Hitting with 16 against dealer 10?

The wizard says stand on 16 against dealer 10 with 3 or more cards but others say only stand with 3 or more cards if one of the cards is a 4 or 5. Who is right?

assume the WoO is correct if you consider being correct as having the best outcome against the House Edge. [and he has given this one enough attention you can be sure it wouldnt be a calculation error]

also in this case other considerations, such as reducing variance, would not apply

you might double check to make sure the other advice still pertains to the exact same thing, such as number of decks

I usually find out that when I have 16 and the dealer has 10, I might as well hit since it will turn out he has 20. That way, I don't have to remember any extra rule. I just go ahead and hit. Will I get that 5? Probably not, but I might as well try.

It all boils down to the count. Even if you don't count cards, you probably know how it works since you're a user of this forum. When you have a 16 vs 10 in a fresh deck/shoe, the count MUST be -1. Any combination of two cards that comprise a 16 have a combined count of zero (8&8, 9&7, 10&6 are all 0) The dealer's 10 is the -1 card that makes the overall situation -1. HOWEVER, to achieve a 3-card 16, we require small cards. It is impossible to get a 3-card 16 without small cards exceeding large ones. This brings the count to at least 0. At a true count of 0, a card counter's "index" play would be to stand rather than hit. So, in the absence of any other cards counted (which would be the case if you're just following BS without counting), you can play your 16v10 the same way a counter would.

But really just find a store with LS and surrender the damn thing already.

Quote: kmcd

It all boils down to the count. Even if you don't count cards, you probably know how it works since you're a user of this forum. When you have a 16 vs 10 in a fresh deck/shoe, the count MUST be -1. Any combination of two cards that comprise a 16 have a combined count of zero (8&8, 9&7, 10&6 are all 0) The dealer's 10 is the -1 card that makes the overall situation -1. HOWEVER, to achieve a 3-card 16, we require small cards. It is impossible to get a 3-card 16 without small cards exceeding large ones. This brings the count to at least 0. At a true count of 0, a card counter's "index" play would be to stand rather than hit. So, in the absence of any other cards counted (which would be the case if you're just following BS without counting), you can play your 16v10 the same way a counter would.

But really just find a store with LS and surrender the damn thing already.

The stand/hit question doesn't boil just to the true count, but to the number of ranks left in the shoe. For example in single deck game:

6+5+5 vs. 10 = Stand (Count +2)

But

6+6+4 vs. 10 = Hit (Count +2)

So count is the same in both cases but the decision is different. Here the fact that all Fives remain in single deck favor hitting in the latter situation.

Source: https://wizardofodds.com/software/bossmedia-apx1.html

Quote: kmcd

At a true count of 0, a card counter's "index" play would be to stand rather than hit.

What I could never understand is how coma the basic strategy (calculated at TC=0) says hit, and the index says stand at the same TC. Does anyone know where that that index row come from (I mean, how it is calculated and why it is different from BS).

Quote:

But really just find a store with LS and surrender the damn thing already.

It would be problematic with 3 cards :)

Quote: Jufo81

Quote: kmcd

It all boils down to the count. Even if you don't count cards, you probably know how it works since you're a user of this forum. When you have a 16 vs 10 in a fresh deck/shoe, the count MUST be -1. Any combination of two cards that comprise a 16 have a combined count of zero (8&8, 9&7, 10&6 are all 0) The dealer's 10 is the -1 card that makes the overall situation -1. HOWEVER, to achieve a 3-card 16, we require small cards. It is impossible to get a 3-card 16 without small cards exceeding large ones. This brings the count to at least 0. At a true count of 0, a card counter's "index" play would be to stand rather than hit. So, in the absence of any other cards counted (which would be the case if you're just following BS without counting), you can play your 16v10 the same way a counter would.

But really just find a store with LS and surrender the damn thing already.

The stand/hit question doesn't boil just to the true count, but to the number of ranks left in the shoe. For example in single deck game:

6+5+5 vs. 10 = Stand (Count +2)

But

6+6+4 vs. 10 = Hit (Count +2)

So count is the same in both cases but the decision is different. Here the fact that all Fives remain in single deck favor hitting in the latter situation.

