help: changes in odds of dealer busting at various counts?

Does anyone know if the odds of dealer busting increase or decrease with the count for various upcards (after checking for BJ)? And by how much?

For example, a dealer with a 4 showing would probably bust more often at higher counts, but what about with a 7 or an Ace?
I am particularly interested in the ace....

This is what picked my interest:
I had 8 bets ridding on an 11 vs dealer A with TC +5 (HiLo), 2 decks remaining (6D, DAS, S17). Insurance didn't work (dealer did not have BJ). I doubled down (16 bets on the table), got myself a 16. Dealer busted his ace. Dealer busting an ace is 17% chance under standard circumstances. What is it under high counts, knowing he does not have BJ?
I am just very curious. tried to check with ToBJ or simulations, but the outputs do not have information that can help.

So basically my question is: what are the odds of dealer busting various upcards at different count levels?

Thanks to anyone who can help!!

"Dealer busting an ace is 17% chance under standard circumstances..."

Its just over 11%, not 17%

dealer busting an ace is ~17% after checking for BJ and he does not have BJ (of course).

dealer busting an ace is ~11% before checking for BJ.

dealer having BJ is 4/13 = ~31% chance. .69x.17= ~.11.

at TC+5, dealer has more chances of having BJ, but _after_ checking for BJ, does he have more OR less chances of busting his Ace? I just can't figure it out.

It would be interesting (at least to me) to see how dealer bust chances for various upcards change with count. I don't know if stats already exist on this. I don't know how to generate them myself.

According to this: http://www.blackjackincolor.com/useless2.htm, the dealer bust rates go down with higher counts (well, we all knew this), but I want to find out how much this varies for each upcard.

I was going by before checking and a count of zero. Obviously if he doesnt have one there is more of a chance to pull them and bust given that he doesnt have 6-9 under. I am sure that they bust more with 6 or less and less with 7+ up but someone will do the figuring I'm sure. I'm not much into the math of the game. Counting works and thats all I need to know.

"at TC+5, dealer has more chances of having BJ, but _after_ checking for BJ, does he have more OR less chances of busting his Ace? I just can't figure it out."

More chances. Goes to a little over 20% at +10, for example.

"It would be interesting (at least to me) to see how dealer bust chances for various upcards change with count. I don't know if stats already exist on this."

I've never seen them. Such a a chart would be nice. Of course, a set of rules would have to be specified. Then, say, TCs of -10 to +10, for each upcard, could be designated. The changes are not enormous, however, as you can see by the ace example. 17% goes to 20+%, for TC = +10.

"According to this: http://www.blackjackincolor.com/useless2.htm, the dealer bust rates go down with higher counts (well, we all knew this),"

You'd be surprised. Ask the average player why a counter wins in positive counts, and many will include, among the reasons, "the dealer breaks more frequently," which, as you state, is false.

"but I want to find out how much this varies for each upcard."

Maybe some industrious soul will generate the data. I can answer specific questions, such as the one above, but I don't have the energy to do the whole array.

Don

... because of the soft nature of the hand...

unless he has a 6-9 under, then the possibilities become almost endless as the hand goes from soft to hard and will easily get to the 3-4 cards combinations... hence my inability to figure it out...

I hope someone can though! There must be some people here who grasp the maths well enough to at least have some good approximations.

... I might give it a shot, but I have no idea how to get info out of simulations or how to set them up (CVData)....

I would of course start with: 6D, DAS, S17, pen 4.5 (if that actually has any impact, I don't see why it should as the TC is a remaining percentage of higher cards rather than full number).
I believe the decks remaining would have an impact even if we use TC (ToBJ to the rescue!).

Well, depending on how laborious this is I might do more. I would in preference do it for HiLo (as the reference), but would do Red7 too (the count I use with TC for betting as it is so easy to use).

I'm sure that there are many math guys on here. I am sort of, thats why I guess I can understand the reasons all this works unlike a friend I taught to count. He wants to know the specific math behind just about any play you can think of. I dont need to know the exact percentages behind them as long as the play I make is the correct one.
Still would like index numbers for the double on split aces rule when you happen to catch an ace on one (or both) thats been split and you cannot resplit but are allowed to double. I would guess in zero or higher counts you would double for a full bet amount against a 5 or 6 but what if the count was positive and you made a more than minimum bet, then when its your turn to play the hand the count has tanked to negative territory at that point. Would you double for the full or double for less? The math behind it isnt necessary for me but having the right call in this situation is.

This was one of the first outputs my CA-program was able to produce some 10 years ago:
Probabilities of dealer results with various upcards at various count.
I'll just give you the most interesting figure.
For the dealer five the chances of busting go up from 42% for neutral to 46% for TC+5.
If you ask specific questions, I can reveal more data.

Francis Salmon

I have more material than you might imagine. Stop tempting me!!

Don

I have more material than you might imagine. Stop tempting me!!

Oh, come on, you can't be that busy, LOL. Write the book and I'll be one of the first to buy it.

I can almost see the wheels turning in your head right now....

:-)

Regards,
drumz1