Thanks for doing that. I've always stood on a 12v3 when it was dealt but I'm interested in this hand from the perspective of a 9v3 being hit with a 3. Most people will double this hand, and so be stuck with a 12.
If you take the view that if all of the three additional cards per 52 are 10s, it means that, on average (of course) 19 cards out of 52 (10s, 16+3) would bust the hand, but 33 wouldn't - 21 cards would have little effect (2-6 - x17 - plus 4xAs), and the unknown 7,8,9 (average of 12 of them) would result in a strong hand. With the dealer having a three there's a strong chance of it turning into a made hand, which will stuff the 12.
If, at the other end of possibility, the three additional cards at TC+3 are all aces, then it would mean that 16/52 cards would bust the hand, but 36/52 wouldn't, which I would think would shift the odds of busting out a fair bit. But unless you're keeping a side count of aces you can't know.
Oh. . . and when I referred to "little in it" it was meant relatively speaking as a value of the benefit of just this deviation over the longer term. If you view this example relative to the far end of the scale, ie whether to double or hit an 11v6 (the longer term difference being 33.6p in the £ - so the loss in EV for hitting rather than doubling on that one is far, far greater) it's not a huge cost. In actual fact, the loss in EV in hitting a 12v3 at TC+3 rather than standing looks to be virtually the same as not doubling A2v6 at a neutral count but just hitting it.
Anyway, those figures have enlightened me. Thanks again.