Game Volatility at Baccarat

Introduction | Mathematics | Variable Betting | Conclusion |

Clearly not all bets occur at the table maximum and thus it may be appropriate to consider both the average bet likely to be achieved and the variance of the associated bet distribution.

If the following bet distribution is considered indicative of future playing patterns then it is possible to forecast the level of turnover which needs to be generated for results to fall within a certain tolerance level of the mean, with a particular degree of certainty.

					Bet Size		% of Wagers						Weighted Average
					$200,000		0.5%						$ 1000
					$150,000		0.5%						$ 750
					$100,000		1.0%						$ 1000
					$ 75,000		4.0%						$ 3000
					$ 50,000		4.0%						$ 2000
					$ 25,000		9.0%						$ 2250
					$ 10,000		11.0%						$ 1100
					$ 5,000		70.0%						$ 3500
					TOTAL		100.00%						$14600
	The number of decisions required may be calculated using the additional variable of the variance of the bet distribution which for the above is 3.86. (The second moment over the squared mean of wagers).
		n=		1 / [( T / C)^2]					x V		x Vb
	If the degree of tolerance which is desired is equal to 0.04% then:
		n=		1 / [( 0.04% / 2.33)^2]					x 0.975		x 3.86

With an average bet of $14,600 as described previously, a turnover of $1.86 tn is required.

To calculate the period required to generate this volume of turnover it is a simple case of dividing this number by the future forecast annual turnovers volumes.

Based on forecast annual turnover volumes, this degree of certainty would be achieved after $1.86bn divided by the annual turnover volumes.