Online Casinos: The Mathematics of Bonuses
Online casino players know that casinos that provide a variety of bonuses. "Free-load" appears appealing, but do they actually provide are they really worth it? Are they worth the money for gamblers? This is a question that depends on many factors. Mathematical calculations can help us answer this question.
Let's begin with a typical bonus for deposits. You transfer $100 and receive another $100. It is possible after you stake $3000. It is a typical example of bonus for the first deposit. Although the size of a deposit or bonus may vary, so can the stake rates. But one thing is certain: the bonus amount is still able to be withdrawn following the wagering requirement. It is currently impossible to withdraw cash in the majority of cases.
If you are going to be playing at an online casino for a long duration and with a lot of intensity 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)=$2000), after that the amount of bonus will be over. However, there are some issues to be aware of, for example, if you want to simply take a look at a casino, but not having to play for long or if you like roulette or any other game, prohibited by casino rules for winning back bonuses. In most casinos you will not be able to withdraw cash or simply refund a deposit when a wager isn't made on games permitted in the casino. Bonuses can be won by playing blackjack or roulette however, only if meet the minimum stakes of 3000. In the 95% of payouts the odds are of 3000$ (1-0,95) equals $150. You lose $50 and also forfeit the bonus. In this instance it's best not to take the bonus. If blackjack and poker are allowed to claim back the bonus, with a casino's profits of just 0,5%, then it is possible that once you have repaid the bonus you will have $100-3000*0,005=$85 of the casino's money.
"sticky" or "phantom" benefits:
A growing amount of popularity in casinos is gained by "sticky" or "phantom" bonuses - equivalent to casino chips that are lucky in real life. It's not possible to cash out the bonus. The bonus must be placed on the account like it "has stuck". It could appear that an offer isn't worthwhile. It isn't possible to withdraw any money, however this is not true. If you are a winner, there's really no use in the bonus, but in the event that you lose the money, it could help you. Already, you've lost $100 with no bonus. Even if the bonus is not "sticky", $100 will still be in your account. This will allow you to wiggle from this mess. The chance of winning back the amount you received is less than half (for this, you'll have to bet the entire amount of the bonus in 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 low stakes, you'll slowly and surely lose because of the negative mathematical expectations in games. Moreover, 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. It is recommended to fix the desired amount of your profit, for instance $200, and then try to win it, while 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:
There is a seldom encountered type of bonus, which is the return of lost. It can be distinguished into two variants - the complete refund of the deposit lost and the cash is typically paid back as with an ordinary bonus, or a partial return (10-25 percentage) of the loss during the specified time (a week or a month). In the second case, the situation is practically identical to the case with a "sticky" bonus. If we win, there's no point in the bonus, but it is helpful in the event of loss. In the second case, the "sticky bonus" mathematical calculation will be analogous. The principle of the game is similar - we gamble to win as frequently as is possible. You can play with the money we've earned, even if we fail to take home the prize. A partial return on the loss for an active gambler can be considered to be an unimportant benefit of casinos in games. If you play blackjack with the math expectation of 0,5%, then, having made stakes on $10,000, you'll lose an average of $50. With 20% of return 10 cents will be returned to you, that is you losing will amount to 40 dollars, which is equivalent to the growth in the math expectation up to 0,4 percent (ME with return=theoretical ME the game (1percent of return). But, the bonus can also be derived benefits, which means you'll need to be playing less. With the same stakes in roulette, we place one, however it's a large stake. We win $100 in 49% of instances and $100 is taken home by 51% of players. However, we have to lose $100 in 51% of instances. At the end of each month, we get back 20 percent of our winnings from $20. As a result the effect is $100*0,49-($100-$20)*0,51=$8,2. As you see, the stake has a positive math expectation, however the it's a big dispersion, as it to be played this way only every week, or every month.
Let me briefly address the issue. This is a bit off topic. One of the forum participants claimed that tournaments weren't fair. He stated, "No normal person will ever put a stake in within the final 10 minutes." The 3,5-fold increase is more than the amount of prize ($100) in the case of maximum losing, so as not to lose. What's the issue?"
Does it really make sense? The situation is very similar to the variant that has a return on losing. If a stake has won the stake is already in the black. We'll receive a tournament prize of $100 if it fails to win. 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 we'll get $350 the next day in the course of a year. playing each day, we'll build up 16 000 dollars. Having solved a simple calculation, we'll see that stakes of up to $1900 are profitable for us! Of course, for such a game , we'll must have hundreds of dollars in our accounts and we can't blame casinos for dishonesty or gamblers who are foolish.
Let's look back at our bonus offers, especially the highest "free-load" ones, without any deposit. One has noticed increasing numbers of ads that promise $500 free of cost, without deposit. The way to look at it is this you actually get $500 on a special account and limited time for play (usually one hour). After an hour, you will receive only the amount you gains, but not more than $500. You must win the bonus back on a real account. In most cases, you've run it 20 times in slot machines. It sounds great but what's the exact value of this bonus? Well, the first part - you need to be able to win $500. We can determine that the chance of winning $500 is 50% based on the simplified formula. However, in practice it's much less. In order to win the bonus, you must stake $10 000 on slots. The pay-out percentages of slot machines aren't known. playing video games are generally around 95% and fluctuate between 90-98 percent for various types. The average slot gives us between $500 and 000*0.05=$0. This isn't an unreasonable amount. If we're lucky enough to choose a slot with high pay-outs, we can expect to win $500-10 000*0.02=$300. Even though the probability to choose a slot with the highest payouts is 50% (you have listened to the comments of other gamblers as randomly, this chance will be less than 10-20%, as there are only a handful of slots with high payouts) In this instance, the value of a huge deposit-free bonus amount to $300*0,5*0.5%=$75. A lot less than $500 but still not too bad, even though we observe that even with the most ideal suppositions, the final value of the bonus has decreased seven-fold.
I'm hoping this look into the mathematical realm of bonuses will be useful to gamblers. If you'd like to be successful, all you need is to think and do calculations.