# Math or poker folks, a question **URL:** \ **Category:** Factual Questions\ **Created:** [December 30, 2016, 3:38pm UTC](https://boards.straightdope.com/t/math-or-poker-folks-a-question/775904 "2016-12-30T15:38:12Z")\ **Posts on this page:** 17\ **Page:** 1
**Author:** ![harmonicamoon](https://avatars.discourse-cdn.com/v4/letter/h/65b543/32.png) [@harmonicamoon](https://boards.straightdope.com/u/harmonicamoon)\ **Post date:** [December 30, 2016, 3:38pm UTC](https://boards.straightdope.com/t/math-or-poker-folks-a-question/775904/1 "2016-12-30T15:38:12Z")
Been playing a lot of free Texas Holdem 7 card stud. Cheap entertainment. What are the odds of getting a flush with two suited hold cards? Seems it rarely happens. Thanks troops. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [December 30, 2016, 3:45pm UTC](https://boards.straightdope.com/t/math-or-poker-folks-a-question/775904/2 "2016-12-30T15:45:59Z")
[4.5%](https://www.cardschat.com/f57/suited-hole-cards-185297/) according to answer #5 here. ---
**Author:** ![harmonicamoon](https://avatars.discourse-cdn.com/v4/letter/h/65b543/32.png) [@harmonicamoon](https://boards.straightdope.com/u/harmonicamoon)\ **Post date:** [December 30, 2016, 4:21pm UTC](https://boards.straightdope.com/t/math-or-poker-folks-a-question/775904/3 "2016-12-30T16:21:33Z")
Very nice link. Thank you very much! ---
**Author:** ![RickJay](https://avatars.discourse-cdn.com/v4/letter/r/bb73d2/32.png) [@RickJay](https://boards.straightdope.com/u/RickJay)\ **Post date:** [December 30, 2016, 4:51pm UTC](https://boards.straightdope.com/t/math-or-poker-folks-a-question/775904/4 "2016-12-30T16:51:20Z")
Wait, are you playing Texas Hold 'Em or 7 card stud? Those are two entirely different poker games. ---
**Author:** ![OldGuy](https://avatars.discourse-cdn.com/v4/letter/o/3bc359/32.png) [@OldGuy](https://boards.straightdope.com/u/OldGuy)\ **Post date:** [December 30, 2016, 5:03pm UTC](https://boards.straightdope.com/t/math-or-poker-folks-a-question/775904/5 "2016-12-30T17:03:45Z")
They are different games, but in each case after your two down cards you know only those two and receive 5 more cards so the odds of a flush are the same. The odds will change later though as more cards are revealed in 7 card stud as the game progresses. In Hold 'em you see the 5 common cards. In stud you see everyone’s up cards. ---
**Author:** ![harmonicamoon](https://avatars.discourse-cdn.com/v4/letter/h/65b543/32.png) [@harmonicamoon](https://boards.straightdope.com/u/harmonicamoon)\ **Post date:** [December 30, 2016, 5:12pm UTC](https://boards.straightdope.com/t/math-or-poker-folks-a-question/775904/6 "2016-12-30T17:12:11Z")
> [@RickJay](#): > > Wait, are you playing Texas Hold 'Em or 7 card stud? Those are two entirely different poker games. Sorry, the website calls it Texas Hold 'Em. I just mentioned the number of cards, in case there is a 5 card holdem. Don’t know much about poker names. But now, I know odds of getting a flush with two suited cards is a poor bet. And that’s what makes a flush a winning hand. ---
**Author:** ![Really\_Not\_All\_That\_Bright](https://avatars.discourse-cdn.com/v4/letter/r/e8c25b/32.png) [@Really\_Not\_All\_That\_Bright](https://boards.straightdope.com/u/Really_Not_All_That_Bright)\ **Post date:** [December 30, 2016, 5:16pm UTC](https://boards.straightdope.com/t/math-or-poker-folks-a-question/775904/7 "2016-12-30T17:16:41Z")
Well, yes and no. You’re not going to call a large pre-flop bet just because your cards are suited. But you might call a large bet after the flop with two suited cards in the hole and two more on the board. ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [December 30, 2016, 5:48pm UTC](https://boards.straightdope.com/t/math-or-poker-folks-a-question/775904/8 "2016-12-30T17:48:12Z")
