Looking for some average probabilities (per 100 hands)

[Fun_at_21]

Hi all,

I know this may be a rather "meaningless" question in the overall scheme of the game, but as a lover of the simple hand probabilities etc in blackjack, I was wondering if anyone had accurate/specific figures for how often one can expect any given TWO CARD total out of every 100 hands dealt?

For example, how many times (on average of course) will a player be dealt a two card total of 2 (A,A) per 100 hands?

What about a two card total of 3 (2,A)?

A two card total of 4 (2,2 or 3,A)?

A two card total of 5 (2,3 or 4,A)?

Etc, etc, etc... all the way through a two card total of 20 (10,10 or A,9)...

The probability of a two card 21 (blackjack) out of 100 given hands is the only one I in fact know already...

For the sake of these two card totals per 100 hands I'm assuming single deck, S17 and also am asking without care of what the dealers upcard is - essentially just looking for how many times I can expect every TWO card total to arise out of a 100 dealt hands from a fresh deck...

I appreciate any help!

 

[UK-21]

100 hands is far too small a sample.

If you search through the forum posts for postings by FLASH, he has a link to a library of useful stuff that lives on a server somewhere. Within this is the latest edition of Blackjack Attack by Don Schlesinger. This contains many useful tables, including hand frequency per 100,000 hands.

If you find it useful please support the Author by putting your hand in your pocket and buying the book.

Good luck.

 

[Fun_at_21]

100 hands is far too small a sample.

Well I'm not looking to use the 100 hands as a sample of what hands should be played properly or anything. I understand that 100 hands doesn't give a lengthy enough figure to determine exact odds. I was just referring to 100 hands as a percentage figure of how many times a two card total of 2 will be dealt to you for any given 100 hands. Or a two card total of 3, 4, 5, 6, 7, etc... I'm not looking at what to DO with the totals or even the expectation of winning with any two card total but just how often I can expect any two card total to pop up (as commonly expressed out of 100 hands or therefore as a percentage).

But I'll try and check out that link. I definitely can reduce the out of 100,000 hands figures to a percentage (out of 100 hands) on my own I suppose.

Thanks

 

[QFIT]

See Modern Blackjack Page 346.

 

[politcat]

See Modern Blackjack Page 346.

great set of charts in the following pages. thx!

I hadn't gotten that far into the book

 

[Fun_at_21]

See Modern Blackjack Page 346.

Thanks! I think that's pretty close to what I'm after.

I do notice the figures are for SIX deck rather than one deck. My instinct (which I know is bad to involve) makes me wonder if some of these percentages would be higher in just a single deck? But perhaps not noticeably so...

But thanks! For practical purposes I think this should work!

 

[QFIT]

Thanks! I think that's pretty close to what I'm after.

I do notice the figures are for SIX deck rather than one deck. My instinct (which I know is bad to involve) makes me wonder if some of these percentages would be higher in just a single deck? But perhaps not noticeably so...

But thanks! For practical purposes I think this should work!

Single deck is on the next page.

 

[Fun_at_21]

Single deck is on the next page.

Oh thanks! That should definitely work.

 

[StandardDeviant]

Hi all,

I know this may be a rather "meaningless" question in the overall scheme of the game, but as a lover of the simple hand probabilities etc in blackjack, I was wondering if anyone had accurate/specific figures for how often one can expect any given TWO CARD total out of every 100 hands dealt?

For example, how many times (on average of course) will a player be dealt a two card total of 2 (A,A) per 100 hands?

...

I appreciate any help!

Since there are 4 aces in a 52 card deck, the probability of drawing one off the top of the deck is 4/52. Then the probability of drawing a second ace is 3/51. So the probability of drawing two aces is the product (4/52)*(3/51), which 12/2652. This is about 1/2 a percent or about 220 to 1.

 

[Fun_at_21]

Since there are 4 aces in a 52 card deck, the probability of drawing one off the top of the deck is 4/52. Then the probability of drawing a second ace is 3/51. So the probability of drawing two aces is the product (4/52)*(3/51), which 12/2652. This is about 1/2 a percent or about 220 to 1.

Thanks! Now I even have an idea of the math behind it, which I like (even though math is unfortunately not my strong suit). But the above seems straightforward enough...