This is a subject very near and dear to my heart. I have talked about my vision problem before on this board, and how counting is difficult to impossible for me because of distinguishing between certain cards at a distance. I have always thought that, except for possibly telling tens from nines, I could identify face cards and aces. So I have been interested in finding a way to make use of the information I can gather in this way.
Of course, I have also mentioned in another thread having talked with an accomplished counter who told me that knowing the ratio of tens to non-tens in the unplayed deck doesn't help with betting or with playing indices, simply because when you do have a surplus of tens, you don't know if they are balanced by a surplus of small cards to pair up with to make stiffs. And the only way to know that is to track the middle cards and the low cards too.
The real value of counting only the tens is insurance, as a ten count is a perfect insurance indicator. I have thus far, however, been reluctant to employ this tactic into my game, because I don't want to get booted from an otherwise favorable game because it is obvious that I'm only insuring at high counts. Maybe I'm just being paranoid about that though.
Now, as to whether the ten count would be good to know on doubling opportunities, I suppose knowing it would be better than not knowing; but I will have to think about it a little to see if I see enough value there to be worth the trouble of keeping the count. To my way of thinking, you have the same balance problem with using it this way as you would using it to size your bets.
Let's say that thirteen cards are played in the first round of a single deck game that is dealing two rounds between shuffles. If you see four tens come out, you'd think that the deck was still neutral. However, if, in addition to those four tens, you see 9 small cards (2-6), the deck is actually fairly strongly in your favor for the next round. On the other hand, if you see four tens come out along with 9 medium cards (7-9), the deck is strongly stacked against you on the next round. So just knowing that the right proportion of tens have been played on that round doesn't tell you anything in and of itself.
Now let's say that you saw no tens in the first round. If the thirteen cards you did see were all middle cards, you'd double into that situation thinking you had an edge, when, in fact, the deck is still neutral. The same is true the other way around. If you saw six tens on round one, but also saw seven small cards, you'd have a slight edge in round two, but would think you were behind the count.
Just knowing the ratio of tens to non-tens isn't a great help in and of itself.
Then, you have the issue of the aces, which especially complicates the double down situation. How many times have you doubled an eleven and drew an ace? In my opinion, most ace-included counting systems are weak in predicting the probability of this sort of bad beat. So If I were going to run a counting system just for the purpose of doubling down, I'd want said system to be strong in this area.
So if you want to accomplish that, you'd need a side count of aces, along with your ten count. Now you start to get into the situation where you have to wonder if keeping a count of tens, a count of aces, and adjusting for cards played is about as complicated as an unbalanced counting strategy like Red 7 or KO.
Still, it is thought provoking for someone like me, who might be able at some point to figure a way to do something within my abilities to give myself some edge. Currently, when I play single-deck, I do what I call "casual counting", which is to say I take a mental picture of the balance of cards I have seen, between big and small, and I vary my bet slightlyu on the next round based on that balance. It isn't exact, so I am careful not to adjust my betting too much based on that alone.
Actually, I play a progressive system, and use this "casual count" to adjust my bets within the progression, or set stop points at which I won't continue the progression. In other words, if my first bet is $10, and I lose, I would go up to $20 if the "count" was in my favor, or up to $15 if it wasn't. I might then also say to myself that with the current "count" I'll take this to $50, or I'll take it to $100. This has worked somewhat in single deck games; but shoe games require more precision than I can achieve with my "casual count".
Even single-deck games need to be just right in terms of the mix of players at the table. If it is too few, I don't see enough cards per round to be very accurate. If it is too many, I don't get but one round dealt. In that situation, I probably mostly revert to what someone else pointed out in another thread, if you sit at third or near the end of the rotation, if there are a lot of players on the table, you can use the cards that have already been played in that round to get an idea as to whether a hit, stay, or double is in order.