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Do the math

BenchmarkBenchmark Member Posts: 297
edited February 2016 in Poker Chat
Wasn't sure where to post this one, but here goes.

You hold a pocket pair, say KK. The turn is an innocuous 2 7 T.

What are the odds of hitting a full house or better (i.e. quads) ?

It sounds simple at first but I don't think it is, as when the turn card gives you a set instead of 2 pair, the numbers change.

Naturally, an explanation of the math would be nice, as opposed to a computer generated figure.

Bench.
«1

Comments

  • aussie09aussie09 Member Posts: 8,033
    edited February 2016

    it is not so complex bench

    the board just needs to pair any of the cards, on each of the two remaining cards to be dealt.

    so a K, 2, 7 or J.

    there are 11 remaining on the turn, from 40 cards ..let say a 25% chance.   similar numbers for the river.

    25% x 25% = 0.16

    say a 1 in 6 chance

    5 to 1 odds






  • Phantom66Phantom66 Member Posts: 5,542
    edited February 2016

    Turn odds are 11/47 (unless you know whether or not your out cards have already been dealt)

    Then

    If a K hit (2/11) you have 10 outs to a FH or quads - 10/46

    If a 2,7,T or hit (9/11) you have fewer outs.

    Only 2Ks and 2 of the card you just picked up will improve to FH - 4/46

    So overall the odds are (11/47)*(10/46)*2/11 + (11/47)*(4/46)*(9/11)

    =2.6% or 1/50 roughly (edit 1/40)

    But my stats are a bit rusty so could be wrong

  • NoseyBonkNoseyBonk Member Posts: 6,186
    edited February 2016
    sssssss

    ;-)

  • aussie09aussie09 Member Posts: 8,033
    edited February 2016
    In Response to Re: Do the math:
    Turn odds are 11/47 (unless you know whether or not your out cards have already been dealt) Then If a K hit (2/11) you have 10 outs to a FH or quads - 10/46 If a 2,7,T or hit (9/11) you have fewer outs. Only 2Ks and 2 of the card you just picked up will improve to FH - 4/46 So overall the odds are (11/47)*(10/46)*2/11 + (11/47)*(4/46)*(9/11) =2.6% or 1/50 roughly But my stats are a bit rusty so could be wrong
    Posted by Phantom66

    when you say you could be wrong, you are correct.  you are wrong.



  • BenchmarkBenchmark Member Posts: 297
    edited February 2016


    Yes Phantom, I like the look of that. Was wondering how the odds would be proportioned for the river, but your factors of 2/11 and 9/11 share them out. Nice work.

  • Phantom66Phantom66 Member Posts: 5,542
    edited February 2016

    Aussie I may well be wrong and at least I have the humility to recognise it.

    Odds of improving a pair to a full house on the turn and river = 2.5% from a poker odds website so I think I am close.

    If your answer is correct then I am running worse than I thought not to get so many full houses


  • Phantom66Phantom66 Member Posts: 5,542
    edited February 2016
    In Response to Re: Do the math:
    it is not so complex bench the board just needs to pair any of the cards, on each of the two remaining cards to be dealt. so a K, 2, 7 or J. there are 11 remaining on the turn, from 40 cards ..let say a 25% chance.   similar numbers for the river. 25% x 25% = 0.16 say a 1 in 6 chance 5 to 1 odds
    Posted by aussie09
    1. You do not know whether your outs are mucked or live so you have to count 47 cards not 40
    2. You have used one of your outs when you hit it on the turn yet you haven't considered that
    3. If you hit say a 2 then the 7 and 10 are no longer outs on the river
  • RLT16RLT16 Member Posts: 1,433
    edited February 2016
    im sorry but anyone who thinks 0.25 x 0.25 = 0.16 doesnt get to come onto the forum and tell other people they are wrong about anything.

    there is no way an overpair on the flop ends up being a Fh 1 in 6 times 

    Id bet my Br its closer to the 1 in 50 that phantom has come up with
  • aussie09aussie09 Member Posts: 8,033
    edited February 2016
    In Response to Re: Do the math:
    im sorry but anyone who thinks 0.25 x 0.25 = 0.16 doesnt get to come onto the forum and tell other people they are wrong about anything. there is no way an overpair on the flop ends up being a Fh 1 in 6 times the 1 in 50 quoted by phantom may not be quite right either, but id bet my Br its a **** of alot closer to that than 1 in 6
    Posted by RLT16
    yes, you're right

    0.25 x 0.25 = 0.0625

    which is 1 in 16

    or 15 to one odds.