> [@Really\_Not\_All\_That\_Bright](#): > > Well, yes and no. You’re not going to call a large pre-flop bet just because your cards are suited. But you might call a large bet after the flop with two suited cards in the hole and two more on the board. This is where it gets tricky. While you now have a 35% chance (by my rough calculation) of getting the flush, the problem is that if you don’t get it on the turn, you have only about a 20% chance of getting it on the river and if the same person who bet heavily on the flop bets heavily again, you are in a box. I’m not sure what odds you want here. ---
**Author:** ![JSexton](https://avatars.discourse-cdn.com/v4/letter/j/96bed5/32.png) [@JSexton](https://boards.straightdope.com/u/JSexton)\ **Post date:** [December 30, 2016, 8:30pm UTC](https://boards.straightdope.com/t/math-or-poker-folks-a-question/775904/9 "2016-12-30T20:30:15Z")
> [@Really\_Not\_All\_That\_Bright](#): > > Well, yes and no. You’re not going to call a large pre-flop bet just because your cards are suited. But you might call a large bet after the flop with two suited cards in the hole and two more on the board. You probably don’t want to call a large bet there, actually. You might well want to be the first to put in a large bet, or you may want to re-raise them, but flat calling is not a good idea, because you’re probably the underdog. Remember, Hold’em is a game where you see who is willing to put more money in the middle. The cards themselves are just a tiebreaker. Flat calling when you are less then 50% to win the tiebreaker is not a good idea, broadly speaking. ---
**Author:** ![Really\_Not\_All\_That\_Bright](https://avatars.discourse-cdn.com/v4/letter/r/e8c25b/32.png) [@Really\_Not\_All\_That\_Bright](https://boards.straightdope.com/u/Really_Not_All_That_Bright)\ **Post date:** [December 30, 2016, 8:46pm UTC](https://boards.straightdope.com/t/math-or-poker-folks-a-question/775904/10 "2016-12-30T20:46:52Z")
True. My point was merely that the odds of drawing to a four-flush are not terrible. ---
**Author:** ![harmonicamoon](https://avatars.discourse-cdn.com/v4/letter/h/65b543/32.png) [@harmonicamoon](https://boards.straightdope.com/u/harmonicamoon)\ **Post date:** [December 30, 2016, 9:40pm UTC](https://boards.straightdope.com/t/math-or-poker-folks-a-question/775904/11 "2016-12-30T21:40:32Z")
In the link posted by puly, a person said to bet because your hold cards are good, not because they are suited. If they are good and suited, it is a bonus. As you have more options. As for me I like a cheap flop. You can have garbage hold cards but they may come to life with the flop. But since it is a free game, players toss large bets, before the flop, like it is nothing. Which it is. You are not going to lose the farm. ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [December 31, 2016, 9:15am UTC](https://boards.straightdope.com/t/math-or-poker-folks-a-question/775904/12 "2016-12-31T09:15:32Z")
> [@pulykamell](#): > > > [@](#): > > > > What are the odds of getting a flush with two suited hold cards? Seems it rarely happens. > > [4.5%](https://www.cardschat.com/f57/suited-hole-cards-185297/) according to answer #5 here. I get that the chance of flush (or rather combined chance of flush and straight flush) is (c(11,3)\*c(39,2) + c(11,4)\*c(39,1) + c(11,5)\*c(39,0)) / c(50,5) = 19371 / 302680 ≈ 6.399828% Now, what are the odds that I’m wrong and [www.cardschat.com](http://www.cardschat.com) answer #5 is correct? :eek: ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [December 31, 2016, 12:12pm UTC](https://boards.straightdope.com/t/math-or-poker-folks-a-question/775904/13 "2016-12-31T12:12:51Z")
> [@septimus](#): > > I get that the chance of flush (or rather combined chance of flush and straight flush) is > (c(11,3)\*c(39,2) + c(11,4)\*c(39,1) + c(11,5)\*c(39,0)) / c(50,5) = 19371 / 302680 ≈ 6.399828% > > Now, what are the odds that I’m wrong and [www.cardschat.com](http://www.cardschat.com) answer #5 is correct? :eek: We’re _both_ wrong. :smack: I neglected to add in the 3\*c(13,5) / c(50,5) chance that the five common cards form a flush in a suit _different_ from your hole cards. This gives you _total_ flush chance of 69729 / 1059380 = 6.582057%. (Of course I’m ignoring the 2.35% chance you get a full house or quads to beat a flush.) ---
