Crazy Odds Question for Math Wizards

[Phoebe]

I am seeking what the odds are of a very, very unusual blackjack hand!!! Ready for this scenario??

A six deck blackjack table. (standard blackjack.)

A player is dealt two aces (A1 & A2). She splits.
A1 is dealt an ace (A3) - so she splits again.
A1 is dealt an ace (A4) - so she splits again.
Review: there are now four aces in front of the player.
A1-A4 are all dealt a tens (3 face cards, 1 ten).
Review: there are now four blackjacks in front of the player.

What are the odds of this happening?

 

[Meistro]

well the odds on resplitting AA to four hands are 1/13 to the 4th power or


0.000035153041

or
%0.0035


but then you need to multiply that # by .307 4 times to account for the ten cards.


so pretty unlikely.

%0.00031

should see this maybe once every 333,000 hands or so?

technically this could also happen the other way, by getting tens and splitting them and getting aces. that should be equally unlikely, so if you want to solve for that as well just take the complement of our probability and square it to account for both the ace splitting and ten splitting means

 

[DSchles]

well the odds on resplitting AA to four hands are 1/13 to the 4th power or


0.000035153041

or
%0.0035


but then you need to multiply that # by .307 4 times to account for the ten cards.


so pretty unlikely.

%0.00031

should see this maybe once every 333,000 hands or so?

technically this could also happen the other way, by getting tens and splitting them and getting aces. that should be equally unlikely, so if you want to solve for that as well just take the complement of our probability and square it to account for both the ace splitting and ten splitting means

It's proper to split aces (although not so common to be permitted to resplit them), but very wrong to split tens (unless counting), so let's just stick with the first scenario. Odds are less than you indicated, because you didn't factor in depletion of aces and tens as you go along, and you made a math error.

More exact odds are: (24/312) x (23/311) x (22/310) x (21/309) x (96/308) x (95/307) x (94/306) x (93/305) = once in 4,034,212 hands.
Your math above, in any event, is not correct. You're off by a factor of more than 10. Finally, for the original poster, the hands are not "blackjacks"; they're just normal 21s.

Don

 

[Phoebe]

Don,
1 in 4,034,212 is what I heard from someone else. I thought it would be much higher! Some casinos do consider those hands blackjacks actually. It's rare though. Indian casinos have some wacky rules! The place I was at where this hand happened to my friend, they did not pay 3-2, just even money (21's).

 

[Taff]

Its the norm to pay these hands as 21. 3:2 being on first 2 cards only.