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take the flush, or go for more?

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  1. #1

    Default take the flush, or go for more?

    I had 2 hands come up when playing where I could have locked in a flush early on, but had a straight or royal draw... what do you guys think?

    Hand 1







    Notes: Q still live, 1 other spade dead.

    Hand 2







    Notes: 8 still live, 2 other diamonds dead.
    Last edited by givememyleg; 09-20-2013 at 07:52 PM.
  2. #2
    i'm just a math idiot, i wouldn't even know where to begin to start calculating this.
  3. #3
    I think both of these spots are clear-cut: just take the flush. Hand 1 might be close but Hand 2 is a no-brainer.

    The problem you have is that if you're not playing them to make your flush, these cards don't really give you any value. If, in Hand 2, you had 3c 3s in the middle, then yeah I'd go for trips/boat/quads in the middle and a shot at a SF and a huge hand.

    It also sort of depends what hands your opponent(s) are drawing to; if in Hand 2 someone is 4/5ths to a J-high flush, it might be worth it to pass and hope for a higher diamond.
    Playing big pots at small stakes.
  4. #4
    Quote Originally Posted by baudib View Post
    It also sort of depends what hands your opponent(s) are drawing to; if in Hand 2 someone is 4/5ths to a J-high flush, it might be worth it to pass and hope for a higher diamond.
    Very true, at this point there is only a 14.7% chance to catch the royal in hand 1 or SF in hand 2 and that alone is not enough to justify passing up a flush here, but your opponents holdings might make it profitable to do so.
  5. #5
    MadMojoMonkey's Avatar
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    Let S be the number of spades left in the deck.
    Let C be the number of cards to come.
    Let D be the number of cards Hero can not see (left in the deck).

    The chance of drawing EXACTLY 1 more spade in this round:
    (S,1)*(D-S,C-1)/(D,C)
    where the notation (a,b) means "a choose b". E.g. (4,2) = 6

    Then the odds of making your flush is 1 minus the odds you you drawing 0 spades.
    1 - (S,0)*(D-S,C)/(D,C)

    But we know that ANYTHING choose ZERO is always 1. So it reduces to:

    1 - (D-S,C)/(D,C)

    That is the equation to tell you the % chance you will complete your flush.

    Hand 1:
    Assumptions:
    1) You are first to act, so there are 40 cards that you can not see (because they are in the deck).
    * If you are 2nd to act, then there would be 39.

    Givens:
    1) There are 7 spades left in the deck
    S = 7
    2) There are 7 cards left to be dealt.
    C = 7
    3) There are 40 cards left in the deck.
    D = 40

    So your chance of making the flush, if you do NOT place the 9 there now is:
    1 - (D-S,C)/(D,C)
    1 - (40-7,7)/(40,7)
    1 - (33,7)/(40,7)
    1 - 4,272,048/18,643,560
    1 - 0.2291
    0.771

    77.1%


    Hand 2:
    Basically the same as Hand 1, except there is 1 less "spade" in the deck. Here, we can just replace "spade" with diamond.
    S = 6, C = 7, D = 40

    1 - (D-S,C)/(D,C)
    1 - (40-6,7)/(40,7)
    1 - (34,7)/(40,7)
    1 - 0.2885
    0.711

    71.1%
    Last edited by MadMojoMonkey; 09-19-2013 at 03:37 PM.
  6. #6
    MadMojoMonkey's Avatar
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    Quote Originally Posted by Filik View Post
    that alone is not enough to justify passing up a flush here, but your opponents holdings might make it profitable to do so.
    This is ignoring the value of royalties, no?
  7. #7
    MadMojoMonkey's Avatar
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    I guess I'd go for the SF in both cases. The Royalty of 25 or 15 points for the RF or SF, respectively, in the back is pretty huge. With over 2.5:1 in favor of me making the flush anyway, even if I pass it up now, I think it's worth the gamble.
    Last edited by MadMojoMonkey; 09-19-2013 at 03:52 PM.
  8. #8
    Quote Originally Posted by MadMojoMonkey View Post
    I guess I'd go for the SF in both cases. The Royalty of 25 or 15 points for the RF or SF, respectively, in the back is pretty huge. With over 2.5:1 in favor of me making the flush anyway, even if I pass it up now, I think it's worth the gamble.
    Good point, I didn't even think about the odds of hitting the flush if we were to pass it up on 7th. I guess the calculations are correct, so yeah, I guess I was wrong, passing up the flush in both hands seems +EV
  9. #9
    Tom1559's Avatar
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    This is all a bit of a mystery to me. I have enough problems working out the odds in NLH and Omaha without getting into this kind of game. I am however impressed with the guys who play this game well.
    Scottish Cowboy
  10. #10
    MadMojoMonkey's Avatar
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    I think this can be roughly generalized in 2 ways:

    Quote Originally Posted by MadMojoMonkey View Post
    Let S be the number of spades left in the deck.
    Let C be the number of cards to come.
    Let D be the number of cards Hero can not see (left in the deck).

