Question about Blackjack basic strategy

There are 2 what seem to be paradoxes in the blackjack basic strategy that have been bugging me for a while. I know that the BS is derived from billions of hands of BJ simulations, but these things just don't make sense to me logically.

1. Why does the BS say to DD on 11 against A in a H17 game but just hit in a S17 game? Hitting a soft 17 is more likely to improve the dealers hand than making it worse, so wouldn't it be logical to DD 11 against A in a S17 game as well?

2. Almost every BJ card counting system tell you to stand 16 against 10 if the TC is 0 or greater, this means on average there would be more occasions where you should stand a 16 against 10 than to hit it, so why does the BS tell you to always hit 16 against 10?

Thank you for any help!

I've thought the same things. Maybe someone can show the math to us. But here's what I think:

1. Dealer standing on soft 17 v player 11 wins more than dealer hitting soft 17 v. player 11. H17 is better for dealer, but I guess not for this case.
2. I think I saw a statistic where you lose 77% of the time when you stand. And you lose 75% of the time when you hit. The numbers may be off, but as you can see, it is very close.

Quote: Numpkin

There are 2 what seem to be paradoxes in the blackjack basic strategy that have been bugging me for a while. I know that the BS is derived from billions of hands of BJ simulations, but these things just don't make sense to me logically.

1. Why does the BS say to DD on 11 against A in a H17 game but just hit in a S17 game? Hitting a soft 17 is more likely to improve the dealers hand than making it worse, so wouldn't it be logical to DD 11 against A in a S17 game as well?

2. Almost every BJ card counting system tell you to stand 16 against 10 if the TC is 0 or greater, this means on average there would be more occasions where you should stand a 16 against 10 than to hit it, so why does the BS tell you to always hit 16 against 10?

Thank you for any help!

1. Because if the dealer hits soft seventeen they are more likely to make stronger hands more often, and they are also going to bust more often. in a S17 the dealer is going to have 17 more often to where hitting is correct for the player because if you hit your 11, and get a 12-16 you will hit again and make a 17-21. in a S17 game those hits will most likely make you a winning hand or a hand that pushes. in a H17 you might hit twice to get to 17 or 18 and lose to a stronger hand more often. So basically you are going to need a stronger hand on average with H17, and the dealer is also going to bust more because they are going to hit their soft 17s. This puts the EV in favor of doubling (slightly, you still double against an ace at a true of 1 in S17 which is going to be fairly common).

2. No it doesn't mean on average there are more occassions where you hit. These plays are so ridiculously close the actual index is anything greater than zero. so if the TC is .16 you stay. There are more 16s where you stay than where you hit. hands like 9 7 or 10 6 (both make the count -1) are more common than 556 and all the other multi card 16s, but barely. The computer is averaging all of those outcomes and the EV of all of those outcomes making hitting slightly favorable.

The TLDR version is that the computers are not wrong you can trust them :)

Quote: OzzyOsbourne

1. Because if the dealer hits soft seventeen they are more likely to make stronger hands more often, and they are also going to bust more often. in a S17 the dealer is going to have 17 more often to where hitting is correct for the player because if you hit your 11, and get a 12-16 you will hit again and make a 17-21. in a S17 game those hits will most likely make you a winning hand or a hand that pushes. in a H17 you might hit twice to get to 17 or 18 and lose to a stronger hand more often. So basically you are going to need a stronger hand on average with H17, and the dealer is also going to bust more because they are going to hit their soft 17s. This puts the EV in favor of doubling (slightly, you still double against an ace at a true of 1 in S17 which is going to be fairly common).

2. No it doesn't mean on average there are more occassions where you hit. These plays are so ridiculously close the actual index is anything greater than zero. so if the TC is .16 you stay. There are more 16s where you stay than where you hit. hands like 9 7 or 10 6 (both make the count -1) are more common than 556 and all the other multi card 16s, but barely. The computer is averaging all of those outcomes and the EV of all of those outcomes making hitting slightly favorable.

The TLDR version is that the computers are not wrong you can trust them :)

Thanks for the clarification!

