Speedpoker
Joined: Apr 6, 2014
• Posts: 5
April 6th, 2014 at 4:53:04 PM permalink
Hi everyone,

First time poster, long time fan.

Simple question for all the Math guru's out there.

What are the odds of being dealt a specific Perfect Pair in Black Jack, 6 decks?

For example, what are the odds of being dealt 2x Ace of spades, or 2x King of Diamonds?

I am aware of the Perfect Pairs Side bet and the relevant odds, (Pays 25-1 I believe).

However, what are the odds on specific perfect pairs?

I appreciate the help.
RS
Joined: Feb 11, 2014
• Posts: 8623
April 6th, 2014 at 4:59:57 PM permalink
Chance of being dealt two Ace of Spades is (6/312)*(5/311). If you're wondering what the chance of being dealt any perfect pair, then the chance is 5/311.
AxiomOfChoice
Joined: Sep 12, 2012
• Posts: 5761
April 6th, 2014 at 5:00:08 PM permalink
Well there are 312 cards in the shoe and 6 of whatever card you want.

So you have a 6/312 chance of getting your card for the first card. If you do, now there are 311 cards left and 5 of the ones that you want.

So the answer is 6/312 * 5/311 = 30/97032 = about 0.03%
Sonuvabish
Joined: Feb 5, 2014
• Posts: 1342
April 6th, 2014 at 5:23:15 PM permalink
Quote: Speedpoker

Hi everyone,

First time poster, long time fan.

Simple question for all the Math guru's out there.

What are the odds of being dealt a specific Perfect Pair in Black Jack, 6 decks?

For example, what are the odds of being dealt 2x Ace of spades, or 2x King of Diamonds?

I am aware of the Perfect Pairs Side bet and the relevant odds, (Pays 25-1 I believe).

However, what are the odds on specific perfect pairs?

I appreciate the help.

REINSTATED as 1 in 3234 chance.
Speedpoker
Joined: Apr 6, 2014
• Posts: 5
April 6th, 2014 at 6:40:42 PM permalink
Thanks very much gang - Appreciate the quick responses.

This is exactly what I need.
arcticfun
Joined: Oct 2, 2013
• Posts: 175
April 7th, 2014 at 1:09:26 PM permalink
Quote: Sonuvabish

Approximately 0.03%. 1 in 3234 chance. Obviously, if it paid 1000 to 1, it is still a terrible bet. 25-1, don't play.

Not quite right if OP is asking about *any* perfect pair. For a specific pre-defined pair (ie, Ace of Spades), then yes, it's 6/312 * 5/312. Otherwise, the probability of getting *any* pair is
312/312 * 5/311 = 0.0161 = 1.6% or about 1 in 62.
Sonuvabish
Joined: Feb 5, 2014
• Posts: 1342
April 8th, 2014 at 3:35:56 PM permalink
Quote: arcticfun

Not quite right if OP is asking about *any* perfect pair. For a specific pre-defined pair (ie, Ace of Spades), then yes, it's 6/312 * 5/312. Otherwise, the probability of getting *any* pair is
312/312 * 5/311 = 0.0161 = 1.6% or about 1 in 62.

Oh you're right. I calculated it like the royal match, results felt off. Thanks for pointing it out. Hope OP reads it. I PMed him, all I can do!
Sonuvabish
Joined: Feb 5, 2014
• Posts: 1342
April 8th, 2014 at 3:44:20 PM permalink
duplicate
Speedpoker
Joined: Apr 6, 2014
• Posts: 5
April 8th, 2014 at 5:09:27 PM permalink
Thanks everyone.

Appreciate the feedback.

I was referring to specific Perfect Pairs, such as Ace of Spades and Ace of Spades as the first two cards for a player.

Appreciate the follow up however, and thanks to Son for the PM.
Sonuvabish
Joined: Feb 5, 2014