    The chance of drawing EXACTLY 1 more spade in this round:
    (S,1)*(D-S,C-1)/(D,C)
    where the notation (a,b) means "a choose b". E.g. (4,2) = 6
    From here, we can replace the number of spades, S, with the number of outs, O, and replace the 1 with a 2 for the case of drawing to 2-pair or a set with 3 non-paired cards.

    The chance of drawing 2-pair or better, with 3 non-paired cards is:
    (O,2)*(D-O,C-2)/(D,C)

    Quote Originally Posted by MadMojoMonkey View Post
    Then the odds of making your flush is 1 minus the odds you you drawing 0 spades.
    1 - (S,0)*(D-S,C)/(D,C)

    But we know that ANYTHING choose ZERO is always 1. So it reduces to:

    1 - (D-S,C)/(D,C)

    That is the equation to tell you the % chance you will complete your flush.
    Again, if we replace the number of spades to the number of outs, then it gives the chance to make at least 1 of those outs.
  11. #11
    MadMojoMonkey's Avatar
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    Quote Originally Posted by givememyleg View Post
    i'm just a math idiot, i wouldn't even know where to begin to start calculating this.
    Let X be the number of outs left in the deck... (I don't like using O, as it looks too much like 0)
    Let C be the number of cards to come.
    Let D be the number of cards Hero can not see (left in the deck).

    The chance of drawing EXACTLY 1 more spade in this round:
    (X,1)*(D-X,C-1)/(D,C)

    I can break this down for you.

    There is a numerator and denominator.

    The denominator is the total number of things that can happen.
    Here, (D,C) means we're choosing C cards from a deck of D cards.

    Some examples you may be familiar with:
    There are 1,326 possible starting hands in Texas Hold'em, which is (52,2)... I.e. we are choosing 2 cards from a deck of 52.
    There are 22,100 possible 3-card combinations of cards, which is (52,3),
    but for any given hand of poker, there are 19,600 possible flops, which is (50,3)... We choose 3 cards from a deck of 50, due to our knowledge of our own 2 cards.

    The numerator describes the way we want to group the objects.
    We must represent all groups.
    So we have to describe the group we take AND the group we leave.
    Here, (X,1)*(D-X,C-1) has 2 terms.
    (X,1) represents the number of ways we can draw exactly 1 of our X outs. We choose 1 card from a sub-deck of X cards.

    (D-X,C-1) represents all of the ways our hand plays out, given that we catch exactly 1 out.
    We had C cards to come, but we already counted 1 of them, so there are C-1 left to come.
    We are calculating the odds of drawing exactly 1 out, so the rest of our C-1 cards to come must be from the portion of the deck which does not contain our outs, which is D-X.

    E.g. the chance of flopping a set (exactly) when you start with a PP:
    (2,1)*(48,2)/(50,3) = 11.5%
    which you can verify by many sources.
  12. #12
    Eric's Avatar
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    Quote Originally Posted by MadMojoMonkey View Post
    I guess I'd go for the SF in both cases. The Royalty of 25 or 15 points for the RF or SF, respectively, in the back is pretty huge. With over 2.5:1 in favor of me making the flush anyway, even if I pass it up now, I think it's worth the gamble.
    Yeah, they're both one out gutters but the royal is worth 25 while the ten high sf is only worth 15. I'd go for the royal but I'm not sure about the ten high sf. Also, the royal has more backup outs for hands like pair up front, pair in the middle and pair in back.
  13. #13
    Thanks for the math help, MMM, interesting looking at the numbers.

    Not that it matters much (results oriented ftw) I opted to skip the flush on both since I thought I was still high % to hit. i didn't make a royal or straight flush on either but ended up taking a flush with 3 or 4 cards to come.

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