1. So if I'm understanding correctly, you don't double a 11 against A in S17 game is because the opportunity of hitting for the 4th card is more favorable to the player, because S17 is more beatable than H17? Same idea as why one should hit 16 against a 7 until a higher TC than against a 10?

2. As for this one, so the TC for standing a 16 against 10 is actually 0.16 not 0? So in the future I should basically be standing a 16 against 10 at any positive running count, and hitting at RC of 0 or below?

Quote: Numpkin

1. Why does the BS say to DD on 11 against A in a H17 game but just hit in a S17 game? Hitting a soft 17 is more likely to improve the dealers hand than making it worse, so wouldn't it be logical to DD 11 against A in a S17 game as well?

Assuming an otherwise full deck, dealer shows an A, no dealer natural, the dealer will have to draw 2/3rds (6/9ths) of the time in H17, vs 5/9ths in S17. If you are holding an 11 you can double on (not a soft 21), it is comprised of some of the cards that would improve a soft 17. Doubling (vs hitting) 11 v A is borderline play, and this rule difference is enough to shift the odds of one vs the other, even for a basic strategy player.

If you're familiar with card counting, the index on this play is TC0 for H17 (that is, it's recommended whenever the deck is neutral (not rich in low cards), vs TC1 for S17 (that is, whenever 1 low card per remaining deck has been removed from play).

Quote: Numpkin

2. Almost every BJ card counting system tell you to stand 16 against 10 if the TC is 0 or greater, this means on average there would be more occasions where you should stand a 16 against 10 than to hit it, so why does the BS tell you to always hit 16 against 10?

Basic strategy tells you to surrender 16 vs 10. That means you are expecting to win less than half the time. (You can't push on a 16.) Surrender is often not allowed, however.

Remaining options are double, hit, stand, or split (in the case of 8-8). Doubling a hand you can bust on has a very poor chance of being effective, so it is not recommended. Splitting 8's is recommended. Hit is marginally better than standing on a 2 card hand... .again why the index is TC0.

Once you get into composition dependent strategy (vs total dependent strategy), the advice changes for multi-card hands, since to make a multi-card 16, you have already removed some of the small cards from the deck.

All things being equal, we strive to play only S17 shoe games. All things are seldom equal, however, and that may occasionally find us at a H17 game after careful evaluation of all the games offered. If the added 0.22% house edge sticks in your craw as it does in mine, you can take solace in a couple of things.

As the count increases, the dreaded 0.22% decreases. When you push out that max bet it has gone down quite a bit. If you are fortunate enough to have the late surrender option it's even better

Let me remind anyone who stumbles upon this thread that although doubling A vs 11 was touched upon, there are other changes to basic strategy when playing H17. There are three extra double downs and three extra surrenders if applicable.

1.) In a H17 game the Dealer has a slight chance of having/drawing to Soft-17, then breaking. Just enuff to tip the scales.
2.) Without a surrender option, hit is the better choice of H/S ON THE INITIAL 2 CARDS. What Basic does not tell you is what one does when drawing 1 card to hard 16 against that 10-value. In general, one stands with 3+ cards. The exception is if a 6 is in the hand without a 4 or 5. So iff one holds 3-6-7 Hit, if its A-6-9, Hit, if its 4-5-7 Stand, if its A-5-X Stand, etc. The fewer decks in play the more prominent this decision.

3.) If surrender is availible 2.) is moot, as one suurrenders a 2-card hard 16 vs. 9 10 or Ace. The tricky one is surrender hard 17 vs. Ace. Yup, thats a must-do.

Quote: Numpkin

There are 2 what seem to be paradoxes in the blackjack basic strategy that have been bugging me for a while. I know that the BS is derived from billions of hands of BJ simulations, but these things just don't make sense to me logically.

Remember those billions and billions of simulations report what the optimal strategy. The Second Place choice may be only a teensy weensy bit from first place. So it really doesn't always matter between the BS card and your gut instinct.

