What are the odds on this?

unknown_username

one for the maths fans.  Just what the odds of two players making quads?
Hand History #312797042 (00:57 30/11/2010)PlayerActionCardsAmountPotBalancepewtSmall blind £0.05£0.05£17.10ParaPokerSBig blind £0.10£0.15£3.60 Your hole cardsQ7   TALLENTFold    azzypFold    ertikinsRaise £0.40£0.55£26.53pewtCall £0.35£0.90£16.75ParaPokerSAll-in £3.60£4.50£0.00ertikinsFold    pewtCall £3.30£7.80£13.45pewtShow55   ParaPokerSShowJJ   Flop  3J5   Turn  J   River  5   ParaPokerSWinFour Jacks£7.21 £7.21

emilyegg

The sock-filler commonly known as Merenovice we be along to belittle you shortly.....

hope this helps.

Tikay10

Thin, Mr Ertikins.

So thin, in fact, that I suspect even MereStat cannot work it out, or he'll have replied by now. You know how he loves these geeky maths equations.

Perhaps, as the Americans say, he is "doing the math". (Yuk yuk yuk, their dreadful dumbing down of our beautiful language is just horrible to behold).

YOUNG_GUN

in before mere :-)

NoseyBonk

In Response to Re: What are the odds on this?:

Thin, Mr Ertikins. So thin, in fact, that I suspect even MereStat cannot work it out, or he'll have replied by now. You know how he loves these geeky maths equations. Perhaps, as the Americans say, he is "doing the math". (Yuk yuk yuk, their dreadful dumbing down of our beautiful language is just horrible to behold).
Posted by Tikay10

Odd (hoho), he had replied earlier this morning...

GaryQQQ

The odds chance of a player making quads from 52 cards is 1/595. So at a 6-handed table on average somebody will make quads about once in every 100 hands. It will seem less often than this when you're playing because many hands are finished without all 5 community cards being dealt, ie the player who would have made quads will never know, and often the player who would have made quads will have folded at some stage (eg 27o UTG is folded preflop and the board runs out A2422).

That leaves each opponent only 48 cards to make one of the 12 other possible sets of quads. The maths gets very difficult now and I can't work out the odds, but it's going to be even less likely than 1/595. Maybe MereNovice will be able to crack this one.

I would estimate the chance is only 1/500,000, probably even less. Suprisingly though it's not quite as rare as you might think, some other sites run a bad-beat jackpot, to claim it you usually have to lose with quad 8s or better, these jackpots are often won by quads over quads. 312 million hands have been dealt on Sky to date, so quads v quads could have been dealt around 600 times if my estimate isn't too far off.

MereNovice

Sorry folks, I got distracted.

The probability of a single player making quads (assuming that the hand goes to showdown) in Texas Hold 'Em is:

3/51*2/50*1/49*35

which is equivalent to odds of 594 to 1.


Now, lets consider what has to happen for two people to get quads assuming that the quads are not shared in the community cards.
At least one player has to have a pocket pair.

The possible hand combinations are:

AA/BB/AABBC
AA/BC/AABBB
AA/BC/AACCC
BC/AA/AABBB
BC/AA/AACCC

which represent Player1/Player2/Community

The probability of the fiirst is: 3/51*48/50*3/49*30/1,712,304
The probability of each of the last four is: 3/51*48/50*44/49*10/1,712,304


To get the total probability we add these up.

This gives odds of 803,124 to 1.

Apologies if this isn't very clear.


As always, I'm happy to be corrected.

Talon

in the absence of our maths expert i have had a look at this and done some rough calculations.


 Based on the following odds.
 Chance of having a pocket pair 1 in 16
 Chance of 2 pocket pairs on the same table are 1 in 16 X 1 in 16 divided by 5.
 Chance of turning PP into quads is 2 in 40 X 1 in 39 with 10 permutations.
 Chance of the other PP becoming quads is 2 in 40 X 1 in 39 with 3 permutations.

 Which very rough calculations gives me the odds of 1,172,183 to 1.

 This is of course making several assumptions like none of the cards being dealt out and the hand going all the way to the river. If i have made any mistakes in theses calculations i am happy to be corrected.

aussie09

about a million to one.

if i have made any mistakes in these calculations i am happy to be corrected.

emilyegg

cracking work Vince..........you can go back to typing one-handed now.

unknown_username

so its not very likely then ;-)