How can certainty equivalents be used in a practical setting?
A4: The need for the use of logarithms and exponentiation makes the calculations quite difficult when analyzing a complex game such as blackjack. A formula for approximating the certainty equivalent (that is very accurate when your advantage or disadvantage is 10% or less) is CE = E – V/2kB where CE is the certainty equivalent, E is the expected winnings, V is the variance of those winnings (i.e. the square of the standard deviation), B is your bankroll and k is your Kelly Number, a measure of the amount of risk you wish to take. The Kelly criterion corresponds to k = 1.0 and in this situation this formula closely approximates calculations based upon the log(x) utility function. When k is not 1, the utility function that you are approximating is x^(1-1/k) / (1-1/k). For the $200 coin flip above which has E = $20 and V = $$39600 (the standard deviation is $198.997) the formula gives a CE = $13.40 which is quite close to the exact value of $13.38 derived above.
