Repeating Hands in Hold'em

What would be the probability of a player getting the same hole cards and the same (meaningful) board in 50 or so hands of Texas Hold’em? For instance the hole cards could be the Q/10 ♥ and the board produces let’s say the 8/9/J ♥ plus 2 junk cards.

Quote: jdauwe13

What would be the probability of a player getting the same hole cards and the same (meaningful) board in 50 or so hands of Texas Hold’em? For instance the hole cards could be the Q/10 ♥ and the board produces let’s say the 8/9/J ♥ plus 2 junk cards.

You need to be much more specific as to "the same meaningful board".

As for your specific situation, assuming the specific suit does not matter (i.e. having Q/10 of Spades as your hole cards and 89J of Spades on the board):
There are 1326 possible pairs of hole cards, of which 8 are Q/10 suited.
Of the remaining 50 cards, there are 2,118,760 sets of board cards, of which 1081 include 8,9,J of the same suit as the hole cards.
The probability for one hand = 8 / 1326 x 1081 / 2,118,760 = 1 / 324,870.
The probability for at least once in 50 hands = 1 - the probability of none in 50 hands = 1 - (324,869 / 324,870)⁵⁰, or about 1 / 6498.

Note that this is the probability of it happening once in 50 hands - it assumes that you were already dealt this just before the start of the 50 hands.

I frequently get repeating hole cards - different suites - in poker stars. I've gotten kings once 4 times in one tournament. Not in a row. What I think you mean is - what I think you are speaking about is what well call "situational coincidences". You get a pair of kings and a person had aces and you go all in. On occasion the kings flops flop a set to crack the aces but for the most part it follows exact odds. Or when you get a straight and someone had flopped a flush. Or you backdoor a flush but the dude had a boat by the turn because when the board pairs you're usually screwed.

First I am very happy with what I have seen so far! Hope to clarify my "same meaningful board" statement - as long as the cards making the straight flush are included, the other 2 can be ANYTHING (so a #C2 option would work). But I also want to clarify those hole cards a little better --- not interested in other suits, BOTH hands had the EXACT same hole suited cards holding the ranks of Q/10 respectively.

Hope that clarifies things and I look forward to additional changes this may make. A REAL interesting twist has yet to be added ... along wit the idea this specific situation actually did occur.

Thanks again....

There was a similar problem posted elsewhere.

The probability of being dealt the same pair of hole cards two or more times in 50 hands = 1 - the probabililty that 50 hands have 50 different pairs.
There are 1326 different pairs, so the probability of at least one duplicate pair in 50 = 1 - (1325/1326)⁵⁰ = about 1/27.

Of course, not all pairs may have a "meaningful board." What would a meaningful board be for, say, 9/2 offsuit?

Quote: ThatDonGuy

Of course, not all pairs may have a "meaningful board." What would a meaningful board be for, say, 9/2 offsuit?

92xxx, 99xxx, 22xxx, 922xx. 992xx, 999xx, 222xx,

Although most of those would usually not make much money.

If repeat cards occur a little more than anticipated in a home game, one thing to consider is the shuffling procedure of the dealer when it happens. I once heard that the minimum amount of shuffles to make the next hand truly random is 7. If the repeated cards happen online, I'd be much more skeptical given the above math.

The original "for instance" is what actually happened, TWICE, with a minimum of 40 hands between repeats. I was simply estimating 50 hands for sake of argument. Both times I was dealt Q/10 of hearts, both times the board filled the straight flush with the 8,9 and Jack of hearts. Thus the other 2 cards were meaningless in my eyes. The probability of this happening ONCE is slim, the probability of this occurring TWICE, in the same game, should be astronomical! Exact same hole cards, exact same result --- the EXACT same straight flush!

And believe it or not, there is EVEN MORE to the story!!

I really appreciate the numbers ... I am a former math teacher but my area of expertise is algebra based, not probability.

Quote: jdauwe13

First I am very happy with what I have seen so far! Hope to clarify my "same meaningful board" statement - as long as the cards making the straight flush are included, the other 2 can be ANYTHING (so a #C2 option would work). But I also want to clarify those hole cards a little better --- not interested in other suits, BOTH hands had the EXACT same hole suited cards holding the ranks of Q/10 respectively.

Hope that clarifies things and I look forward to additional changes this may make. A REAL interesting twist has yet to be added ... along wit the idea this specific situation actually did occur.

Thanks again....

In (Europe?) they do something called duplicate bridge. That’ll be my last comment here because that’s what’s happening in my opinion. Just with poker.

Quote: jdauwe13

The original "for instance" is what actually happened, TWICE, with a minimum of 40 hands between repeats. I was simply estimating 50 hands for sake of argument. Both times I was dealt Q/10 of hearts, both times the board filled the straight flush with the 8,9 and Jack of hearts. Thus the other 2 cards were meaningless in my eyes. The probability of this happening ONCE is slim, the probability of this occurring TWICE, in the same game, should be astronomical! Exact same hole cards, exact same result --- the EXACT same straight flush!

And believe it or not, there is EVEN MORE to the story!!

I really appreciate the numbers ... I am a former math teacher but my area of expertise is algebra based, not probability.

Was this in a home game?