How high does the count need to be

If the dealer shows a 10, according to the Wiz, he will break 0.229784833. As the count increases, I assume his likelihood of breaking does as well, but how much can you move the needle? Is there a point where you can predict he'll bust 26%? It seems like a high count also increases the likelihood he already has a good hand, so I'd imagine the bust rate doesn't change substantially. If anyone knows where I could find that answer, I'd appreciate it.

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Yeah, for a 10 to bust, the unseen hole card must be a 2,3,4,5, or 6. As the count gets higher, it is less likely that it will be these cards. So the opposite of what you suggest is true.

Quote: surrender88s

Yeah, for a 10 to bust, the unseen hole card must be a 2,3,4,5, or 6. As the count gets higher, it is less likely that it will be these cards. So the opposite of what you suggest is true.

Cool thread; int questions.

Surrender88, you make a good point, but wouldn't that phenomenon be at least partially offset by the fact that in those fewer instances when the dealer DOES end up with 12 thru 16, he'll bust more often with the higher count than he otherwise would?

Are we sure the "fewer hands from 10 showing to 12 thru 16 total" phenomena is greater than the "but, for those 12 thru 16's he does get, he'll bust more often" phenomenon? (I openly admit to not having a clue).

Quote: hmmm23

Cool thread; int questions.

Surrender88, you make a good point, but wouldn't that phenomenon be at least partially offset by the fact that in those fewer instances when the dealer DOES end up with 12 thru 16, he'll bust more often with the higher count than he otherwise would?

Are we sure the "fewer hands from 10 showing to 12 thru 16 total" phenomena is greater than the "but, for those 12 thru 16's he does get, he'll bust more often" phenomenon? (I openly admit to not having a clue).

Right- I thought in a card counting strategy a higher count says not to hit 16 against a 10, so here again I wasn't sure if it is because the player is too likely to bust, or if the odds of the dealer busting went up as well.

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Just thinking it through (not sure how to frame the math), regardless of the hole card, a 2 thru 6 will REQUIRE the dealer to take a hit, and therefore a higher probability of busting (assuming dealer hits soft 17). With a 10, more than 1/2 the hole cards will not require a hit. No 2 card combo can bust, so there has to be significantly more risk in taking a hit regardless of whether it results in a win. Or am I missing your point? I think you have to hit 16 against a 10 just because the dealer's odds of not having to take a hit are better than 50/50.

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basic strategy and the deviations live the illustrious 18 are correct. It's good to ask questions and learn the theory and math of it, and even to question it- but when I do this I keep coming back to sticking with the time-tested strategies. Just realize you'll run into a lot of people who stick to these ideas without questioning them and they might not be as patient with you.

IF the dealer has a 12-16 (what you're hoping for with his 10 showing), he is more likely to break. But if the count is anywhere above 0, we know that there are more 10's and A's, and quite possibly 7-9's, than 2-6's.

With a 10 up, there's a 8/13 chance of dealer not busting and standing with two cards. Even with the other 5 cards that give dealer a two-card 12-16, there's still a likelihood of breaking that is somewhere around 40%. This gives some amount of balancing effect, but not enough to overcome the difference from the first card being more likely to be a 7 or higher.

But what the numbers and deviations are saying is that, as the count increases, it becomes more likely that higher dealer values,10-A will make hands, and that it is more likely that 2-6 will break. Not sure, but I think it's also more likely that 7-9 will make hands.

Quote: Ibeatyouraces

Even though the dealer will bust less often with a higher up card [with a positive count]

Are we sure a dealer w/ a 10 up will bust less often with a positive count?

True, a dealer with a 10 up will get a two card total of 12 thru 16 less often than with a zero count. But at least partially offsetting that is the fact that when the dealer does get those (fewer) 12 thru 16's, he'll bust them a higher proportion of the time than he would with a zero count.

So I guess my question is, are we sure the impact of # 1 is greater than the impact of # 2?

1. The fewer 12 to 16's the dealer gets due to the high count.
vs
2. The more of those 12 to 16's he busts due to the high count.

Quote: surrender88s

But what the numbers and deviations are saying is that, as the count increases, it becomes more likely that higher dealer values,10-A will make hands, and that it is more likely that 2-6 will break. Not sure, but I think it's also more likely that 7-9 will make hands.

Interesting stuff. You mention the increased bust percentage for a high count dealer's 12 to 16 provides some balancing effect, but not enough to offset, the higher % of two card pat hands the dealer will get owing to the high count.

That actually agrees with my own gut reaction, but some things in this game aren't self evident. Are you certain of that conclusion because you've seen the numbers behind it somewhere?

For simplicity, I've assumed that a low card will be a 4, and that a mid card will be an 8. You can analyze this if you want. There are situations where dealer would make a hand with 10+low+mid. He could also bust with 10+low+low(10+6+6). Either way, the chance of dealer busting most certainly does not increase as the true count increases.

TC Low Mid High Total Dealer first must hit low: Then must hit Mid or High Chance of bust
0 500 300 500 1300 38.46% 61.54% 23.67%
2 400 300 600 1300 30.77% 69.23% 21.30%

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Quote: Ibeatyouraces

They only bust more often when faced with a stiff (12-16), not overall which is where most beginners are confused.

Interesting- so when you hear people say the dealer will bust more with a high count, it really means he will bust more often "when you are relying on him to bust". So, with a 2-6, chances are good he has a high card buried and another on the way. But with a high card already showing, his likelihood of busting goes down or remains nearly the same.

Yup. That's part of the reason why you surrender more at higher counts.