Infinite deck, probability dealer busts

Hi all - I have set up a spreadsheet to determine probabilities of dealer busting with the various combinations of the dealer's up-card. According to this website all my numbers are correct except when the up-card is an Ace:

www.blackjackinfo.com/bjtourn-dealercharts.php#TIDS17

My calculations get, P(bust w Ace) = 11.52863%
Other site says it is 16.65% probability.

I assume dealer sits on soft-17.

Can anyone help me out with where I might be going wrong? I feel like my number might be right.

The 16.65 is after the dealer checks for blackjack. 11.53 is about 9/13 of that. That's the only thing I can think of. But then your dealer up card of 10 would be 12/13 of 22.98 (about 21.21).

Thanks Miplet - I am basing it on Australian casinos where there is "no peeking", i.e. the dealer does not check for blackjack. After thinking it through some more I am pretty sure the 11.52863% is correct.

If any one can confirm it would help me sleep tonight... :)

Wardos

I believe you are right

Thanks Pokerface.

As Miplet said, my number of 11.52863% is 36/52 of 16.65%, so the website my operate being able to peek. 36 being in an infinite deck 52 minus 16 picture cards.

Many thanks.
Wardos

Infinite deck?
I've always assumed that an infinite deck was similar to an airplane with an infinite wingspan: easy for calculations but a bit impractical in real life.

Just as an infinite wingspan makes the plane a bit difficult to get into a hangar, some real world problems arise with the concept of an infinite deck.

I remember the days of "Dealer Must Draw to 16, Stop on all 17s". Then it became Dealer hits on a soft 17. It also became a cards coming not just out of a shoe but they have these devices that shuffle automatically. Some seem to introduce those shuffled discards back into the shoe so the deck does seem to be of infinite length.

Unfortunately I've never been able to differentiate between the devices but have concluded that I've played most often at devices that shuffled but did not re-introduce the discards into the shoe in any manner. If I play most often at a table wherein there is a shoe to dealers left and a separate device to dealers right from which a stack of cards is removed from time to time, should I consider this to be an infinite deck or an 8 card deck? Does it really make a difference?

FleaStiff - I live in Melbourne, Australia. My closest casino is Crown Casino where they have ShuffleMasters everywhere. After each hand, those cards are inserted in the machine where in theory you can get them back the next hand. Whether infinite deck or 8 deck probabilities are more accurate, I am unsure but my gutfeel is infinite is better.

To, any one that can help?

As per the earlier thread, I have been trying to re-create infinite deck expected returns in my own Excel spreadsheet. I know there are sites with optimal play strategies but I wanted to crunch the numbers myself. I have been referring to Wizard of Odds, Appendix 1 to the Blackjack section:

I have been able to set up all the dealer probabilities of either: (i) going bust; or (ii) reaching totals of 17-21 (and agree with the Wiz). But I can't reconcile all the expected returns when hitting. When calculating the players first two card totals of 16-21 I agree with the Wiz but then there doesn't appear to be any consistency with lower Player first two card totals.

For example, Player is on Hard 15. I work out odds of hitting one more card A, 2, 3, 4, 5, 6, 7, 8, 9 & T. Hitting for a 7, 8, 9 & T = bust, for 2, 3, 4, 5 & 6 I pick up the expected returns when the player sits on the new total which is 15 + 2 thru 6 = 17, 18, 19, 20 & 21. Problem I have is with the Ace??

I would have thought the returns I pick up were the same as the expected returns for sitting on 16. For each of the Dealer's cards I thought it would be:
2 = -0.2928
3 = -0.2523
4 = -0.2111
5 = -0.1672
6 = -0.1537
7 = -0.4754
8 = -0.5105
9 = -0.5431
T = -0.5404
A = -0.6670

This matches the Wiz for Dealer's up-card for 2, 3, 4, 5 & 6 but differs for the others 7, 8, 9, T & A. It looks like the Wiz for these numbers uses:
7 = -0.4148
8 = -0.4584
9 = -0.5093
T = -0.5398
A = -0.5171

, which if you look at the tables is picking up the expected returns for the previously derived expected returns for 16.

I would have thought this is inconsistent? Either you pick up the row for the previously derived expected returns or you use the sitting expected returns. Basically, I don't understand the logic used.

The way I think it should work is Player is on Hard 15 and hits, gets say a 2 which is the same expected returns as sitting on 17. Then you evaluate the expected returns for sitting and hitting on 17 to determine what to do, but it doesn't look like this is the way the Wiz has done it.

If any one is about to help it would be appreciated, I can always email my worksheet if that helps?

On Monday I'll see about posting my infinite deck spreadsheet at docs.google.com.

Thanks Wizard - I would be most interested to see your infinite deck spreadsheet. I have never used docs.google.com but have signed up in the hope of you sharing that with me. My email address is njmward@bigpond.net.au

I have poured through your Wizard of Odds site in much detail and can't find anything about actually crunching the numbers. I am doing it the old fashion way in Excel and have so far conquered:
1) all dealer probabilities of going bust, 17, 18, 19, 20, 21 or BJ with the 13 different up-cards
2) expected return for player sitting on all totals
3) expected return for player doubling

but am having a lot of trouble for player hitting expected returns. It's actually doing my head in, so would love some help. I can't seem to pick up the logic to reconcile with your Blackjack Appendix 1 expected returns for hitting.

Anyway, I will standby for your spreadsheet.
Cheers
Wardos

Okay, I just put my appendix1.xls spreadsheet on Googledocs, and allowed anyone to view it. Here is the link.