What to do with the worst position in Blackjack?
[Let's assume 6/8 decks, standard rules, no surrender]
For hard 16 vs a 10, we're given a Weird rule: 'Hit a two card hard 16, but Stand a three card hard 16.'
Hmmm, Ok, so we're supposed to Hit a hard 16 into 10 when our hand's made up of only two cards (10-6 or 9-7 only; 8-8's a split), but Stand a hard 16 into 10 when our hand's made up of 3 or more cards (say, 7-6-3, or whatever).
Since the difference between the two plays is so razor thin, in real life you're fine either way you play it, but if you're like me and sort of dig figuring out which option's better, I have a Rule proposal that needs peer review.
First, here's how crazy close the two options are (standard loss per dollar bet):
Stand 9-7 vs 10 = - .537 per $1 bet. Ouch.
Hit 9-7 vs 10 = - .535 per $1 bet. Basically the same Ouch, but ever so slightly less.
Those outcomes are so close that having just one 'safe' card (an A thru 5) inside your hard 16 (the '3' in the 7-6-3 example), and therefore unavailable to you if you Hit, is enough to flip the correct percentage play from Hit to Stand.
But here's the thing: there's more info available to you than just the cards making up your hard 16 when it comes time to make the Hit or Stand decision: namely, an entire table full of other players' cards and hits.
Since those other players' cards are also no longer available for your Hit, they matter exactly as much as the cards making up your hard 16 and they should be included in the Hit or Stand calculation.
[I'll be lucky if even 1 person on earth reads this far down, so if anybody has, you rock!]
So, now my proposed Rule:
1. For all players' hands and hits, total up how many safe cards (A thru 5) and how many unsafe cards (6 thru K) you see on the table (include your own hand, but not the dealer's 10).
2. Subtract 2 from the unsafe cards total (this represents a 2 card hard 16, which has to be out of the shoe before the decision becomes so razor sharp).
3. Calculate the percentage of safe cards on the table. The equation's: safe cards total / (safe cards total + unsafe cards total after step 2)
4. If that percentage is greater than 38.5%, Stand. If it's less than 38.5%, Hit.
Clear as mud? OK, the 38.5% is 5 divided by 13, the 5 types of safe cards divided by the 13 total types of cards in a deck.
What we're doing is finding out whether the concentration of safe cards on the table -- no longer in the shoe -- is greater or less than the 38.5% concentration that 'should' be on the table. If the concentration of safe cards on the table's higher than it 'should' be, then more safe cards are out of the shoe than should be, meaning fewer safe cards are left in the shoe. Fewer safe cards and more bust cards left in the shoe than the shoe's composition upon which the Stand = - .537 vs Hit = - .535 was calculated means you can be sure that tiny advantage for Hit has been flipped by the cards revealed on the table in front of you. You should therefore Stand.
Conversely, if the concentration of safe cards on the table is lower than the 38.5% that 'should' be there, then more safe cards remain in the shoe than the shoe's composition when the Stand - .537 vs Hit - .535 was calculated, so the advantage remains with Hit, and is even larger than the .002 advantage calculated on a regular composition.
Example: You get a 9-7 into a 10, no Surrender available. Hit or Stand?
1. Add up the total of safe cards (A thru 5) on the table, including your hand. Let's say there's 5. Add up the total of unsafe cards, including your hand. Let's say there's 8.
2. Now subtract 2 from the unsafe card total, leaving 6.
3. The percentage of safe cards on table is now 5/11, or 45.5%
4. Since the concentration of safe cards on the table, 45.5%, is greater than the concentration of safe cards in the entire shoe, 38.5%, it means there's 'too many' safe cards on the table, and therefore 'too few' safe cards left in the shoe, so we should Stand, even though our Example's only a 2 card hard 16, which the original rule told us to Hit (although it's quicker just to say 45.5% is greater than 38.5%, so that means Hit).
Of course, I'm not positive of this stuff, so on the outside chance anybody's still reading this, I'd def appreciate your input.

You are correct that almost every decision in Blackjack is fluid depending on the remaining composition of the deck. The more information you have allows you to make better decisions. (ie. it is correct to hit or split two tens against a ten if you know that the only remaining cards in the deck are Aces).

DRich, thanks very much for replying.
I figured the O/U for replies on this thread was: 0.5, UN - 150, so you're a hero to the OV's.
Cool example. Splitting those 10's vs 10 and getting two BJ's would certainly get you some unwanted attention from the eye in the sky, at least until the dealer pushed you.
PS: Hey, your tagline's better than mine.

Many people, especially ignorant people, want to punish you for speaking the truth. - Mahatma Ghandi

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When I get a face/6 against a dealer face, I always hit.
If it's a 9/7, I surrender against a dealer face.

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Heh, Clark W. Griswold, I like your screen name.