Game Volatility at Baccarat

Introduction | Mathematics | Variable Betting | Conclusion |

It is clear, based upon the above calculations that the variation in win percentage from theoretical should decrease as turnover volumes increase. The quantum of turnover required for the actual win percentage achieved to fall within a certain level of tolerance can be calculated based on the following formula:

n =

1 / [( T / C )^2]

x V

x Vb

where n

= number of decisions

T

= absolute deviation from the mean

C

= z score associated with a desired confidence interval

V

= Variance of a single game (average squared result)

Vb

= Second moment over the squared mean of wagers

turnover

= n x average bet

This same formula may be modified depending on which variables may be known. For example, it is useful if full play details are known to calculate the probability of the result. To do this the formula is solved to determine the value C. C = T / [( V x Vb/ n )sqrt]

where T

= the actual deviation from the mean

n

= actual turnover divided by the average bet

Once C is calculated a z score has been established representing the standard deviation from the mean of a normal distribution curve. z score statistical tables may then be reviewed to determine the probability of the actual result occurring.

This information once calculated can be very useful in establishing that the games are being conducted legitimately. A highly improbable result may be worthy of follow up and investigation.

As has been shown, the actual win percentage will tend to converge on the theoretical percentage over time. The level of turnover required for the actual win percentage to fall within a small level of tolerance from the mean can, however, be astronomical, so Analysts and Senior Management need to have very strong stomachs if involved in Baccarat high end play.es.