What's the math behind standing on 16 vs. 10 and vs. 9?

[socal_bj]

I often wonder about this one.

Using Zen count, balanced. Playing double deck, no surrender.

Index for standing on 16 is ZERO if dealer has 10.
Index for standing on 16 is +8 if dealer has 9.

What is the mathematical reason for this? At +7 I am more likely to bust than ZERO.

So when true count is +7 why must I take a hit if dealer shows 9, and stand if dealer shows 10?

 

[The Chaperone]

At just about any count you are more likely to bust a 16 than not. And certainly more likely to bust it than ZERO :laugh::laugh::laugh:


The reason for standing at higher counts is because it maximizes your EV for that hand.

 

[tthree]

You have to think about the likelihood of the dealer busting as well. If he has a made hand when he flips his holecard the only way to beat him is hitting. High count you bust more often even though he has a made hand more often. You need a 2, 3, 4 or 5 and still beat his made hand. More high cards and less low cards make your chances shrink to minimal if you hit. If he flips a stiff hand you have a good chance of winning especially if there are more high cards than low cards. If the count is low he is more likely to make his stiff but you are more likely to make your hand. To sum it up you stand at non negative counts because the sims show it is better in the long run, same with hitting on negative counts, so all this logic is pointless.

 

[socal_bj]

At just about any count you are more likely to bust a 16 than not. And certainly more likely to bust it than ZERO :laugh::laugh::laugh:


The reason for standing at higher counts is because it maximizes your EV for that hand.

I'm not sure if you understand my question.

I get that standing on higher count make sense. So why do I need to hit my 16 at a higher count just because the dealer's up card is 9 instead of 10?

Let me re-state my original question:

My Hand, Dealer's Up Card , Zen Index for Standing
==== ====== =======
16 , 10 , ZERO
16 , 9 , +8

So my question is assuming the count is +7, WHY do I hit when dealer has 9 but I stand when dealer has 10?????

It seems to me I should STAND when true count is +7 regardless of whether dealer shows 9 or 10.

Can anyone give me the reason for this. +7 is higher than zero, so why hit instead of stand just because dealer has 9 and not 10?

 

[sagefr0g]

I'm not sure if you understand my question.

I get that standing on higher count make sense. So why do I need to hit my 16 at a higher count just because the dealer's up card is 9 instead of 10?

Let me re-state my original question:

My Hand, Dealer's Up Card , Zen Index for Standing
==== ====== =======
16 , 10 , ZERO
16 , 9 , +8

So my question is assuming the count is +7, WHY do I hit when dealer has 9 but I stand when dealer has 10?????

It seems to me I should STAND when true count is +7 regardless of whether dealer shows 9 or 10.

Can anyone give me the reason for this. +7 is higher than zero, so why hit instead of stand just because dealer has 9 and not 10?

errrhh well assuming late surrender was not allowed, i think you would stand (going by ev's) if you had 10,6 vs 10 & 10,6 vs 9 if the true count was tc>=7 for the hi/lo count (at least for a six deck game)......... don't know about zen

 

[sagefr0g]

looks pretty much the same for zen, as well..... errhh at least for the pack state used....

 

[socal_bj]

Here are the ZEN indexes on Casino Verite.

Can anyone tell me why you would HIT the 16 if true count is below +8 when dealer shows 9???? I doesn't make sense to me.

 

[jnrwilliam]

i get ur pt

I'm not sure if you understand my question.

i get ur point.
the difference is dealer is likely to end up as 19 or 20 when his Up is 9 or 10.
u hit to become 17-19 still likely lose to his 20 when Up is 10.

 

[tthree]

Why are you using different deck compositions with the 2 hands?

 

[socal_bj]

I'm not sure if you understand my question.

i get ur point.
the difference is dealer is likely to end up as 19 or 20 when his Up is 9 or 10.
u hit to become 17-19 still likely lose to his 20 when Up is 10.

OK, I think I see the logic now.

If dealer has 9, if I hit, there are TWO cards that can beat him: a 4 or 5 (slight possibility)

If dealer has 10, there is only ONE card that can beat him with 5 (very slim chance, so just stand and see what happens)

Either case my chances of busting is pretty high, but in the case of the 9, I have a better the chance of beating the dealer by hitting, right?

