Cashback Casino Promotion:

Deposit amount: $1000

Maximum bet: $500

Turnover: $2500

House edge: 2.5%

If you lose all your money, receive $100


*Turnover is the total amount of bets the player has to achieve before losing all his money to be able to claim the bonus. (e.g bet $500 5 times)

*House edge in this case means the casino has a 52.5% chance of winning.

*the 10% cashback bonus can be used to continue betting, or can be kept by the player who decides to stop betting.

Is this exploitable?

  • $\begingroup$ i think it's probably irrelevant. I've deleted that part already. please take no notice of it. thanks for coming $\endgroup$ – DANNY.OCEAN Apr 10 '16 at 7:03
  • $\begingroup$ wouldn't the expected value for the player decrease over time? the more he plays the more he gives back to the house. $\endgroup$ – DANNY.OCEAN Apr 10 '16 at 8:02

Using the same method as I did in in this question

Is this casino promotion expolitable?

We have the following expression for the gamblers ruin probability:

$$P(k) = \frac{(q/p)^k - (q/p)^N}{1-(q/p)^N}$$

In this question we are looking for $P(k)$, with $k = 2$, $N = 7$, $p=0.475$, $q =0.525$.

$$P(\text{lose the game}) = P(2) = \frac{(0.525/0.475)^2 - (0.525/0.475)^{7}}{1-(0.525/0.475)^{7}} = 0.7817$$

$$P(\text{win the game}) = 1 - P(\text{lose the game}) = 0.2183$$

Let $G$ be the random variable taking on values $\$2600$ if the gambler wins the game, i.e. the gambler wins the turnover amount + bonus, and $-\$1000$ if the gambler loses the game.

The Casino Cashback Promotion is exploitable if the expected value of the game is greater than zero.

$$E[G] = 0.2183 \cdot \$2600 + 0.7817 \cdot (-\$1000)= -\$214$$

Hence, far from exploitable.

(Notice the necessary assumption that the gambler stops when he reaches the turnover amount)


What I've come with so far is this:

I'm counting the odds of achieving the bonus starting from the lowest number of bets:

5 BETS of 500 dollars:

Win Win Lose Lose Lose

Win Lose Win Lose Lose

Odds: 3.125% x 2 = 6.25%

Best case scenario is player has 6.25% chance of winning 100 dollars with 5 bets (or 2500 turnover)

I'm trying to figure out what the average turnover a player will have, as 2.5% of that amount will reflect whether the promotion is exploitable?

I think it's something to do with Gambler's Ruin or Huygens' Result.


protected by Community Oct 1 '16 at 17:31

Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).

Would you like to answer one of these unanswered questions instead?

Not the answer you're looking for? Browse other questions tagged or ask your own question.