The Math Behind Online Casino Bonuses
All online casinos have a lot of bonuses going on. To see whether they are worth it, we have analyzed the most common ones from a mathematical point of view.
One of the most common bonuses is the deposit Bonus. If you want to stake $3000 in an online casino's game and initially deposit $100, the casino will double your first deposit so that your account would reflect $200, but you cannot withdraw this total immediately. It would only be accessible to you once you have completed your wager requirements.
In the long run, this will work well for you as you are getting free money. You could earn $2000 on slots with a 95% payout. $100/(1-0.95)=$2000. Online casinos put a catch to these bonuses and allow them to be played only on specific games. If for instance, winning back the bonus is only for slots but your prefer blackjack or roulette, and still play anyway, then it would be to your disadvantage.
With $3000 of required stakes and an average of 95% payout you would lose: $3000x(1-0.95)=$150. You wasted the $100 bonus and spent an extra $50. But if your preferred games are applicable for the bonus and you win, you get to earn: $100-(3000x0.005)=$85.
Phantom or Sticky Bonuses are money that cannot be withdrawn and stays in your account until your first withdrawal. It may seem useless if you're winning but it is useful if you're on a losing streak. If you've already consumed your initial deposit of $100, you could use the phantom bonus and try to win your money back. The possibility is less than 50%, but if you use the 'all-or-nothing' strategy, then this might work in your favor.
Even a $49% probability would give you positive expectancy as ($200x0.49)-($100x0.51)=$47. For this, it is advisable to use the Martingale system and other progressive strategies. If you get a $150 phantom bonus when you deposited $100, and you plan to increase it to $500, your probability of success can be computed as: (100+150)/500=50%. With zero mathematical expectancy, the real value of the bonus is [(100+150)/500 x (500-150)]-100=$75.
Cash Back Bonuses are a return of your losses completely or partially over a period of time. As with the phantom bonus, this bonus is only useful if you are losing and the calculations are the same. If you play blackjack with 0.5% math expectancy and a $10,000 stake, your average loss is $50. If theoretically your cash back bonus is 20%, $10 would be returned to you so you lose only $40 increasing your math expectancy to 0.4%. For $100 in roulette with a 51% lose ratio, you still get 20% off or $20 off from your loss. $100x0.49 - [($100-/$20)x0.51]=$8.20 is your expectancy so play this rarely.
Some casinos advertise Free Money Bonuses like $500 that you need to consume playing with a limited time and you get to keep your winnings. If you want to gain $500 with a 50% probability, you'd have to stake $10,000 in slots which usually have a 95 to 98% payout. $500-$10,000x0.05=$0 for an average payout and $500-$10,000x0.02=$300 for a high payout game. Basically, the value of this bonus is $300x0.05x0.05=$75, which really is not bad at all.