Source: https://wizardofodds.com/software/bossmedia-apx1.html

You are correct. My analysis was not complete. The best decision might not be to stand depending on the specific cards involved. Nonetheless, without considering the specific cards, the on average strategy for a 3+ card 16 would be to stand. Sixes screw things up a bit since they are bust cards that are also +1 for the count.

Quote: weaselman

What I could never understand is how coma the basic strategy (calculated at TC=0) says hit, and the index says stand at the same TC. Does anyone know where that that index row come from (I mean, how it is calculated and why it is different from BS).


It would be problematic with 3 cards :)

Heh, you're right. Somehow after going into detail about 3-card 16's I managed to forget that we were talking about after you've already hit. I'm retarded. That said, my explanation above is the precise answer to your first question. Good "total dependent" basic strategy engines do not assume a true count of 0, rather what the count (or if you want to be more specific, the average effect of removal of the cards dealt to reach the situation at hand) would be if you were playing your hand against the dealer head's up as the very first hand of a shoe (i.e. all other cards are unknown). Any other players cards you might as well consider are just sitting somewhere behind the cut card and will forever be unknown. So since 16v10 out of a fresh shoe (or a CSM) does not have a true count of 0, a basic strategy engine would not recommend standing.

In fact that may be the best way to imagine it. Basic strategy = perfect index plays for your initial two cards when playing heads up against a dealer using a CSM. But the 1.0% penetration on 6 decks really means only the 16v10 and other +0 indexes (surrender 15v10) useful.

Quote: kmcd

So since 16v10 out of a fresh shoe (or a CSM) does not have a true count of 0, a basic strategy engine would not recommend standing.

I can't agree with this, I am afraid, because an infinite deck analysis shows that hitting 16 v 10 is better than standing, and the true count in an infinite deck is always 0, and there are no card removal effects.

Quote: weaselman

I can't agree with this, I am afraid, because an infinite deck analysis shows that hitting 16 v 10 is better than standing, and the true count in an infinite deck is always 0, and there are no card removal effects.

Despite my best efforts I am unable to refute this argument. So I pose the question to anyone else reading:

Why do the illustrious 18 index plays have an index of +0 for 16v10, when in an infinite deck you're better off hitting? Note: H17/S17 is irrelevant to this discussion as the dealer cannot possibly obtain a soft 17 if showing a 10, and the number of decks is irrelevant as well, as we have already converted to the true count. Also LS is irrelevant because you would obviously surrender if you could rather than either of the other, inferior options (hit and stand)

Thoughts?

Perhaps it has to do with the EOR of zero-value hi-lo cards, which bust a 16?

The number of decks does become important. Presuming 6 or 8 decks and Basic Strategy:

1.) Surrender 2-card 16 vs. 10-value: otherwise hit.
2.) 3-card 16 vs. 10-value: stand unless at least one card is a 6 (NOT Basic Strategy, but a draw result of the first two cards) EXCEPT 5-5 that draws a 6 vs. a 10-value will stand.

N&B

First of all, if you don't take into consideration the number of cards, then always hitting is better than always standing. However, it is such a borderline play that the effect of removal of just one card can change the math. If the 16 is composed of 2 cards, the average is 8. If the 16 is compared of 3 cards the average is 5.33. That is more small cards out of the deck, leaving more big cards remaining, making hitting more dangerous, tipping the odds in favor of standing.

I should knowing the exception is not help much. It would be better to stand if you have a 4 or 5, regarding of the number of cards in your hand, because those are the best cards to get by hitting, and there is one less in the shoe.

I'm going to take a guess about why the index value is 0 for 16 vs. 10. After a freshly shuffled deck the running count is already -1 by the time you adjust it for your two cards and the dealer's card. Your two cards will cancel with the hi-lo, but the dealer's 10 makes it -1. If we did not round it would just take a tiny negative count to favor hitting. The first round of a shoe we have that tiny small count with 16 vs 10. However, a true count of 0 suggests that a small card came out before to cancel out the dealer's 10, leaving more tens in the shoe, making hitting more dangerous.

