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 $\endgroup$ 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. $\endgroup$ 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.


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