Player Loss

Introduction | What is the cost of rebating? | How large a value? | Unit Normal Linear Loss Integral | Baccarat (Player/ Bank 50% Equivalent) | Roulette (single number play on single zero Roulette) | Conclusion |

What is the cost of rebating a percentage of loss to a player or Junket organiser?
Firstly, it is important to recognise that the theoretical loss by a player is a combination of all winning and losing events experienced by a player in a game for a given number of results. Because most Casino games are fundamentally biassed against the player, that result is a negative from the player’s perspective. Simply, that result may be calculated by multiplying the house advantage by the number of decisions and the average bet. Rebating a percentage of theoretical loss takes into account therefore both winning and losing situations and provides a long term validity to the policy of rebating a percentage of theoretical loss.

Thus, when theoretical loss is dealt with factors such as average bet, time played, decisions per hour and house advantage are incorporated. However, when actual loss is being dealt with most policies only deal with the amount of the loss. It is critical that other factors such as the number of decisions are incorporated, as criteria are essential to ensure that the policy is valid. This is because it is erroneous to believe that the percentage of actual loss rebated provides the same percentage of theoretical loss. In fact, if a policy rebates a fixed percentage of loss which is something greater than the house advantage, then the theoretical cost to the company will range from approximately the rebate percentage divided by twice the house advantage and would minimise at the rebate percentage. If the rebate on loss percentage were 10% and the house advantage 1.25%, then the theoretical cost of the rebate will range from roughly 400% of theoretical win at maximum, in an even chance game, and minimise at 10%.

The maximum cost would be realised if only one hand were played and then the player settled and were paid the rebate, with the minimum theoretical cost occurring if the player didn’t settle until they had played a very large number of hands. Many would argue that no one would play only one hand and then settle or that of course no rebate would be paid under such a scenario. The real problem is that without play criteria it is the customer who may be in control of the net outcome. Much like the transition from paying complimentaries as a percentage of drop or credit line to basing these on calculations of theoretical Casino win, so to must rebate on loss policies change to mathematically sound business decisions.

When rebating on loss, what must be calculated is the conditional mean of all situations where the player loses. In all cases because we are dealing with biassed games that value will exceed or equal the mean of all possible events, both winning and losing, which we refer to as the player’s theoretical loss.

If a rebate on loss policy is to be sound, it is a percentage of the latter which should be utilised to calculate an equivalent rebate on loss percentage for a given number of decisions. That can be accomplished by determining the percentage of theoretical loss relative to the conditional mean of only player losses.

In a simple one hand example on an even money game, if normally the Casino were prepared to pay back 50% of theoretical loss then for each $1 wagered the player would receive 50% of the house advantage multiplied by the number of decisions. If the edge were 1.2% then 0.6% of $1 would be paid back to the player regardless of whether they won or lost. If it were only the player who lost to be rewarded then that player could be provided nearly twice as much, as the net position would be compensated by the winning player receiving nothing. Why slightly less than double? Because the player would lose 50.6% of the time and thus paying 1.186% of actual loss if settlement occurred after a single hand would be the equivalent of paying 50% of theoretical loss for the example cited.

As the number of hands increases so to does the percentage of actual loss which may be rebated until such time as the number of hands played is so large that in virtually every instance the player loses and thus the rebate percentage on actual loss may equal the percentage of theoretical loss. This is due to the fact that in such a case the theoretical loss (mean) and the conditional mean are one and the same. If 50% of theoretical loss were the general policy to be returned, then the maximum rebate on actual loss would also be 50%.