# Playing vs implied flushes

I run into flushes so often.

What’s the expected rate of someone making a flush at a 4-seat table? Tonight, over my last 100 hands, there were 10 flushes shown to win. This doesn’t count flush-over-flush or flush-under-boat hands that may have happened, and it doesn’t count hands where there wasn’t a showdown, but the board texture and betting strongly suggested a flush.

So at least 1 in 10 hands, one of four players made a flush and won the hand with it. Is that about the expected rate? Or am I just running through natural cluster of flushes (that happens to miss my chair)?

How many of them were me? Zero. To find a hand that I won with a flush, I had to go past the last hundred hands, and finally found one on the 19th page, just barely within bounds of my last 200 hands.

If I’m at a 4 seat table, the expected distribution of the 10 flushes dealt in my last 100 hands would give each player 2 flushes, and two players would get one additional flush. But, you guessed it, the sample size was too small for the distribution to flatten out, and they were (once again) clustered around everyone else at the table but me.

But good old Payoff Puggywug, he hits the good ole two pair on the flop, refuses to fold, and watches the board fun out four flush and then pays off some random one-card flush, every single time. Nut flushes, junk flushes, they soak me to ruin my ROI time after time.

My bad nights come when the cards are cold for me and I can’t make a pair for 40-50 hands, but then the moment I manage to make a hand like top pair or two pair, the best I’ve seen in the last several orbits at least, the board flushes for someone and I get coolered or rivered and lose a big pot. Then I spend the next hour winning enough small pots to come within half a buy-in of break-even, when I get coolered again and then I have to roll the boulder back up the hill again. And I get almost to breakeven, and it happens again.

How can I fix my leak?

• Do I play like a super nit and exploitatively fold any two pair when I flop and the board has two suited?

• Do I overbet the flop when I make two pair, and try to play flopped two pair like a bluff-steal when I make two pair on the flop and there’s two of a suit, knowing the certainty of the turn and river matching the prevailing color and connecting to my opponent is close to 1:1? This seems like a poor strategy – I get to win smaller pots when everyone folds, and when someone calls, it’s because they have me crushed with a set, or believe in the power of their draw, and it gets there despite my fold pressure.

• Do I check-call with my two pair and pray the board remains dry, lose the minimum, and the moment the flush is possible, fold when they bet big? This too seems like a poor strategy – I just let them hit with the free cards that I let them see, but at least the pots will be smaller?

• Do I overfold on the Turn when the board is suited for a flush for V? This also seems like a poor strategy – I let opponents bluff me off every board that looks a little flushy, letting them run all over me.

From what I’ve always read, the odds of making a flush when you’re suited and flop two more of your suit is decent, but only about 40%. So a made hand like two pair should run profitably against draws to flushes (at a fair table).

The odds of making a 1-card flush with 4 on the board are far worse, yet I see that happen so often, too.

Straights and sets have good implied odds because they are not as easy to spot, and so they are more likely to bring in some money through opponents that overlook them. On the other hand, flushes have poor implied odds because of the fact that many players become wary when 3 or more cards of the same suit appear on the board, so the chances of getting paid off are slimmer.

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So just for the heck of it, I went back and looked at your hands. Figured I’d see if your interpretation of what happened matches what I see. I’m absolutely open to being corrected if I missed anything.

“Tonight, over my last 100 hands, there were 10 flushes shown to win.”

Not exactly. I count 11 over your last 200 hands. There were indeed 8 over your last 100 (and two of them were a board flush resulting in a two way chop for the players that stuck it out - so I’m counting that as two flushes - but should it be one??) which might seem high, but then when you make it 200 hands, the frequency sure did drop quite a bit, as expected. And with a large enough sample, I’d be willing to bet the frequency would drop even more - perhaps even (gasp!) into what would be considered statistically “normal” territory with a large enough sample.

“This doesn’t count flush-over-flush or flush-under-boat hands that may have happened”

I saw none of those in any of the flush (or the one full house) hand, so let’s let that go. Sure - some could have been folded - but if we don’t see it, we can’t use it in analysis.

So continuing with a 200 hand sample, lets look at the distribution of those flushes to see how harshly you were victimized over those hands:

Well first, let’s have a round of applause for Alchap!! He was on fire when it came to flushes and picked up 4 of the 11!!! (one of them being the board flush, so should he really only get credit for three?)

After that, the distribution of flushes was - shockingly - reasonably well distributed:

(names may be abbreviated)

Butt: 2
Rubio: 1
Simon: 1
Kipmic: 2 (one being the board flush)
Puggy: 1

And then of course, Alchap putting the pedal to the metal with 4 (one board flush).

Other than Alchap having a fortunate grouping of flushes, Pug, I’m not sure where the complaint is. If it is with 11 flushes over 200 hands - well, I don’t think that is a large enough sample to find any kind of disturbing problem. Yes, there was a cluster of 8 over your last hundred - but that dropped to 3 over the previous 100 - which to me is a great example of how a “cluster,” (which we all know happens) can skew overall perception.

