Basic strategy H17 vs S17

Midwestern

Well-Known Member
#1
I was hoping that someone could explain the math behind the minimal differences in basic strategy between H17 and S17.

Namely, why DBL on soft 18 vs 2 in h17.
Or why DBL soft 19 v 6 in h17?

Any kind of insight into the theory that developed these particular BS is appreciated.

Thanks!
 
#2
how BJ strategies are generated

No theory. BJ strategies are generated by exhaustive computer simulations. No logic involved only what is the best move in the long run in computer sims.

if you must try to figure it out. The difference is if the dealer make a hand of soft 17 he must hit. An ace downcard for the 6 and adding soft 15 total to the 2.

The strategy is NOT derived by reason so sometimes it doesnt make sense but it is always right.
 

Sucker

Well-Known Member
#3
To explain this mathematically you would have to go through a very complicated combinatorial analysis, taking into account all the different possibilities of hit cards and double down cards. It's much easier to simply run simulations of each problem.

When you run a sim of one million hands each, you find that when the dealer hits soft 17, your EV is slightly higher by doubling these two hands; and when the dealer STANDS on S17, you make more money by NOT doubling.

In order to logically explain the reason WHY, it's necessary to look towards the dealer's bust frequencies. In S17 (single deck), if the dealer has a 2 up he will bust about 36.4% of the time. If he HITS soft 17 he busts about 36.6% of the time. Because of the fact that when you double on a soft hand there are more cards to HURT the hand than there are to improve it; when you soft double, you NEED this slightly extra bust frequency in order to swing the deal.
 
#4
A good tutorial

Very well said sucker. I wasnt sure I would pick the right words to explain it so I left it to others.

A very good example of how labor intensive the math is in even the simplest situations is found in THE THEORY OF BLACKJACK by Peter Griffin. I have the sixth edition. Chapter 2, "the basic strategy" , has a great illustration of some of the simplest computations involved in hand to hand matchups.

If you are interested in the "reason" for making decisions in blackjack or the other nuts and bolts in the machine of advantage play or basic strategy pick up a copy. You wont regret it.
 

Gamblor

Well-Known Member
#5
The differences makes some sense to me.

You double A8 v 6, since there is a reasonable chance dealer has A6, and is more likely to bust than in a S17 game.

Double A7 v 2, because there is a chance that dealer gets a soft 17, and will bust, thus busting more often than a S17 game. Keep in mind doubling A7 v 2 is pretty close to a coin flip in a S17, the increase chance in busting in H17 tips the balance.

Similar reasoning behind doubling 11 v A in H17.
 
#6
I was about to post a similar post on this subject - why if S17 has better odds are there more doubles with H17. A friend asked me about that, and the reasoning I gave was that it's because of one of the properties of doubling down - you only get one more card. Since after doubling you may end up with a stiff had that you can't do anything about and will win only if the dealer bust, the higher bust rate with H17 can make doubling the right play in borderline cases that you wouldn't double on with S17. Although H17 also means that the dealer is more likely to make a good hand, that is less of an issue when doubling since you wouldn't draw more cards anyway if you had a pat hand. Am I correct in this reasoning?
 
#7
neversplit5s said:
I was about to post a similar post on this subject - why if S17 has better odds are there more doubles with H17. A friend asked me about that, and the reasoning I gave was that it's because of one of the properties of doubling down - you only get one more card. Since after doubling you may end up with a stiff had that you can't do anything about and will win only if the dealer bust, the higher bust rate with H17 can make doubling the right play in borderline cases that you wouldn't double on with S17. Although H17 also means that the dealer is more likely to make a good hand, that is less of an issue when doubling since you wouldn't draw more cards anyway if you had a pat hand. Am I correct in this reasoning?
H17 effects are threefold:

1) your double becomes a stiff and you need the dealer to bust.
In this case the only difference is if the dealer hits to so soft
17(you lose at S17) but the dealer must hit giving you a second
chance the dealer to bust. Obviously this is good.

2) your double becomes 17. This is identical to above except instead of
a loss in S17 you would start at a push on dealer soft 17. H17
changes that push to another chance for the dealer to bust or
push but now you may lose where you would have pushed.

3) your double becomes a pat hand of 18 to 21. Here in S17 you would
win against soft 17. However in H17 the dealer has a second
chance to beat you. Obviously this is not good.

The cumulative affect of the probability of these three possible interactions for each hand match up determines whether H17 helps or hurts a particular double decision. Sometimes this affect is enough to change the basic strategy tables in one direction or the other.

Hopefully this helps clear up any questions on the subject.
 

MangoJ

Well-Known Member
#8
Marginal decisions don't have a "simple" answer because they are marginal by definition. Think about it: It's a almost identical call. There is no simple reason for it.

For marginal decisions you need to face the "whole problem" (that is full combinatorial analysis) - a simplification is not good enough here. Hence there is no "simple" reason besides the only (valid) reason: it is the outcome of evaluating the full combinatorial analysis.

For a combinatorial analysis, you need two ingredients (actually there are three): Distribution of dealer standing hands D. And distribution of player hands (simplest for stand and double) P. Also you need the blackjack paytable B (it's a simple matrix of which player hand beats which dealer hand, which hands pushes etc...)

EV is P * B * D (where "*" is vector/matrix multiplication).

Running full combinatorial analysis, one gets
P(double) * B * D(H17) > P(stand) * B * D(H17)
and
P(double) * B * D(S17) < P(stand) * B * D(S17)
The only reason to double rather than stand is because you get a better EV. This is as "simple" as possible (while still being accurate).
 
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