Odds of Opponent having a Flush on Three Suited Flop?

[Erik343]

Hi,

I read in Daniel Negreanu's book Power Hold'em, that against a calling station you keep betting top pair relentlessly. You even bet if you see three suited cards, such as three diamonds! I am kind of nervous about betting in this situation even if it is the right thing to do. If I knew the odds of an opponent having a flush in this situation, the correct play would be easier...

So my question is: what are the odds of an opponent flopping a flush if there were three diamonds on the flop. What is the odds of him having two diamonds in his hole cards? Please assume that my opponent plays any two cards or even trash. Also, can you please explain how to perform these statistics calculations? I took stats in college, but I cannot remember how to do the calculations. Also, assume that I am playing heads up against one other opponent.

Thanks,
Erik W.

 

[Tero]

If I recall correctly, there is less than one percent chance for a player to make a flush (any flush, not just diamonds) on the flop. But that is human nature for you - we always expect the worst.

As for the calculations... well, it might be easier to look up the results (you can find them online) for these kind of spots, and maybe learn by heart the ones you are most interested in. During a game there is no time to make such calculations anyway.

 

[Hermus]

So my question is: what are the odds of an opponent flopping a flush if there were three diamonds on the flop. What is the odds of him having two diamonds in his hole cards? Please assume that my opponent plays any two cards or even trash. Also, can you please explain how to perform these statistics calculations? I took stats in college, but I cannot remember how to do the calculations. Also, assume that I am playing heads up against one other opponent.

This comes down to what range they're playing. If you want to calculate this yourself just look at the number of suited hands that made the flush, proportional to all the hands that range. The range builder in Equilab counts combo's and has suit selection so that would be suitable for answering this question. Determining an open range is more art than science, but if you do the same calculation for a couple of different scenario's (maybe nit, reg, rec, any2) you'll be fairly accurate in most practical situations.

For the record, flopzilla is able to do all this for you and is pretty reasonably priced so that might also interest you if you don't want to go through the maths yourself.

EDIT:
For examples this UTG open RFI AA-66,AKs-A2s,KQs-K7s,QJs-Q9s,JTs,AKo-ATo,KQo-KJo,QJo hits a flush on 2h3h4h (or any other monotone board without most blockers) with 18 out of 226 total combo's or about 8% of the time.

EDIT2:
For any2 there are 43 flush combo's out of a total of 1176 on 2h3h4h or about 3.5% but that is a super unlikely scenario and almost every player plays a higher ratio of suited hands (even recreational players) than that of any2

 

[Hermus]

If I recall correctly, there is less than one percent chance for a player to make a flush (any flush, not just diamonds) on the flop.

That's the pre-flop probability of flopping a flush when you hold a suited hand. That's a distinctly different question than "given this monotone board and villain's range what proportion of their hands made a flush.

 

[Tero]

That's the pre-flop probability of flopping a flush when you hold a suited hand.

Correct.

Given his post title and the way I read OP's post I think that this is exactly what he meant. In my opinion he uses the diamonds only as an example.

 

[Hermus]

Correct.

Given his post title and the way I read OP's post I think that this is exactly what he meant. In my opinion he uses the diamonds only as an example.

I interpreted the post the other way around. In any case, both answers are now there

 

[CourtJester]

What are the odds your opponent flops a flush? Significantly less than them NOT flopping a flush!

Remember - Just because someone flopped a flush doesn't mean they have the nut flush. More importantly, if they believe YOU have the nut flush, or are drawing to it, then you are in a position to bet!

 

[Plut41]

How old is this book? Possibly it could be old and players behave differently than let's say 10 years ago. Not saying it's true but just my guess on it. Because I used to play back in 2008 and I managed to raise my bank roll up to 250$+ by playing like an absolute garbage. Nowadays I play 6max zoom nl2 on pokerstars and oh boy how much people sweat... I barely got to 120 something.

 

[Erik343]

Thanks guys! This helps my game a lot!

 

[Zapahlohotrona]

The likelihood of a flush is the same for "3 on board + 1 in hand" and "2 on board + 2 in hand" situations. 9 outs for 2 streets.

 

[Phoenix Wright]

Hi,

I read in Daniel Negreanu's book Power Hold'em, that against a calling station you keep betting top pair relentlessly. You even bet if you see three suited cards, such as three diamonds! I am kind of nervous about betting in this situation even if it is the right thing to do. If I knew the odds of an opponent having a flush in this situation, the correct play would be easier...

So my question is: what are the odds of an opponent flopping a flush if there were three diamonds on the flop. What is the odds of him having two diamonds in his hole cards? Please assume that my opponent plays any two cards or even trash. Also, can you please explain how to perform these statistics calculations? I took stats in college, but I cannot remember how to do the calculations. Also, assume that I am playing heads up against one other opponent.

Thanks,
Erik W.

