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Thread: Probability question 21+3 sidebet

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    Probability question 21+3 sidebet

    Would appreciate some help on how to calculate probability for the following:
    Sidebet 21+3 pays 9-1 for a flush, straight and 3 of a kind.

    My question is how do I calculate the probability of not receiving a flush, straight or 3 of a kind for x amount of hands. It is dealt from a 6 deck shoe.

    Many thanks

  2. #2


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    The wizard does a good job posting the probabilities of all the possible hands on his website

  3. #3


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    Quote Originally Posted by tezzadiver View Post
    Would appreciate some help on how to calculate probability for the following:
    Sidebet 21+3 pays 9-1 for a flush, straight and 3 of a kind.

    My question is how do I calculate the probability of not receiving a flush, straight or 3 of a kind for x amount of hands. It is dealt from a 6 deck shoe.

    Many thanks
    Try APHEAT.COM
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  4. #4
    Senior Member Bodarc's Avatar
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    Combinations
    Suited Trips 1,040
    Trips 25,272
    Straight Flush 10,368
    Straight 155,520
    Flush 292,896
    Total 485,096
    None of Above 4,528,224
    Total Combinations 5,013,320
    Probability of list
    above:
    = 485096/513320 0.096761
    Probability of not
    getting it :
    = 1 - .096761 0.903239
    For 10 hours at 80 hands / hour
    or 800 rounds hitting a winner say 100 times
    Binomial Probability formula:
    Binomial Prob Formula.png
    n 800
    r 100
    n - r 700
    p 0.096761
    q or (1 -p) 0.903239
    n choose r = combin 800 choose 100 3.4111E+129
    p^100 = 3.7157E-102
    q ^ 700 1.15313E-31
    Probability of hitting 100 times 0.001461541
    Probability of not hitting 100 times
    = 1 - 0.001461541 0.998538459
    Last edited by Bodarc; 02-09-2016 at 06:43 PM.
    Play within your bankroll, pick your games with care and learn everything you can about the game. The winning will come. It has to. It's in the cards. -- Bryce Carlson

  5. #5
    Senior Member Bodarc's Avatar
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    Hi tezzadiver

    I really wasn't ready for that to post without cleaning up but it did it anyway.

    This is how you determine the probability of not getting any of the hands in X rounds. I used the probability of getting it 100 times out of 800 rounds as an example. Therefore not getting it is 1 minus the probability of getting it. You can adjust it to your needs.

    If it needs any corrections, Maybe Don will explain.

    I hope this helps
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    Last edited by Bodarc; 02-09-2016 at 06:49 PM.
    Play within your bankroll, pick your games with care and learn everything you can about the game. The winning will come. It has to. It's in the cards. -- Bryce Carlson

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    Are those the probabilities based on a single poker deck? The OP is playing a game dealt from a 6 deck shoe. Just checking.

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    No, they're for six decks. One typo:

    = 485096/5[0]13320

    Don

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    Thanks very much everyone especially Bodarc. I have had had this running around in my head for the last few days now. The casino in question has a 5 minimum and 200 maximum on the sidebet. I have been thinking of attacking it with a progressive system( I know its doomed to fail!) But was just wondering how likely it would be to not hit a flush( the most common) for about 50 hands. Or any other hand. The formula supplied has helped me understand that.

    This bet appears to become vulnerable if new decks are not shuffled properly, as card suits still group together, especially appears to be advantageous with just 1 player versus dealer.( due to the clumping effect) The obvious mega money maker would be a straight flush on the 21+ Extreme bet at a pay out of 170-1 with a 10 maximum bet. Obviously this effec tends to disappears the more well shuffled the cards are.

    Please correct me if this is illogical

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    Rare events can have a long time between occurrences or stack up with some tightly spaced wins. Not the best type of thing for progression betting. Of course the progression doesn't need to progress quickly but that makes progression failure VERY costly. I am glad to see you understand the futility of the endeavor.

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    Quote Originally Posted by Tthree View Post
    Rare events can have a long time between occurrences or stack up with some tightly spaced wins. Not the best type of thing for progression betting. Of course the progression doesn't need to progress quickly but that makes progression failure VERY costly. I am glad to see you understand the futility of the endeavor.
    I doubt he is seeing the "fultility of the endeveavor". He is determined to go for it.

  11. #11


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    Thank you for you input Zeebabar. In actual fact I am not going to go through with it. Just a suggestion however :If you have nothing positive to contribute to the thread, why not just put a cork in it mate

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