Standard Deviation or Variance of Deuces Wild Strategies

I was reading on WizardofOdds.com about the Optimal and the Simple strategies of full-pay Deuces Wild Video poker. It appears that 4 deuces are more common in the Simple Strategy, yet Wild Royals and 5 of a Kind are more common in the Optimal Strategy. I was thinking that as a short term player it might be worth learning the advanced startegy if it lowers the variance of the game. Can anyone tell me if either strategy reduces the Variance or Standard Deviation of the game? How would I calculate variance?

Quote: IAmSoLucky

I was reading on WizardofOdds.com about the Optimal and the Simple strategies of full-pay Deuces Wild Video poker. It appears that 4 deuces are more common in the Simple Strategy, yet Wild Royals and 5 of a Kind are more common in the Optimal Strategy. I was thinking that as a short term player it might be worth learning the advanced startegy if it lowers the variance of the game. Can anyone tell me if either strategy reduces the Variance or Standard Deviation of the game? How would I calculate variance?

Using the Wizard's results in the first table on this page, I find that the variance is lower for the optimal strategy, but the difference is small. I get 25.9 for the simple strategy and 25.8 for the optimal strategy.

You can calculate both variances by first pasting the table into Excel. Then make two new columns. In each cell of the first new column, put a formula to calculate the square of (the pay minus the simple strategy return). And in each cell of the second new column, put a formula to calculate the square of (the pay minus the optimal strategy return). For example, the cells in the royal flush row would be =(800-1.007085)^2 and =(800-1.00762)^2. Then to calculate the simple strategy variance, do the sumproduct of the simple strategy probabilities with the simple strategy new column. And the optimal strategy variance is the sumproduct of the optimal strategy probabilities with the optimal strategy new column.

Chester is right. It doesn't matter. There are certain very small penalty-card deviations for when to hold onto a 5oaK with three deuces versus going for the four ducks, and when to hold three cards to a wild royal with one deuce versus just holding the deuce.

It really doesn't matter in the long run so you should be fine making the lower variance play (holding onto the 5oaK and holding the single deuce in both the above situations).