James85
• Posts: 21
Joined: Nov 8, 2014
December 17th, 2020 at 8:38:35 PM permalink
How true is the below table as the deck is shuffled every hand?

In one of the website I have seen the below table.

Here’s the frequency of paying hands in Pair Plus:

Paying hand .........................................................Frequency
Mini-royal .........................................................1 in 5,525
Straight flush in game with mini-royal .......1 in 502
Straight flush in game without mini-royal.... 1 in 460
Three of a kind.........................................................1 in 425
Straight ......................................................................1 in 31
Flush ...........................................................................1 in 20
Pair ......................................................................... 1 in 6

Is it true that one in a 6 cards dealt is a Pair?
ChesterDog
• Posts: 1571
Joined: Jul 26, 2010
December 17th, 2020 at 9:02:20 PM permalink
Quote: James85

How true is the below table as the deck is shuffled every hand?

In one of the website I have seen the below table.

Here’s the frequency of paying hands in Pair Plus:

Paying hand .........................................................Frequency
Mini-royal .........................................................1 in 5,525
Straight flush in game with mini-royal .......1 in 502
Straight flush in game without mini-royal.... 1 in 460
Three of a kind.........................................................1 in 425
Straight ......................................................................1 in 31
Flush ...........................................................................1 in 20
Pair ......................................................................... 1 in 6

Is it true that one in a 6 cards dealt is a Pair?

See the Wizard's page https://wizardofodds.com/games/three-card-poker/ for the numbers of combinations for each hand of Three Card Poker.

The total combinations for hands of three cards is 22,100. And there are 3,744 combinations to make a pair. Then 3,744 divided by 22,100 is about 1 in 5.90277778.

So, about 1 in 6 hands is a pair.
gordonm888
• Posts: 5128
Joined: Feb 18, 2015
December 17th, 2020 at 9:06:01 PM permalink
The frequency of a three-card hand that is "a pair plus a singleton" is:

13*6*48/combin(52,3) = 0.169412 =1/5.903 approx.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
James85
• Posts: 21
Joined: Nov 8, 2014
December 17th, 2020 at 9:21:47 PM permalink
Quote: gordonm888

The frequency of a three-card hand that is "a pair plus a singleton" is:

13*6*48/combin(52,3) = 0.169412 =1/5.903 approx.

Yes,

1 in 6 times.

But as the deck of cards are shuffled every time.
Is this - 1 in a 6 times true?
gordonm888
• Posts: 5128
Joined: Feb 18, 2015
December 18th, 2020 at 8:36:10 AM permalink
Quote: James85

Yes,

1 in 6 times.

But as the deck of cards are shuffled every time.
Is this - 1 in a 6 times true?

If the shuffle process effectively randomizes the cards then this is true.

Are you implying that the cards are shuffled once (and shuffled perfectly) and asking about "shuffle tracking?"
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
ThatDonGuy
• Posts: 6414
Joined: Jun 22, 2011
December 18th, 2020 at 8:54:55 AM permalink
Quote: James85

Yes,

1 in 6 times.

But as the deck of cards are shuffled every time.
Is this - 1 in a 6 times true?

Yes - in fact, right after the deck is shuffled is pretty much the only time when we know it is true, as the calculation depends on all 52 cards being available for the deal.
FatGeezus
• Posts: 564
Joined: Jun 12, 2010
December 18th, 2020 at 9:32:51 AM permalink
Quote: ThatDonGuy

Yes - in fact, right after the deck is shuffled is pretty much the only time when we know it is true, as the calculation depends on all 52 cards being available for the deal.

If you eliminated 3 cards (the dealers) and 3 cards for every player, wouldn't the calculation change?
gordonm888
• Posts: 5128
Joined: Feb 18, 2015
December 18th, 2020 at 10:17:46 AM permalink
Quote: FatGeezus

If you eliminated 3 cards (the dealers) and 3 cards for every player, wouldn't the calculation change?

It would if you knew what those cards were. Probabilities always depend upon knowledge -the more you know, the more the probabilities change.

If you don't know what those cards are in the dealer's and other players' hands, then the probabilities remain unchanged.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.