Standard Deviation

In analyzing blackjack play with CVCX, CVCX gives a standard deviation per hour assuming x number of hands per hour. The standard deviation will obviously change with different game conditions, i.e. game speed, penetration etc.

If I take multiple sessions with different playing conditions and use CVCX to determine a standard deviation for each session, would I be able to take those multiple standard deviations per hour and pro-rate it to get a average standard deviation for all sessions put together.

For example if I put in playing conditions and determined that for one session the standard deviation was $546/hour and played for 3 hours and in another session the standard deviation was $450/hour for 1 hour, could I take ($546*3/4)+($450*1/4) and get a standard deviation per hour of $522 for all session combined.

If this is not correct is their a way to take multiple sessions with different individual standard deviations per hour for each session and get a combined standard deviation per hour for all sessions.

For example if I put in playing conditions and determined that for one session the standard deviation was $546/hour and played for 3 hours and in another session the standard deviation was $450/hour for 1 hour, could I take ($546*3/4)+($450*1/4) and get a standard deviation per hour of $522 for all session combined.

The variance is the square of the standard deviation and can be added.

Using your example, take the squares of the standard deviations to get the variance:

546 * 546 = 298,116
450 * 450 = 202,500

Now you can multiply them:

298,116 * 3/4 = 223,587
202,500 * 1/4 = 50,625

And add them together:

223,587 + 50,625 = 274,212

Finally, take the square root to get the standard deviation:
sqrt(274,212) = 523.65

Which is surprisingly close to your result, but that was only by chance.