I put in an Email to Don Schlesinger to confirm this, for now it is my educated guess.

I stand by my post above. Here is how I plan to word it in my next Ask the Wizard column:

First, it bears repeating that 16 Vs. 10 is an extremely borderline hand between hit and stand. If you're allowed to surrender, that is much better than both hitting and standing for the basic strategy player. Otherwise, hitting is a tiny bit better, on average. It would take the removal of just one small card to sway the odds in favor of standing, because with one less small card there are more large cards left, making hitting more dangerous. That is why I say that if your 16 is composed of three or more cards you should stand, because a 3-card 16 has removed at least two small cards from the shoe.

Second, the basic strategy is the correct strategy for the non-counter, based on the first hand after a shuffle. In creating the computer will considers the deck composition after the removal of the player's first two cards and the dealer's up card. The player's 16 will either be 10+6 or 9+7. In terms of the Hi-Lo count the 10 and 6 cancel each other out with one high and one low card. Removing a 9 and 7 is also neutral, because both are neutral cards. However, there is also the removal of the dealer's 10. So, the running count after the three cards are exposed is -1, meaning the rest of the shoe is small-card rich. Just that one ten removed is enough to sway the odds in favor of hitting.

Thus, I would argue that the basic strategy and Hi-Lo do not contradict. If it wasn't for rounding the Hi-Lo counter would have a true count of -0.167 in a six-deck game with 10+6 Vs. 10 after the shuffle. With any true count below zero the right play is to hit.

>First, it bears repeating that 16 Vs. 10 is an extremely borderline hand between hit and stand.
I'm glad you start out with this statement. It allows me to respond to the emotion involved rather than adhering to strictly optimal but emotionally undesirable play. Even my companion has asked me why I keep hitting when I have 16 since I always lose when I do it.

>If you're allowed to surrender, that is much better than both hitting and standing for the basic strategy player.
I understand what you are trying to say but think this is awkwardly phrased. Better than either hitting or standing OR better than hitting and better than standing might be alternative phraseology. "both hitting and standing" is cognitively difficult for me to read since obviously its not allowed.

>Otherwise, hitting is a tiny bit better, on average.
>It would take the removal of just one small card to sway the odds in favor of standing,
>...why I say that if your 16 is composed of three or more cards you should stand,
>because a 3-card 16 has removed at least two small cards from the shoe.
Wouldn't this situation be the one that is most likely to occur?

Quote: Wizard

However, a true count of 0 suggests that a small card came out before to cancel out the dealer's 10, leaving more tens in the shoe, making hitting more dangerous.

Wouldn't this be the same as the infinite deck that situation? Consider the following:

(a) An infinite deck always has a hi-lo count of zero, as it contains an infinite number of each type of card. Infinity = infinity, therefore there is no excess of any particular type of card, we have an equal likelyhood of receiving any card.

(b) Now, imagine a shoe with a 2,3,4,5,6,8 and A removed. We are then dealt a 7 & 9 and the dealer takes a 10 for himself. At this point the TC is zero, and we are playing with exactly n-.25 decks with a TC of zero and no unusual EOR based off of the specific cards that were removed. We have an equal likelyhood of receiving any type of card, as we do in an infinite deck.

So again I wonder why is it that that in situation (a) per the WOO website advises hitting, while situation (b) as published as part of the illustrious 18 advises standing? Is there a difference between these two situations?

My newest hypothesis is that the discrepency is due to the way that the illustrious 18 is rounded. The index is really a small number such that 0 < index <0.5. If this is the case, then a TC of zero actually favors hitting. However, the index value is closer to 0 than it is to 1, so it is reported as 0.

Sound about right?


Also:

Quote: Wizard

If it wasn't for rounding the Hi-Lo counter would have a true count of -0.167 in a six-deck game with 10+6 Vs. 10 after the shuffle. With any true count below zero the right play is to hit.

I've found for the TC = 0 index play there is no point bothering to convert to the TC. Any positive RC = a positive TC (and the inverse is also true.) So the effects of rounding the TC are not worth considering if the index is based on exactly 0. Thing is, as I mention above, the index presumably isn't exactly 0, it's something close, and positive.