$11.35
mickpk,
I ran CVData for the rule set you specified, with the player using Complete Basic Strategy and flat-betting $10 per hand. At 100 rounds per hour, the total action was $1135.26 per hour. That means that the average amount bet on each round is $11.3526.
You didn't specify the penetration or the total number of players, so I guessed three total players and 50% pen (all the SD, S17, DAS games I know have 50% pen). No doubt the average bet will depend slightly on these values... perhaps in the fifth significant digit. In addition, since you didn't specify a count system, I had the player use Complete Basic Strategy. If you specify a particular strategy, the average bet may change a bit, due to more splitting and doubling at high counts, and less of each at low counts.
By the way, even with flat betting the player's Initial Bet Advantage was 0.042%, while his Total Bet Advantage was 0.037%.
Hope this helps!
Dog Hand