Anyway - back to work for me!!! (and last caveat, though I don’t think I miscounted anything, I certainly could have)

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@Elvoid, I am SO proud of you … I remember you well from the days when you believed in a rigged game and look at you now!

In this thread and others, you’re showing that you’re thinking and looking at evidence and acknowledging the maths that you quite obviously learned in school.

What else can I say?

Very kind regards,
TA
(Proud member of the Elvoid cheer squad)

Yes, as I stated I had to fold a bunch of other hands where the board got too flushy for me to stay in with my junky nothing pairs and gutshot draws. So I suspect that there were a few more flushes out there that are not being counted if we only count those that get shown at the river, perhaps a lot more. But we don’t really know.

When I counted, I paged through my hand history for ten pages, and counted ten hands that were won by flush. It could be I miscounted, so if it was actually 8 then I pretty badly miscounted.

Whether it’s 8 or 10, out of 100 hands, it does feel like a cluster. Getting 1 out of 8 or 1 out of 10 is just bad luck. Getting the other 7 or 9 out of 8 or 10 against me when I happened to flop two pair makes it feel personal, but likely is just bad luck.

I’d still like to know what the expected rate of flushes is for a 4-seat table per hundred hands, to know how atypical the 8 or 10 in 100 cluster is.

For whatever it is worth, pretty comprehensive “odds of whatever hand” sites can be found on the internet - some of them (like the wikipedia page) even show the math applied (which if I learned anything by having to show my work in grade school, lends some legitimacy to the final number, or at least shows your teacher your tried really, really hard even though you’re wrong by a country mile.)

Seems like most settle on 3 percent as the probability of a player hitting a flush in a standard seven card hand of Texas Hold 'em. So that’s for any one player, I guess.

Someone smarter than me is going to have to chime in on what does the percentage become for a flush being hit at the table when there are four players - or six or nine or whatever. Is it 3 percent for the table as well no matter the number of players, or does the probability of a flush being hit rise with the number of players? Intuitively I think it would rise, right?

I’m sure there is a formula that could be applied. But I’m no math major.

It’s been a fun journey of sorts - but it didn’t take me long to realize that what I was feeling was undoubtedly something rooted in “recency bias” to clusters than any kind of overall “rigged” game.

Very kind regards right back atcha!

Where did I imply in this thread anything about suspecting the game is rigged?

Well first of all, my response was to a comment The Analyst directed to me, not you. So there’s that. Matter of fact, that eliminates the need for “first of all.” It’s just “all.”

You’re taking a single comment that had nothing to do with you - and everything to do with me - and applying it to you.

Right, the “odds of whatever hand” articles cover a lot of the basic odds an common situations, but don’t answer my specific question.

I’m decent with math, but probability does give me a headache.

I’m not sure, but I think the way to calculate the odds is to figure out what the odds are of having 3, 4, or 5 cards on the board of the same suit, and comparing to the odds of a player being suited for that board.

The odds of two cards of the same suit on any 5-card board is 100%, since there are only 4 suits. Therefore, (not accounting for card removal) the odds of the board having 3 of a suit should be about 1-in-4 for the 3rd card matching the suit of the two matching cards, with a further 1-in-4 chance for the 4th card, and a further 1-in-4 chance for the 5th card. If I am not mistaken, we can treat the 3 1-in-4 chances as a 3-in-4 chance, so therefore the odds of any given 5-card board would be about 75% (again, not accounting for card removal).

Of the 75% of boards that have at least 3 of a suit, we have a 1-in-4 chance of the 4th card matching, and a 1-in-4 chance of the 5th card matching. So that works out to 50% of the 75% will actually be 4-suited boards. So 28% of the time the board should be 4-suited, not accounting for card removal. This seems really high, though, so I suspect my method is incorrect.

If I look at it another way, the probability of the first card being of any of the four suits is 100%. The probability of the next card matching is 25%. If it does match, the probability of the third card matching the first two is again 25%, so 6.25%. And the probability of the 4th card matching the first 3 would then be 25%, so about 1.5%. A 5-card board flush would then be expected about 0.39%. The 5th card also gives the 3-match boards a 2nd chance to improve to a 4-match, which improves those odds, I would think to about 3%.

So the two ways I can think about it, one suggests about 1-in-100, while the other suggests almost 1-in-3. I’m pretty sure the 1-in-3 is incorrect, but I’m too stupid to work out why. I’m neither proud nor ashamed of being too stupid to work out why, but I think I might be able to understand it if someone who was sure they knew the correct answer could explain it for me.