My 2 cents: When you DD with an 11 vs a dealer ace, you will only get a 10-value card about 31% of the time. You'll have junk if you get an A,2,3, or 5. And when you get one of these cards you don't want the dealer to S17 because he's already beat you. Obviously, overall, the S17 game favors the player, but not when using basic strategy to DD 11 vs dealer ace.

Re: #2) Basic strategy dictates how you play your first two cards vs any dealer up-card. If the dealer's up-card is a 10 and the player's first two cards total 16, the count, once figuring in the probability of all the possible player's two-card (non-8,8) 16s, is slightly less than 0.

Basic Strategy is not just calculated with Simulations but with Full Combinatorial Analysis. That means that it has been analysed taking into account every possible combination of cards. And these days with today's computer power this is a trivial matter with such calculations done in split seconds.
And the Basic Strategy for different rules has been calculated by many different people using different software for decades now and confirmed by every single one of them. So it can be trusted absolutely as being correct.
Also some of the plays are very close and different rule change the BS over such close plays in ways that is difficult to explain.
16 v 10 is one of the closest plays having a difference of only around 0,5% between Hit and Stand.

Quote: Numpkin

2. Almost every BJ card counting system tell you to stand 16 against 10 if the TC is 0 or greater, this means on average there would be more occasions where you should stand a 16 against 10 than to hit it, so why does the BS tell you to always hit 16 against 10?

I am under the impression that BS for a single-deck or double-deck game is to stand on 16 against a 10, and only hit if it is three decks or more. I assume that a BS that includes a TC assumes that you are not playing with more than 2 decks as it makes counting that much harder.

And AceTwo is correct - BS is calculated from mathematical analysis, not from simulation. The "quick version" of how I did it, at least in terms of Hit or Stand:
1. Start by calculating the probabilities of the dealer getting 17, 18, 19, 20, 21, or bust for each possible up card, remembering to ignore 2-card 21s. This needs to be done separately for each combination of (a) number of decks and (b) whether it is H17 or S17.
2. Determine the "average result" if you stand on hard 21, and the "average result" if you hit hard 21. (Hint: the latter is -1 - i.e. you lose every time.) The "hard 21 result" is the better of the two.
3. Determine the "average result" if you stand on hard 20, and the "average result" if you hit hard 20. (This is 1/13 x the "hard 21" result + 12/13 x -1.) The "hard 20 result" is the better of the two.
4. Repeat this for hard 19, hard 18, and so on through hard 12, then do it for soft 21, soft 20, and so on through soft 12, then for hard 11, hard 10, and so on through hard 4. (Yes, the hard 4-11 will always be "hit", but you need the numbers to determine whether hitting or doubling is better.)

Quote: AceTwo

Basic Strategy is not just calculated with Simulations but with Full Combinatorial Analysis. That means that it has been analysed taking into account every possible combination of cards. And these days with today's computer power this is a trivial matter with such calculations done in split seconds.
And the Basic Strategy for different rules has been calculated by many different people using different software for decades now and confirmed by every single one of them. So it can be trusted absolutely as being correct.
Also some of the plays are very close and different rule change the BS over such close plays in ways that is difficult to explain.
16 v 10 is one of the closest plays having a difference of only around 0,5% between Hit and Stand.

But, but.. the flaw!

Quote: AceTwo

Basic Strategy is not just calculated with Simulations but with Full Combinatorial Analysis. That means that it has been analysed taking into account every possible combination of cards. And these days with today's computer power this is a trivial matter with such calculations done in split seconds.

Careful. *Full* Combinatorial analysis is not that trivial as you describe, and don't take trust in "absolutely being correct". The problem are the splits. If you want to make a full combinatorial analysis of the EV of a split, you need to take account all possible ways the first hand may play out for each and every possible way the second hand may play out. This effectively squares a quite considerably large number of possible plays. Matters get much worser if you take into account resplits.

If you want split-second response, you need to simplify the split evaluation considerably. It can be justified (splits and resplits are comparably rate to occur, and the gained margin is small). But one should not label it with *full* combinatorial analysis.