Flush Odds

Anyone know the odds of flopping a flush?

my spider senses are telling me its like 1%.

That sucks

Assuming you hold two suited cards?

It's low enough not to factor the odds.

11/50 * 10/49 * 9/48 = 0.0085 = 0.85%

That sucks even more.

ur suited hole cards flop a flush only 1 in 120 times

ya, what are the odds in flopping a straight flush, I did it once Razz

It's not likely. The exact probability isn't very interesting or even useful.

ill talk my way through this...
Assuming you have a suited connecter, no gaps 2 cards connect with with your hole cards, 2 connect with those 3, and 2 connect with those 4.
2/50 * 2/49 * 2/48=
.04 * .04816 * .0416= .0000801 =.008%...which doesnt sound right...

odds of flopping a straight flush... that's tough. just looked it up, its 4899 to 1 if you're holding 98s, so .02%. someone on here might know how to figure it but not me.

ive flopped a straight flush once too. had 97 hearts flop came 6 8 10 of hearts, it was nice.

yeah thats what i said

Thanks dsax I've been wondering that.

its ok, you might wanna get that checked out haha

The biggest freak accident hand I've been involved in is when I had 45 hearts, flop came 678 hearts, flopped a straight flush! But someone else had the 9 and 10. I lost my stack.

I've also flopped a royal flush, but that was playing limit Omaha, so the odds are better. Everyone folded (probably should not have bet) so I didn't even get to show it down. Hey, at least I didn't lose.

I folded 76s pre flop in a casino tournament to see, in numerical order, 8 9 10s come down. It was like it was taunting me by making itself unmissable.

The 4899:1 odds are correct. Here is why.

I'm only calculating the probability of flopping a straight flush with suited connectors with at least 3 cards on both sides that can be used. (ie, JQ will not work since you only have AK above that). To do this, you need to consider all straight flushes possible. For 98s, these cards must be considered:

Five of Spades

Looking at the diagram above, you can see that we can make 4 different straight flushes here. Let's narrow down to a single straight flush, say:

Eight of Spades

The odds of flopping this flush if you hold the 8 and 9 is:

Odds = 3/50*2/49*1/48 = 1/14700 = 0.0068%
(incidently, this is the odds of flopping a royal flush if you hold 2 suited cards T or higher)

Explained quickly, there are 3 cards that can come up on the first flopped card, 2 on the second, and one on the third. Now, going back to before... since there are 4 different straight flushes we can get with 98s, the odds of flopping a flush are the above multiplied by 4. This is:

Odds = 4(3/50*2/49*1/48) = 1/4900 = 0.02%

Dancing

Good to know that after 4900 hands you might flop a straight flush. Sucks that you probably got it in EP and folded it.

D'oh!

Darkwing

I've only flopped it once, with 47s limping from the button in a family pot, heh.

No idea what the odds are, but I did it today.... Thought I must have read the cards wrong when the flop came.

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What happened to DWDuck anyway? Too pro for us now?

He could compute the odds of flopping a straight flush..

He's a probably a millionaire by now Very Happy

At a live home game, my friend flopped a royal flush with KTs and pushed all in. Obviously, everyone folded and he showed it. Lol odds of that are insane and yet he wasted it.

It'd probably be better to flop a straight flush than a royal- when you flop a royal flush no one is gonna have better than a 9-high flush so you won't get any play. Flop a straight flush the A and K might believe they're ahead.

I had J 10 of spades. flop came 9 Q K spades could not belive it. i checked some guy bet big i just called. Q on the turn i checked he pushed all in and i called. he showed me KQ then i hit the As on the river giving me a royal... would love to know the odds of flopping the SFlush and then hitting the royal on the river.

Last night in a live game, I was holding KJs (spades) and called an all-in preflop bet of about $30 (just wanted to give the guy action since I had pushed him out of a $200 pot earlier with TPTK). No more action on the table and I turn over. Flop comes 10 Q A (spades) for the flopped royal. I jumped out of my chair (not over the money, I don't get excited when I win $1000 pots).

The royal pays $250 jackpot there, but just hitting that was a flipping rush.

Hey I have a question, and this is because I'm bad at math, not cause I doubt anyone's calculations:

Why is it that pre-flop odds are 23.5% for getting suited hole cards, and 15.7% to get connectors, when the odds of hitting a straight are much better than hitting a flush?

