Suited Odds?

I normally play pretty tight, but the other day, I fancied playing loose, and called the big blind with 2s 3s on the button. (6max 10NL)

It got to the river, I got my flush, and I got stacked, with the Villian having Ks 5s.

So here's what I'm wondering. If you've got 23s (Example hand, to make the mathematics easier), in a 6 player game, what are the odds of two higher suiteds of the same suit as yours being dealt out?

Cheers.

Pf this is a HUGE calculation.

You start by first calculating the odds that 1 to 5 suited cards arrive at your 5 opponents.

50 cards left in stack, 11 suits, 39 offsuits.

Denominator D=50x49x48x47x46

case 1 suit: Divisor D1=(11x39x38x37x36)x5
=> 5 configurations to divide 1 suits and 4 offsuits

case 2 suits: Divisor D2=(11x10x39x38x37)x10

case 3 suits: Divisor D3=(11x10x9x39x38)x10

case 4 suits: Divisor D4=(11x10x9x8x39)x5

case 5 suits: Divisor D5=11x10x9x8x7

So to get the odds one guy gets a suit on the first card, you calculate D1/D etc.

Now for each of these cases you need to calculate the same odds again, for 1 to 5 suits being dealt to each of the 5 people, again multiply by the amount of configurations, but then divide to compensate for the ones that don't give the suit to a guy that already had a suit.

In the case 1 guy got a suit.

45 cards left, 10 suits, 35 offsuits.

D'=45x44x43x42x41

In the case of 1 suit being dealt:
Divisor D'1=10x35x34x33x32
This we have to multiply by 5, and then divide by 5 since only one configuration of those 5 will have the suit at the guy who already had the suit.

Case 2 suits being dealt:
TEMPORARY D'2=10x9x35x34x33
This we multiply by 10 (amount of configurations) of which only 4 deal the card to the guy who had the suit, so:
D'2=(10x9x35x34x33)x(10/4)

So the chance for one guy getting a suit, everyone else an offsuit, and then the same guy gets a suit again while the others get offsuits, we get:

chance=(D1/D)x(D'1/D')

Like that you have to calculate all 25 possibilities (1-5 on first card TIMES 1-5 on second card) and add them all up. So yeah, a huge calculation I don't feel like doing right now.. but if anyone wants to, they can ofcourse :P


Maybe there's an easier way to calculate this though, but can't readily see one.. (I was thinking about going from a negative, but you'd still have to account for all the configurations overlapping, so I don't see much gain in calculation time there..)

The odds that any of your opponents have suited cards of the same suit as yours arent too great, but when you have a 3 and a 2 of that suit, if your opponent have two cards of the same suit as yours 100% of the time they will be higher. Do you have a hand history for this hand? That would help analyze the situation a lot as we could see if you played any of the streets wrong or if you should have gotten stacked there. I have a hard time committing my whole stack with the lowest possible flush anyways though, but Id really like to see how the hand played out

Wow, didn't expect the calculation to be that huge! Cheers though.

I was on tilt, and playing like an absolute retard. I played decently, up nutil the river, where the Villian bet half his stack and 3x the pot. I thought "Well if I've played these cards, I've got the hand I was looking for, why not call? He's probably bluffing anyway!"

So yeah, I got stacked and I deserved it. I played the hand well until the river when the 3rd spade dropped.

And please don't belittle me for playing like such a donk, I've seen it and I'm sorting my shit out.

Originally Posted by Ash256

Wow, didn't expect the calculation to be that huge!

Yeah, if he has the flush too, there are no other 2 cards he could have that could be lower than yours. So 100% of the time he has the same two suits as you he has you beat.

EDIT: Sorry, you meant the calculation in the post a couple above mine that I didn't read! well, i'm retarded.

Originally Posted by Ash256

I was on tilt, and playing like an absolute retard. I played decently, up nutil the river, where the Villian bet half his stack and 3x the pot. I thought "Well if I've played these cards, I've got the hand I was looking for, why not call? He's probably bluffing anyway!"

So yeah, I got stacked and I deserved it. I played the hand well until the river when the 3rd spade dropped.

And please don't belittle me for playing like such a donk, I've seen it and I'm sorting my shit out.

My biggest losses in the past came from hitting a straight or flush but my opp having a bigger one. It's just one of those things you have to learn the hard way to really start to look out for them I guess. At first I was like "ZOMG I hit a flush!! You bet 2x the pot? Haha! Why not make it all-in!!!" Now it's more like "hm, a flush.. but there's a potential bigger one.. better be cautious and observe what this guy does."

Originally Posted by Ash256

And please don't belittle me for playing like such a donk, I've seen it and I'm sorting my shit out.