**Author:** ![Riemann](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/riemann/32/3133_2.png) [@Riemann](https://boards.straightdope.com/u/Riemann)\ **Post date:** [December 31, 2016, 4:47pm UTC](https://boards.straightdope.com/t/math-or-poker-folks-a-question/775904/14 "2016-12-31T16:47:17Z")
> [@harmonicamoon](#): > > …your hold cards… fyi the word is **hole** cards. It’s not an obvious term, does anyone know the etymology? ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [December 31, 2016, 4:53pm UTC](https://boards.straightdope.com/t/math-or-poker-folks-a-question/775904/15 "2016-12-31T16:53:57Z")
> [@septimus](#): > > I get that the chance of flush (or rather combined chance of flush and straight flush) is > (c(11,3)\*c(39,2) + c(11,4)\*c(39,1) + c(11,5)\*c(39,0)) / c(50,5) = 19371 / 302680 ≈ 6.399828% > > Now, what are the odds that I’m wrong and [www.cardschat.com](http://www.cardschat.com) answer #5 is correct? :eek: Yeah, [this site](http://www.suntzupoker.com/poker-odds.aspx) says 6.25% (which I expect is just approximate), so I suspect your numbers are correct. I’m not counting table flushes. ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [December 31, 2016, 6:18pm UTC](https://boards.straightdope.com/t/math-or-poker-folks-a-question/775904/16 "2016-12-31T18:18:02Z")
> [@Riemann](#): > > fyi the word is **hole** cards. It’s not an obvious term, does anyone know the etymology? Webster’s doesn’t specify ‘place of concealment’ in its definition of ‘hole’ but the usage is common, e.g. [QUOTE=William Shakespeare] [From _King John_]: PEMBROKE. O death, made proud with pure and princely beauty! The earth had not a hole to hide this deed. [From _King Richard the Third_]: FIRST MURDERER. So do not I. Go, coward as thou art. Well, I’ll go hide the body in some hole, [From _The Tragedy of Titus Andronicus_]: CHIRON. An if she do, I would I were an eunuch. Drag hence her husband to some secret hole, And make his dead trunk pillow to our lust. [/QUOTE] Interestingly [the English word ‘hole’ ultimately derives from](http://www.etymonline.com/index.php?term=hole) "the PIE root \*kel- (2) “to cover, conceal.” ---
**Author:** ![RickJay](https://avatars.discourse-cdn.com/v4/letter/r/bb73d2/32.png) [@RickJay](https://boards.straightdope.com/u/RickJay)\ **Post date:** [January 3, 2017, 4:08pm UTC](https://boards.straightdope.com/t/math-or-poker-folks-a-question/775904/17 "2017-01-03T16:08:09Z")
> [@Hari\_Seldon](#): > > This is where it gets tricky. While you now have a 35% chance (by my rough calculation) of getting the flush, the problem is that if you don’t get it on the turn, you have only about a 20% chance of getting it on the river and if the same person who bet heavily on the flop bets heavily again, you are in a box. I’m not sure what odds you want here. It all depends on how much money you have left, how much your opponent has left, how likely you think it is they’ll continue betting if a flush does come up, and whether or not your flush would be the best hand. Suppose the pot is $50 and you have Ace-Ten of hearts. The board is two hearts and a spade; no card is repeated. Your opponent bets $20. Should you call? Maybe. You are betting $20 to win $70, a 3.5-to-1 bet, which is not quite the odds of hitting the flush on the next card (sure, you get the river card, but we have to assume you might have to call another bet.) But if you do hit the flush, the betting isn’t over. You might be able to have a bet called, adding more money to the pot, or your stubborn opponent might keep betting and cheerily hand you more money. How likely your opponent is to give you more money after you ht a flush affects the wisdom of your decision. (In this case of course, hitting another ace could conceivably win you the pot as well.) If your opponent is drunk and playing with $600 of luckily won money, he might be loose enough to make a terrible call.