 

[sagefr0g]

Why are you using different deck compositions with the 2 hands?

right i think i know what you mean, errhh i was just trying to come up with compositions that gave a tc close to seven.......
but i guess there are loads of compositions that do that, with maybe different ev's that result?
so but like for the cv index's posted (http://www.blackjackinfo.com/bb/showpost.php?p=239297&postcount=7), i guess that takes all or near all the possible states into consideration through sims.

 

[Gamblor]

OK, I think I see the logic now.

If dealer has 9, if I hit, there are TWO cards that can beat him: a 4 or 5 (slight possibility)

If dealer has 10, there is only ONE card that can beat him with 5 (very slim chance, so just stand and see what happens)

Either case my chances of busting is pretty high, but in the case of the 9, I have a better the chance of beating the dealer by hitting, right?

Yes, what jrnwilliam said. With a 16 v 10 your basically spitting into the wind, might as well let the dealer take a shot a breaking. Much easier to beat a lower card like dealer 7 (and probable 17), of course the lower the easier.

With a 10, a dealer has:

20 - 4/12 times
19 - 1/12
18 - 1/12
17 - 1/12

With a 7 a dealer has:
18 - 1/13
17 - 4/13

I try to explain this to ploppies but goes in one ear and out the other

 

[Lonesome Gambler]

Correct answer: who cares? The optimal play (ie. index play) has been determined by simulating billions of rounds of blackjack. It doesn't need to make sense or be intuitive, it just needs to be the mathematically correct play. I understand that this answer may not seem as satisfying, but any hand-wringing over why a correct index or BS play is what it is is wasted time.

 

[MangoJ]

Correct answer: who cares? The optimal play (ie. index play) has been determined by simulating billions of rounds of blackjack. It doesn't need to make sense or be intuitive, it just needs to be the mathematically correct play. I understand that this answer may not seem as satisfying, but any hand-wringing over why a correct index or BS play is what it is is wasted time.

I completely agree. Marginal decisions are just that: marginal.
You need to go deep into detail to "fully" understand it.

 

[The Chaperone]

Correct answer: who cares? The optimal play (ie. index play) has been determined by simulating billions of rounds of blackjack. It doesn't need to make sense or be intuitive, it just needs to be the mathematically correct play. I understand that this answer may not seem as satisfying, but any hand-wringing over why a correct index or BS play is what it is is wasted time.

[x] Best Answer

 

[The Chaperone]

the difference is dealer is likely to end up as 19 or 20 when his Up is 9 or 10. u hit to become 17-19 still likely lose to his 20 when Up is 10.

[x] 2nd best answer (but also correct)

Now let's end the thread or at least move it to the "Re-inventing the Wheel" forum.

 

[21forme]

When the dealer has a 9 up rather than 10, you have more opportunities to beat his hand, even though the likelihood of busting is still high. Don't forget, even though the count may be high, there are still plenty of small cards in the deck. Haven't you seen your share of 5 card dealer 21s in a big count?

 

[Gamblor]

Disagree with those who advocate not having an intuitive understanding of the probabilities involved in blackjack. Give me two people trying to solve a mathematical problem, one who has an intuitive understanding of the mathematics involved and the other who doesn't, guess who'll I'll put my money on to solve the problem best?

Also, an intuitive understanding helps you in those, admittedly, infrequent situations that arise at the tables where you have to think on your feet. You can't ask the pit, "Hey, can we hold up the table for a few hours while I go get my laptop and run a sim on this situation for a few hours?". Trust me, I tried that, the pit will give you a funny look!

 

[Lonesome Gambler]

Although I don't disagree with your point, I don't think the pursuit of an intuitive understanding of the reason for marginal index plays is worthwhile. Thinking about the game and ways to improve your edge is always valuable, but I think there are many more important things to be mulling over than 16 v 9 and 16 v T. Your brainpower could be better used elsewhere.

 

[rrwoods]

Although I don't disagree with your point, I don't think the pursuit of an intuitive understanding of the reason for marginal index plays is worthwhile

... for you.

Not only will it help you remember those indices better, but more importantly, it gives a better intuition for other indices in the future. The more you keep asking *why* and finding the answers for yourself, the better your understanding of the game as a whole.