What's the math behind this seeming contradiction?

since this is all about flush odds, i'd like to ask another...
anyone know the odds for a flush by the river from 2 suited cards? (i.e. 3 or more of 5 board cards having desired suit)
or maybe someone can give me a hint as to how to calculate these?

cheers

It's kind of tedious to calculate, but here is how:

There are 13 hearts, you hold 2. So 11 left, and 50 cards left (we just ignore opponents for now).

You can have a flush with 5 hearts, 4 hearts, or 3 hearts on the board, and the total probability is the sum of these 3 cases.

There are formulae for this, but that won't help you understand it, and I can't remember them off hand.

P(5 hearts/5 cards) = P( 1st card is a heart) * P (2nd card is a heart) * ...

= 11/50 * 10/49 * 9/48 * 8/47 * 7/46 - you can multiply that out.

P(4 hearts/5 cards) is trickier, because the non-heart can appear in all 5 spots. Luckily, this is just 5*P(4 hearts/4cards) .

= 5 * ( 11/50 * 10/49 * 9/48 * 8/47)

P (3 hearts/ 5 cards) - (11/50 * 10/49 * 9/48 ) is the probability of 3 hearts in 3 cards - there are 5 * 4 / 2 = 10 ways you can combine 3 hearts and 2 non-hearts, so multiply this by 10.

Add those 3 numbers up and you should get something like 15%

making a flush with 2 suited hole cards is not a 15% chance zen. I think it's more around 5%. You only flop a flush draw 10% of the time dawg. So actually it's more like 3.5%

thx for the prompt feedback, guys!
still not quite sure the truth has been unveiled yet though...
i have been thinking about this one because it seems a relevant number for some preflop situations e.g. how much better the chance of winning a pot with AKs in relation to AKo?

i actually follow zenbitz's argument well and think it most likely is the correct process for doing this calculation . you seem to understand the mathematics in this very well.
though doing the calculation outlined i come up with 9.15% on my calculator. (assuming i didnt screw up somewhere on the line)
thats 0.02% (7-flush) + 0.72% (6-flush) + 8.42% (5-flush)

@bigspenda:
arent you neglecting stuff like backdoor flushes?

cheers

I flopped a royal flush at $10NL once calling a UTG raise from the BB with King of Spades

.

I checked, he checked behind!
I bet the turn he folded.

Profit = $0.85

High rollers look out below

I got this off da intaweb so it must be true:

Flush Odds
You have a 3.3-1 (24%) chance of being dealt any two suited cards. If you have two suited cards, the probability of:

# Making a flush by the river: 15-1 (6.4%)
# Flopping a flush: 118-1 (0.84%)
# Flopping a flush draw (two cards of the matching suit on the flop): 8.1-1 (10.9%)
# Making a flush by the river when you flop a flush draw: 1.9-1 (35%)
# Making a flush on the turn when you flop a flush draw: 4.2-1 (19%)
# Making a flush on the river when you have a flush draw on the turn: 4.1-1 (20%)

# Flopping a backdoor flush draw (one card of the matching suit on the flop): 1.4-1 (41.6%)
# Making a flush by the river when you flop a backdoor flush draw: 23-1 (4.2%)
# Hitting a flush on the river when you have a flush draw on the turn: 4.1-1 (20%)

If you have two unsuited cards, the probability of:

# Making a flush by the river: 53-1 (1.8%)
# Flopping a flush draw (three cards of the matching suit on the flop): 88-1 (1.1%)
# Flopping a backdoor flush draw (two cards of the matching suit on the flop): 6.8-1 (12.8%)

have found the probability for flush from 2 suited by river confirmed to be 6.4% with many sources.
also i have found the reason why that calculation by zenbitz dont come out with that number.

the 7flush calculation is correct:
(11*10*9*8*7) / (50*49*48*47*46) =0.02181%

for 6flush you had the right idea but missed a term:
(you suggested: 5 * ( 11*10*9*8) / (50*49*48*47)
should be: 5 * (39*11*10*9*8) / (50*49*48*47*46) = 0.6074 %

similar problem with 5flush
2 more terms and it comes to:
10 * (39*38*11*10*9) / (50*49*48*47*46) = 5.771 %

total: 0.02181% + 0.6074 % + 5.771 % = 6.4%

voila

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