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Math behind the Party Poker Side Bet

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  1. Tilter Tilter is offline

    Canada

    Posts: 310
    Joined: Aug 05

    Oct 9th, 2005 (10/9/2005 5:06am)

    party poker gives you 8 for 1, meaning if you bet $1, you will win $8 (profit $7) which is 1:7 or 1/8 for 12.5%. Remember that bets have to be done before cards are dealt, so you won't be able to make your choices depending on the cards that you are dealt. You can not also base it upon the assumption of 26/52 * 25/51 * 24/50 as this is the assumption you dont know what your hole cards will be.

    Now lets start with the assumption of that you know your hole cards and want the probability of what the flop will be.
    Dealt two red hole cards - odds flop will be all red cards: 24/50 * 23/49 * 22/48 = 253/2450 = 5.06/49 = 10.2%
    Dealt two red hole cards - odds flop will be all black cards: 26/50* 25/49 * 24/48 = 6.5/49 = 13.2%
    Dealt two black hole cards - odds flop will be all black cards: 24/50 * 23/49 * 22/48 = 253/2450 = 5.06/49 = 10.2%
    Deal two black hole cards - odds flop will be all red cards: 26/50* 25/49 * 24/48 = 6.5/49 = 13.2%
    Dealt 1 red card and 1 black card - odds flop will be all red cards: 25/50 * 24/49 * 23/48 = 5.75/49 = 11.7%
    Dealt 1 red card and 1 black card - odds flop will be all black cards: 25/50 * 24/49 * 23/48 = 5.75/49 = 11.7%

    So from above, we have an assumption now of what your hole cards, now we have to weigh it against the probability of what your hole cards will be.

    Probability that your hole cards will be:
    Both black: (26C2)/(52C2) = 24.5%
    Both red: (26C2)/(52C2) = 24.5%
    1 Black and 1 Red: (26C1)(26C1)/(52C2) = 51%

    Now we weigh the probability that you will match for each circumstance:
    D2R = % Dealt 2 Red Cards
    D2B = % Dealt 2 Black Cards
    DBR = % Dealt 1 Black and 1 Red Card
    AR(BH) = % All red flop with two black hole cards
    AR(RH) = % All red flop with two red hole cards
    AB(BH) = % all black flop with two black hole cards
    AB(RH) = % all black flop with two red hole cards
    AR(DH) = % all red flop with 1 red and 1 black hole card
    AB(DH) = % all black flop with 1 red and 1 black hole card

    %Flop will be all red = D2R*AR(RH) + D2B*AR(BH) + DBR*AR(DH) = (.245)(.102) + (.245)(.132) + (.51)(.117) = .117 or 11.7%

    %Flop will be all black = D2R*AB(RH) + D2B*AB(BH) + DBR*AB(DH) = (.245)(.102) + (.245)(.132) + (.51)(.117) = .117 or 11.7%

    So if you were to make 100 $1 bet, your expected value (EV) would be - $0.80
  2. Dunce Dunce is offline

    Posts: 1,153
    Joined: Mar 05

    Oct 9th, 2005 (10/9/2005 11:37am) in reply to Tilter

    I'm not sure about all of your math. But assuming it is correct, then the following is also true:

    In 1000 bets, you will win $8 117 times for a total return of $936.00.
    That's a Total Loss of $64.00 or a Negative EV of 06.4 cents per bet.
  3. beauright beauright is offline

    Saint Petersburg, FL
    United States

    Posts: 1,637
    Joined: Jun 05

    Oct 9th, 2005 (10/9/2005 1:01pm) in reply to Dunce

    UMMMM, the math is much easier than all that, but thanks for reposting it in a separate thread so more people could see how much detail you put in it.

    26/52 * 25/51 * 24/50 = .1176 versus true odds of .125

    for what its worth,
    beauright
  4. JoeChicago JoeChicago is offline

    Grayslake, IL
    United States

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    Joined: Jul 05

    Oct 9th, 2005 (10/9/2005 2:42pm) in reply to Tilter

    Can you tell us what exactly is the bet that the site is offering??
  5. BUCKINATOR BUCKINATOR is offline

    Hoopeston, IL
    United States

    Posts: 3,041
    Joined: Aug 05

    Oct 9th, 2005 (10/9/2005 10:47pm) in reply to JoeChicago

    just how much free time do you have? get laid.
  6. Tim G Tim G is offline

    Las Vegas, NV
    United States

    Posts: 62
    Joined: Aug 05

    Oct 9th, 2005 (10/9/2005 10:55pm) in reply to Tilter

    As far as I am concerned this just verifies my belief that party poker is carnival game bullshit.
  7. Tilter Tilter is offline

    Canada

    Posts: 310
    Joined: Aug 05

    Oct 10th, 2005 (10/10/2005 12:23am) in reply to beauright

    The difference is, if I were to take a game theory quiz, I would get full marks. That would be the half ass part marks response.
    Thread Starter
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