Before we compare different simulators, we need to clarify the definition of variance. The variance of X is equate to the mean of the square of X minus the square of the mean of X. In blackjack, it’s more complicated than this though.
Let’s use this hand, T,6 v A, as an example to demonstrate. Here, X=EV, the gain from a hand. At TC=0, player bets $10 on the main and then loses it, so the variance component from this hand is (10x1)^2=100 minus the square of the mean of EV without insurance.
At TC=+4, player bets $100 on the main and $50 on insurance and then loses all, so the variance component from this hand is (100x(0.5+1))^2=22500 minus the square of the mean of EV with insurance.
The mean of EV is usually tiny, about $10x0.01, so the square of it is 0.01, negligible to the total variance. In your simulator, do you set it as a fixed value of zero? If not, how do you choose the mean of EV with insurance? And without?
by: aceside
I don’t know how insurance always affects variance. Also, I don’t choose EV, it depends on the game, betting, playing. After all the bets and results are recorded, EV, variance and standard deviation are calculated. Also, sometimes insurance is won resulting in 0 won or lost overall on a hand.