Poker math for flopping flush

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tonymin562

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I read on a poker website the odds of flopping a flush is 0.8% or 124/1. However doesn't it feel like it's more like 25/1. Can anyone explain the math behind these numbers please?
 
johnnylawford

johnnylawford

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There are 13 cards of each suit, so the equation would look like:

quicklatex.com-a103d5ec5a4e41c5e1f654cd64a39c88_l3.png


If you have two suited cards there are 50 cards left in deck. 11 of those remaining cards are of your suit. There are
quicklatex.com-19960f5e442c4d47467c9a89106c5d02_l3.png
flops which will give you a flush. There’s a total of
quicklatex.com-62fbde10a421d245e4aac11a0da54e1c_l3.png
possible flops for your hole cards. The probability of you flopping a flush is
quicklatex.com-9044a8c7bc71dc4d02bdf7eaa4ef3de3_l3.png


You can check out this page for more odds and calculations:

https://www.primedope.com/texas-holdem-poker-probabilities-odds/
 
David macdonald

David macdonald

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I read on a poker website the odds of flopping a flush is 0.8% or 124/1. However doesn't it feel like it's more like 25/1. Can anyone explain the math behind these numbers please?
This is how it works:

MATH: =(50/11)*(49/10)*(48/9)

You have 2 cards and there's 50 left in the deck, and 11 suited cards left in the deck so for the first card to come on the flop it's 50/11 then you have one less card on the next flop card and one less flush card so it's 49/10 and 48/9 for last card. So the calculation is 50÷11 =4.54, 49÷10=4.9, 48÷9=5.33 multiply them together.

118-1 or 0.84%

To work out the percentages it's as follows:

11/50*10/49*9/48x100 = 0.84%
 
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David macdonald

David macdonald

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The probability of being dealt two flush cards is 12/51 of the second card being same suit or 23.53%

Probability of flopping a flush draw is

MATH: =(11/50)*(10/49)*(39/48)*3

There is a 11-in-50 chance of the first flop card being a flush card and a 10-in-49 chance of the 2nd flop card being a flush card. Then there is a 39-in-48 chance of the third flop card NOT being a flush card. Then we multiply by 3 because there are 3 different possible flops with 2 of the flush cards.


8.14-to-1 (10.9%)
 
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