I dont think anybody in this thread belittled anybody, I merely asked for the hand history so I could see how it played out. Its tough to give advice on something when I cant see it in front of me, I still am curious about that hand, so if you have the history, plesae post it.

Originally Posted by jackvance

Maybe there's an easier way to calculate this though, but can't readily see one..

The inclusion-exclusion principle does the job.

assuming you hold 2 of suite X (lets say spades)
the chance an opponent will get 2 of the same suite are
(13-2)/(52-2)*(13-3)/(52-3) = 110/2450 = 4.5% per player

if you were holding QQ and hit your trips on a 3-flush board with no over cards or str draws, you would be wary of the flush. It shouldnt be played much different here with the low flush. If opp. has a flush you are beat. If opp. doesnt have flush you win.

Originally Posted by TLR

assuming you hold 2 of suite X (lets say spades)
the chance an opponent will get 2 of the same suite are
(13-2)/(52-2)*(13-3)/(52-3) = 110/2450 = 4.5% per player

Well that's the calculation I did at first too, but I kinda dismissed it. Maybe it's a good approximation though.

The reason I doubted the veracity of this calculation is that it also is the answer to the question: "what are the odds the next two cards dealt are of suite X". Not sure though, not enough experience with these kinds of calculations so I decided to take a more "safe" route.

The other reason I doubted this easy computation was that it doesn't seem to scale very well with players. This "4.5% per player".. on a 10max table this would mean what? That there's a 9x4.5%=40.5% someone else also gets a flush of the same suit? Seems awfully high. On a table with 23 people this gives almost 100% that someone gets the same 2 suits. Not very plausible since there is a fair chance that a bunch of these suits will be dealt out to different people.

I think though that there is a way to calculate this that is not too hard, seems pretty standard textbook-statistics to me actually.But I don't have such handbooks nearby, nor a real urge to look this stuff up. But I think Krimson knows how to calculate it.

I don't see much point in finding out the odds of someone else holding two cards of the same suit as you're holding pre flop, which seems to be what you're trying to calculate here.

More relevant is the odds of someone having two cards of the same suit when you have a flush draw or a made flush. The chance of this is of course lower since now there's only 9 or 8 unseen cards of this suit, not 11. If someone knows how to calculate this it would be interesting.

I think I've only seen one flopped flush over flush in my ~50k hands poker career (and the hand was won by someone else who rivered a full house), but flush draw vs a higher flush draw seems to come along pretty frequently.

That would be the same calculation, except for instead of using a deck with 11 suits on 50 cards, you have to use 8 suits on 47 cards.

And I've also devised a formula to calculate these odds, you'd only have to plug in some numbers and let a math program run it for x=2-10 (or x=2-8 for the second one) to get the solution.. but I doubt anyone really cares anymore lol

Originally Posted by andy-akb

Originally Posted by Ash256

And please don't belittle me for playing like such a donk, I've seen it and I'm sorting my shit out.

I dont think anybody in this thread belittled anybody, I merely asked for the hand history so I could see how it played out. Its tough to give advice on something when I cant see it in front of me, I still am curious about that hand, so if you have the history, plesae post it.

Unfortunately I don't.

And I wasn't accusing you of anything, I just didn't fancy anyone jumping into the thread with "Z0MG!! F15H!!!".

It was all limps pre-flop, the spade draw came on the turn after checks, a TP bet got called by me, the Villian, and some random guy who didn't have much. The flush got made on the river, and I raised the 60% bet to 200%. He proceeded to go all-in, and due to my tilt, I felt that I was pot-comitted, and that he was bluffing.

That's all I remember.

Probability of Losing to Higher Flush
Ace-High 0.00%
King-High 6.36%
Queen-High 11.58%
Jack-High 15.76%
Ten-High 19.02%
Nine-High 21.42%
Eight-High 23.00%
Seven-High 23.79%

uh, my chart doesnt go down to 3-high.

also (10 handd)

Likelihood of Opp Flush
on 3 Flushing Board/You Hold (of the suit)
36%/0
30%/1
24%/2
99.7% (on four-flushed board)/0

and

Probability of Flushing Boards
SUIT DISTRIBUTION/Prob
(2,1,1,1) /26.4
(2,2,1,0) /36.5
(3,1,1,0) /22.3
(3,2,0,0) /10.3
(4,1,0,0) /4.3
(5,0,0,0) /0.2

oh. i dug all that shit outta here. good stuff, from a cdn mathmetician/ pkr plyr

http://www.math.sfu.ca/~alspach/pokerdigest.html

oh, hey, i know i seem to be talking to myself here, but i just made 'flush' in the old boys club (250 posts?)

how ironic, what was the probability of that. yay me.