Setting Table Maximum Betting Limits

Introduction | Key Principles | Setting Limits | Mathematics | Effective Maximum Bet Limits | Variable Betting | Volume Dependence | Maximum Loss Point | Variable Bet Distribution | Non High-End Casino Operation | Analysis of Results | Conclusion |

Another use of this particular information would be to assess daily, weekly, monthly and yearly performance and determine whether or not the actual results fell within an acceptable range, based on probabilistic considerations.

From the above example the following may be calculated as the range of casino win (prior to expenses and fees ) which would be achieved, with a probability of results falling outside these parameters, being likely to occur on one occasion in twenty :

Win = Bav N.E%

Lower probability limit = Bav .N.E%-1.645.Bav sqrt (V.N.( 1 + ( SB/B)^2)) 

Taking into account taxes, expenses and fees the following net profit forecasts may be presented.

Clearly this type of information is essential in establishing possible cash flow discrepancies and whether or not monthly and yearly statements of profit and loss are reasonable. For example, once displayed in this manner, the shareholders may either accept the risk implied, based on the assumptions made and the table maximum bet limits offered, or request a review of those limits to establish tighter, more consistent returns. It should be noted, at this point, that what has been assessed is a situation where all bets made at a table are non-cancelling. That is, that bets have been made by the players on the table on the same proposition and not on opposing bets where the casino essentially takes no risk. At Baccarat, for example, if one player has $5 on “Player”, and another player has $5 on “Banker”, the casino either draws or wins. If “Player” wins, one bet pays the other; but if “Banker” wins, the casino takes 5% . In reality the casino takes a risk only on non-cancelling bets, but must be prepared to accept the risk associated by allowing non-cancelling bets at the bet limits provided. When assessing actual results, in relation to the probability of occurrence based on bet distribution information, it is critical that this be understood.

Another piece of information that may be of use is the calculation of the probability of ruin, from the casino’s perspective, if all bets were made at the table maximum and all bets were non-cancelling.

If the table maximum were $7,000 and the casino had capital of $5,000,000 then the effective number of units (a) which the casino possesses is : $5,000,000/$7,000 which equals 714. If the game under consideration is Baccarat, with a probability of the house winning (p) of 0.50625 and a probability of losing (q) of 0.49375, then based on the following formula (ref 6) we have :

risk = (q/p)^a
risk = ( 0.49375/0.50625 )^ 714
risk = 0.00000002

The casino is not taking much of a chance of going to ruin, and starting with such a large amount of capital, in relation to the maximum bet allowed, would steadily get richer if that capital could accumulate.

____________________________________________________________
ref 6 Allan N. Wilson, The Casino Gambler’s Guide: Enlarged edition page 264.
____________________________________________________________