I've read that book as well

As for the chance of Flopping a Flush, it is less than 2% I believe, but we can just put in the range (100% VPIP for simplicity in this case) into a poker calculator like the free download Equilab I use to see how our hand does against their range (which is all that matters really since we don't know if they have a Flush).

Small detail: the math changes slightly if we also hold a diamond, but I'll just setup a hypothetical scenario where we have unsuited top pair on an all-diamond Flop.

Hero: Ac 5s (example, but no diamonds is all which matters here for the point)

Villain: random hand; VPIP 100%

Hero equity: 69.42%

Villain range equity: 30.58%

Hopefully someone else can show the math by hand for odds of flopping a flush.

Edit: Odds of Flopping a Flush is 118-1 or 0.8% according to a quick Google search

https://www.cardplayer.com/poker-tools/odds-and-outs

 

[Erik343]

Just a quick another question? What are the odds of one opponent having a flush on the river with three diamonds and two other blank cards, like so:
Ad 7d 2d Qc 3s

This is the same idea as with the flop, but it is on the river...
I don't understand the math for this...

Also, if you have a diamond flush on the flop, and have two diamond hole cards, then what is the odds of the villain having a diamond flush too? Not necessarily larger…

Can you answer this based on:
1. UTG open RFI AA-66,AKs-A2s,KQs-K7s,QJs-Q9s,JTs,AKo-ATo,KQo-KJo,QJo (like as before with the odds of an opponent hitting a flush on a three suited flop?)
2. any two cards

Thanks and Merry Christmas
Erik W.

 

[LetterRip]

Hi,

I read in Daniel Negreanu's book Power Hold'em, that against a calling station you keep betting top pair relentlessly. You even bet if you see three suited cards, such as three diamonds!

If they played only suited hands and no pairs, their odds would be 1 in 4. If about 1/2 their hands are offsuit (pairs plus about 1 offsuit hand per 4 suited hands) then about 1 in 8 - this is probably about right for a tight player. For typical player they might have the the flush 1 in 16 (1 in 28 is any two cards).

Doing equity lab
66+,A2s+,KTs+,QTs+,JTs,T9s,98s,87s,76s,65s,ATo+,KQo - on a 4s3s2s has 8.8% flushes and 28.1% Flush draws. So 3 flush draws for every made flush.
(Any Axo) 66+, A2s+, KTs+, QTs+, JTs, T9s, 98s, 87s, 76s, 65s, A2o+, KQo on 4s3s2s has 6.2% flushes and 23.1% Flush draws. So 4 flush draws for ever made flush.

If one of the flop cards is a broadway, it drops a lot of the combos of made flushes and flush draws from their hand.
66+,A2s+,KTs+,QTs+,JTs,T9s,98s,87s,76s,65s,ATo+,KQo - on a Ts3s2s has 8.3% flushes and 26.5% Flush draws. So they lost .5% of made flushes, and 1.6% of flush draws from their range.

If one of the flop cards is an Ace, it drops evem more of the combos of made flushes and flush draws from their hand.
66+,A2s+,KTs+,QTs+,JTs,T9s,98s,87s,76s,65s,ATo+,KQo - on a Ts3s2s has 6.2% flushes and 23.4% Flush draws.

If they are calling they usually have the flush draw and if they raise turn or river most low stakes players will have been slow playing the flush and you can fold.

 

[Erik343]

Thanks! I purchased Flopzilla yesterday!

 

[excel]

Think of it like this...

First consider your "knowns":

• There are three of the same suit (any suit) in Community
• You have two hole cards, which we will assume in this example they do not match the suit in Community.

So if you have one opponent, that means there are: 52 cards minus 3 community minus 2 hole cards (that you have). Therefore there are 47 cards remaining, 10 of which have the same suit as the Community cards.

If you dealt a card to your opponent, they would have a 10 / 47 chance (21.28%) of getting a card that matches the Community suit. If you dealt them another card, they would have a 9 / 46 chance (19.56%) of having another card that matches the Community suit.

So to get the final percentage of BOTH cards matching suit, you'd multiply 21.28% x 19.56% which gets you about 4.16%.

If you have multiple opponents the Math gets a little more involved, but for estimation purposes you can just multiply the 4% times however many players are at the table.

 

[alien666dj]

Hi,

I read in Daniel Negreanu's book Power Hold'em, that against a calling station you keep betting top pair relentlessly. You even bet if you see three suited cards, such as three diamonds! I am kind of nervous about betting in this situation even if it is the right thing to do. If I knew the odds of an opponent having a flush in this situation, the correct play would be easier...

So my question is: what are the odds of an opponent flopping a flush if there were three diamonds on the flop. What is the odds of him having two diamonds in his hole cards? Please assume that my opponent plays any two cards or even trash. Also, can you please explain how to perform these statistics calculations? I took stats in college, but I cannot remember how to do the calculations. Also, assume that I am playing heads up against one other opponent.

Thanks,
Erik W.

Here's a great article: https://www.cardplayer.com/poker-tools/odds-and-outs.