, you only need to think a little and make calculations.

My Website: http://www.firstlinux.com/juegoscasino/