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?

Quote:James85How 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.

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

Quote:gordonm888The 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?

Quote:James85Yes,

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?"

Quote:James85Yes,

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.

Quote:ThatDonGuyYes - 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?

Quote:FatGeezusIf 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.