  • BenchmarkBenchmark Member Posts: 297
    edited February 2016

    I think we can safely call this one closed.
  • aussie09aussie09 Member Posts: 8,033
    edited February 2016

    accurately, without trying to keep it simple, the chances are

    11 cards from 47 multiplied by 10 cards from 46

    which is,

    0.243 x 0.217 = 0.051

    which is slightly better than 1 in 20

    odds are 19 to 1



  • stuarty117stuarty117 Member Posts: 1,395
    edited February 2016
    In Response to Re: Do the math:
    it is not so complex bench the board just needs to pair any of the cards, on each of the two remaining cards to be dealt. so a K, 2, 7 or J. there are 11 remaining on the turn, from 40 cards ..let say a 25% chance.   similar numbers for the river. 25% x 25% = 0.16 say a 1 in 6 chance 5 to 1 odds
    Posted by aussie09
    25% x 25% is not 0.16

    It is 0.0625 or 6.25%

    or 1 in 16


  • MAXALLYMAXALLY Member Posts: 17,647
    edited February 2016



    However, if you do the countdown and play your cards right, the odds come down to fifteen to one.

    Hope this helps ;)
  • Phantom66Phantom66 Member Posts: 5,542
    edited February 2016
    In Response to Re: Do the math:
    accurately, without trying to keep it simple, the chances are 11 cards from 47 multiplied by 10 cards from 46 which is, 0.243 x 0.217 = 0.051 which is slightly better than 1 in 20 odds are 19 to 1
    Posted by aussie09
    I am still not sure about that one aussie

    You cant have 10 outs still on the river otherwise you would be counting 27, 2T, 7T, as acceptable run outs which they are not

  • Phantom66Phantom66 Member Posts: 5,542
    edited February 2016
    Where are Geldy/Teddy/Ivan when you need them?

    My head hurts
  • aussie09aussie09 Member Posts: 8,033
    edited February 2016
    In Response to Re: Do the math:
    In Response to Re: Do the math : I am still not sure about that one aussie You cant have 10 outs still on the river otherwise you would be counting 27, 2T, 7T, as acceptable run outs which they are not
    Posted by Phantom66
    hi phantom,

    it is just a question of having pocket pairs and the odds of getting to quads or house, either will do.  for that, the turn must pair the visibile cards, and so too the river.

    the workings for the turn we agree on 11 from 47.  however, the river must be any one of ten cards.  that is the 11 required less 1 (whatever came on the turn, it doesn't matter what occurred).  that 10 from 46.

    your workings were fine for K on the turn scenraios but didnt account for no King. (imo)







  • BenchmarkBenchmark Member Posts: 297
    edited February 2016

    I'm still with Phantom's original answer.

    Any more offers ?
  • RLT16RLT16 Member Posts: 1,433
    edited February 2016
    In Response to Re: Do the math:
    In Response to Re: Do the math : hi phantom, it is just a question of having pocket pairs and the odds of getting to quads or house, either will do.  for that, the turn must pair the visibile cards, and so too the river. the workings for the turn we agree on 11 from 47.  however, the river must be any one of ten cards.  that is the 11 required less 1 (whatever came on the turn, it doesn't matter what occurred).  that 10 from 46. your workings were fine for K on the turn scenraios but didnt account for no King. (imo)
    Posted by aussie09


    the odds your looking for are 11/47 then 4/46. once u hit 2 pair there are only 4 cards left in the deck left that improve your hand to a FH the other cards become null and hitting them just gives you a different 2 pair
  • EnutEnut Member Posts: 3,644
    edited February 2016
    In Response to Re: Do the math:
    Turn odds are 11/47 (unless you know whether or not your out cards have already been dealt) Then If a K hit (2/11) you have 10 outs to a FH or quads - 10/46 If a 2,7,T or hit (9/11) you have fewer outs. Only 2Ks and 2 of the card you just picked up will improve to FH - 4/46 So overall the odds are (11/47)*(10/46)*2/11 + (11/47)*(4/46)*(9/11) =2.6% or 1/50 roughly (edit 1/40) But my stats are a bit rusty so could be wrong
    Posted by Phantom66
    I'm pretty sure that this is right.

    I worked it out seperately and made it 2.66%, but that's prob just rounding.

    Phantom 1 Aussie 0 (imo of course)


  • gerardirlgerardirl Member Posts: 1,299
    edited February 2016
    Has anyone factored in the odds of folding on the turn? 

    :D
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