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Odds on this hand please....

MAXALLYMAXALLY Member Posts: 17,636
edited September 2011 in Brags, Beats and Variance


3 handed Final table.


AA v KK v KK. Aces held shock.


This was in a pub game and we all tried to slow play them, lol. I had one of KK hands. Pub poker is rigged, init!
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  • GoetheGoethe Member Posts: 370
    edited September 2011
    220-1 are the odds for any given pair to be dealt.

    So it would be:  1/221 x 1/221 x 1/221 ??  = 1/10,793,861

    Seems a bit steep? If it's a hand shuffled game, you have to ask just how random the cards were? Very few people shuffle the cards really effectively - so the next deal is actually random.
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  • BLACK_MASSBLACK_MASS Member Posts: 401
    edited September 2011
    In Response to Re: Odds on this hand please....:
    220-1 are the odds for any given pair to be dealt. So it would be:  1/221 x 1/221 x 1/221 ??  = 1/10,793,861 Seems a bit steep? If it's a hand shuffled game, you have to ask just how random the cards were? Very few people shuffle the cards really effectively - so the next deal is actually random.
    Posted by Goethe
    Or if it was a new pack shuffled lazily.
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  • AMYBRAMYBR Member Posts: 3,432
    edited September 2011
    had a 7 handed game live t'other night where 6 were dealt PP's, the weakest mining it :p

    Seem to remember an episode of late night poker with your setup though. AA vs KK vs KK vs QQ.  One of the K's gets out of the way, the Q's also, A's take it at showdown, but with a Q on board :p
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  • GoetheGoethe Member Posts: 370
    edited September 2011
    In Response to Re: Odds on this hand please....:
    In Response to Re: Odds on this hand please.... : Or if it was a new pack shuffled lazily.
    Posted by BLACK_MASS
    All of the surplus casino sealed decks I've ever opened have the cards in suits, 2-A - so the aces and kings are all 13 cards apart prior to any shuffling? Done so that croups can quickly check them prior to getting them into use on the gaming floor and fleecing the punters.
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  • YOUNG_GUNYOUNG_GUN Member Posts: 8,948
    edited September 2011
    Rigged u even got on a final table, miracles can happen hey ;)
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  • PystermanPysterman Member Posts: 187
    edited September 2011
    In Response to Re: Odds on this hand please....:
    220-1 are the odds for any given pair to be dealt. So it would be:  1/221 x 1/221 x 1/221 ??  = 1/10,793,861 Seems a bit steep? If it's a hand shuffled game, you have to ask just how random the cards were? Very few people shuffle the cards really effectively - so the next deal is actually random.
    Posted by Goethe
    Actually, it's rarer than that since the second pair of KK is much less likely given that another pair is already out. (Also, unless you are specifying who has AA, you have to multiply your answer by 3.)

    The probability of AA v KK v KK is  3 / 59,830,225, approximately 1 in 20 million.

    The more general probability of XX v YY v YY is  36 / 4,602,325, about 1 in 125,000.

    However, you have to be careful about assigning odds to hands that have already happened. The odds of ANY specified combination of cards being dealt multihanded is usually pretty low. For example, the probability of AK v JJ v 76 being dealt is 64 / 12,724,075, about 1 in 200,000, but you wouldn't bat an eyelid if the cards came up this way.
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  • GoetheGoethe Member Posts: 370
    edited September 2011
    Can you expand on the numbers please?

    1/221^3 is the coincidence of three specific value hands all being dealt at the same time? It doesn't take into consideration which order they show up in.
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  • PystermanPysterman Member Posts: 187
    edited September 2011
    In Response to Re: Odds on this hand please....:
    Can you expand on the numbers please? 1/221^3 is the coincidence of three specific value hands all being dealt at the same time? It doesn't take into consideration which order they show up in.
    Posted by Goethe
    1/221 is the probability of a given pair appearing in a given hand.

    However, (1/221)² is not quite the probability of 2 given pairs appearing in 2 given hands, since the events are not independent.

    To simplify, look at a 2-handed table and consider the probability of AA vs KK arising.

    The probability of the first player being dealt AA and the second KK is...

         (4/52) x (3/51)    x    (4/50) x (3/49)    =    6/270725 (about 1 in 45000)

    If the first person has been dealt AA, then the probability of the second person getting KK is slightly higher as there is now a higher proportion of Kings left in the deck (4 out of 50, instead of 4 out of 52).

    ALSO, the above calculation only counts the case where the first person gets AA and the second KK. Of course, you have to count the case where the first person gets KK and the second AA. The probability of this is the same as above, so the probability of AA vs KK arising is 12/270725 (about 1 in 22500).


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  • GoetheGoethe Member Posts: 370
    edited September 2011
    Thank you for that.

    Yes, there are always some slight adjustments to make that reflect the differing order in which the cards could be  dealt out, although most of the time the difference isn't material.

    From your earlier post, where does the multiply it by three come into it?
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  • PystermanPysterman Member Posts: 187
    edited September 2011
    In Response to Re: Odds on this hand please....:
    From your earlier post, where does the multiply it by three come into it?
    Posted by Goethe
    Could have AA v KK v KK,

    or KK v AA v KK

    or KK v KK v AA

    all essentially counting as "a pair of Aces against two pairs of Kings".
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  • GoetheGoethe Member Posts: 370
    edited September 2011
    Have to say I'm a bit confused with this. As you've pointed out, there will be a small variation in the odds dependent on the order in which the cards are dealt, to make up the three hands, but you wouldn't take the odds on one possible coincidence and multiply it by three to get a true figure? I can see a point in taking an average of the three, although materially there won't be too much between them.
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  • Poker_FailPoker_Fail Member Posts: 1,755
    edited September 2011
    In Response to Re: Odds on this hand please....:
    In Response to Re: Odds on this hand please.... : Actually, it's rarer than that since the second pair of KK is much less likely given that another pair is already out. (Also, unless you are specifying who has AA, you have to multiply your answer by 3.) The probability of AA v KK v KK is  3 / 59,830,225, approximately 1 in 20 million. The more general probability of XX v YY v YY is  36 / 4,602,325, about 1 in 125,000. However, you have to be careful about assigning odds to hands that have already happened. The odds of ANY specified combination of cards being dealt multihanded is usually pretty low. For example, the probability of AK v JJ v 76 being dealt is 64 / 12,724,075, about 1 in 200,000, but you wouldn't bat an eyelid if the cards came up this way.
    Posted by Pysterman
    +1, that's pretty much what I was going to badly attempt to convey. I would have failed miserably at explaining however lol
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  • Poker_FailPoker_Fail Member Posts: 1,755
    edited September 2011
    In Response to Re: Odds on this hand please....:
    Have to say I'm a bit confused with this. As you've pointed out, there will be a small variation in the odds dependent on the order in which the cards are dealt, to make up the three hands, but you wouldn't take the odds on one possible coincidence and multiply it by three to get a true figure? I can see a point in taking an average of the three, although materially there won't be too much between them.
    Posted by Goethe
    Google permutations.
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  • pod1pod1 Member Posts: 4,377
    edited September 2011
    lets just say its high!
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