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Strategy: Others

Probabilities in Texas Hold'em

by Indy1701e

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IntroductionAn understanding of basic probabilities will give your poker game a stronger foundation, for all game types. This article discusses all the important, and interesting, probabilities that you should be aware of. Probabilities in poker Pr…
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Comments (23)

#1 theboydave, 03 Sep 09 13:08

What a handy article a download chart of these odds would be a good idea i think thanks.

#2 oedipa, 04 Sep 09 08:52

What a wonderful article !
I've been looking exactly for something like this.
Thank you and keep up the good work :)

#3 ciasteczkoM, 04 Sep 09 09:12

Good job! I was making this equations or at least some of them for my own use from time to time (thanks to format C:) ). Now all i need is here. Thanks again.

#4 NiekamNeidomu, 04 Sep 09 09:47

math T_T

#5 JuiceQuadre, 04 Sep 09 09:58

Nice one!

#6 RahXephon1, 04 Sep 09 10:29

Very nice article. Specially the part with the probability that a better hand wakes up after you. should be usefull to corectly judge the edge an isolation raise should have to be profitable.

The last part is interesting from a theorethic point of view, but it's probably easier to just remember the probabilities for the most important situations, than calculate them. Also the more marginal ones shouldn't be that important for calculating the profitability of the hand.

And BTW, can someone please explain to my opponents they have less than 1% to flop a flush, so they won't take my money everytime I go all in on a suited flop.

Just kidding obviously :)

#7 vladnz, 04 Sep 09 10:36

this is some serious math shit :D

#8 Pardel, 04 Sep 09 14:02

Thanks for this very nice and serious article!

#9 Sinnology, 04 Sep 09 14:02

GREat job.
As someone already mentioned, a download chart of those would be great.
Now I only need to read this like 20 times to absorb everytihng.
Thx

#10 Bojim1, 04 Sep 09 16:26

nice article, thank you

#11 EagleStar88, 04 Sep 09 16:53

@#9, whilst not a download as such, you can of course use the new print function (icon at top right of article) to print off a copy for a little light bed time reading :o)
Great work Indy.

#12 drawback, 04 Sep 09 17:32

Thank you a lot. Will have something really great to study ;)

#13 excelgeo, 05 Sep 09 02:15

what a great article.

i was wondering about this recently.

thanks!

#14 xLFC, 05 Sep 09 04:43

Great article, very useful!

It would also be nice to have the probabilities of improvement from three-of-a-kind to full house (or better) in the charts.

Thanks!

#15 fffgreek, 05 Sep 09 23:19

At least !!!
You made my day guys ;)

#16 Koshburger, 16 Jan 10 10:48

ok

#17 1z2x3y, 21 Feb 10 17:42

Steven Hawkings eat your heart out ! =]

#18 Rap1d007, 06 Mar 10 10:44

interesting charts

#19 sindeon, 21 Feb 11 21:32

Thanks a lot! One of the best and most useful articles i´ve read here.

#20 DukeXIII, 22 Jul 11 10:27

GUYS.... I LOVE U :)

#21 maheepsangari, 23 Apr 12 12:36

Could someone please explain the calculation under 7. Probability of improving on the flop Example 3 where it calculated probability for hitting a set. Shouldn't it be 2C1*48C1*44C1/50C3. Actually what I calculated is also incorrect since that would lead to 4.6:1 odds and not 7.5:1 odds so can someone please explain the calculation here.

#22 maheepsangari, 23 Apr 12 12:53

I mean to calculate set or full house it would definitely be 2C1*48C2/50C3=11.51% meaning 7.68:1 odds so I'm wondering how to calculate for a set only directly without using the subtraction method.

#23 maheepsangari, 23 Apr 12 13:05

2C1*39C1/50C3 doesn't correspond to 11.5% but istead its 0.397%


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Article Contents

  • page 1
    • Introduction
    • Probabilities in poker
    • Probability of being dealt a given starting hand
    • Probability of facing a higher pocket pair when you have a pocket pair
    • Probability of facing more than one higher pocket pair when you have a pocket pair
    • Probability of facing a better A when you have an Ax hand
    • Probability that no overcard will show up on the flop
    • Probability of making a specific hand (5 out of 52)
    • Probability of making a specific hand (7 out of 52)
    • Probability of improving on the flop
    • Probability of improving on the turn
    • Probability of improving on the river
    • Probability of improving from flop to river
    • Probability of seeing a specific board on the flop
  • page 2
    • Deriving the probabilities
    • 1. Probability of being dealt a specific starting hand
    • 2. Probability of facing a higher pocket pair when you have a pocket pair
    • 3. Probability of facing several higher pocket pairs
    • 4. Probability of facing a better A
    • 5. Probability that no overcard will come when you have a pocket pair
    • 6. Probability of being dealt a specific hand
    • 7. Probability of improving on the flop
    • 8. Probability of improving on the turn
    • 9. Probability of improving on the river
    • 10. Probability of improving from flop to river
    • 11. Probability of seeing a specific flop
    • Note

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