Last night, it certainly felt as though the 1-in-3 model was correct, and it’s not the only night I’ve had this happen. I wouldn’t have posted if it was just this night, but it’s actually fairly common that I seem to have this misfortune of running into these clusters. Very often I see monotone flops, and two-tone flops, and it seems like more often than not they threaten, or all but guarantee, a flush on the Turn, with a 3rd (or 4th) suited card coming to match the board.

Google tells me the odds of a rainbow flop are only 40%, so fully 60% of the time I can expect to see two-tone or suited flops. When you’re not holding even one card for the flush suit, how wary should you be about these boards?

If I’m holding one diamond and two diamonds hit the board, I don’t start thinking flush, but if I am holding zero diamonds, I’m immediately thinking flush, particularly if I’ve hit for top pair, or two pair. When the third flush-card hits on the Turn, should I slow down? Give up? Bet high to deny odds to any 1-card flush draws hoping to fill on the river?

All I’d say is the obvious: that when any three suited cards hit the table, one should at least be cognizant of the risk of a flush floating out there - or at the least that an opponent might try to represent one - producing a kind of “Do you feel lucky, punk” type of moment (and heck, maybe that bluffer is you!). If four hit the board, one should be terrified (unless of course you’re holding a good high card for it - but even then you’ve got to see if there is something possibly there that could beat your Ace high flush - though no matter what, you’re probably not folding that - I’d say a fold on that hand would be quite rare.)

We’ve all lost plenty of times when we were overwhelming favorites. Heck, I’ve lost multiple consecutive times when I was an 80/20 favorite to win after the turn. And that just sucks.

But I tend to look at it with a different perspective. A 20 percent chance of losing is still pretty damn high. Put this way: There’s a million bucks on the other side of a 50 yard wide creek with a fast current and a couple of hungry gators. I’m told it’s mine if I swim to the other side and get it - but I have a calculated risk of 20 percent I’ll die in the effort.

I ain’t swimming.

Now poker is not life, and in poker I’m not going to let a 20 percent loss scare me on its own merit. 80% to win? I’m in all day long (barring any other information I glean or a gut feeling I might have or a situational kind of thing - but 99.8% of the time? All in, baby.)

But 20 percent death (chips or life) is, in reality, pretty damn scary each individual time it comes up. Only thing is that in poker, I get to try again and over time 80/20 greatly works to my favor. Life and death situation? Not so much. Perspective.

Anyway, that’s how I feel about it - not for everyone, I’m sure.

I’m with Elvoid. The stakes at risk make a difference. The real penalty (cost of loss) for jay walking isn’t the \$20 ticket you might get if you’re caught by the police, it’s the possible pain and suffering if you get hit by that on-coming bus that makes us look both ways first.

Concerning the strategic portion of the question, about how to play versus flushes, and how often you’ll be against them:

• Most of the time, against 1 opponent, 3 cards of the same suit on the board will not mean you are against a flush. Even if your opponent only played suited cards, folding every pocket pair or off suit hand like AA or AKo, they’d still have a flush significantly less than 25% of the time because the flush cards on the board act as blockers. And of course, probably no opponent plays only suited cards. I sometimes joke about folding AA pre-flop, but I suspect I’ve never really done it (at least not intentionally).
• Still, most people are reluctant to bet big into a board with 3 cards of the same suit, and so if you are facing a large bet on such a board, the probabilities just shifted very significantly.
• When considering calling a bet with a possible flush draw, consider reverse implied odds: will you still pay if they hit? I like to pay careful attention to how often the people I play regularly bluff on different streets (and how often they bluff with different bet sizes). I’m not going to make a big call on a wet board unless I already have evidence that my opponent is capable of taking the same line with a bluff with a frequency that will make the call +EV.
• If you do think your opponent will bluff into a wet board, consider what blockers you have. If you have a card of the same suit, you reduce the combinations of flushes available further, and will be against a bluff or a thin value bet more frequently.
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I’ve been thinking about this recently as well. It’s helpful to play some real poker (or if you can’t find any opportunities, play with a real deck of cards by yourself for a little while). Here’s what I find on the topic of flushes:

1. Three of a suit on the table is extremely common. As has already been pointed out, two of a suit on the table is a certainty, and three of a suit is just one extra - almost without significance.
2. A flush is a high hand. A player having a flush is uncommon, despite the fact that three of a suit appear on the table routinely.
3. Pretending to have a flush when there’s three of a suit on the table is highly effective - most players will fall for it. But should you? No, you shouldn’t. Not necessarily.
4. Four of a suit on the table is uncommon, but when it happens, the chance of a player having a flush is close to 100%.

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@Jabr : Even better is to learn some basic probability and start doing the calculations. It really isn’t difficult.

If that is too much for you, you can look up some tables that have the probabilities of many poker events already calculated for you.

You do not have enough time to manually deal enough cards to get a statistically valid data set and trying to do so will, almost certainly, lead you to draw wrong conclusions.

Just for the record: Replay is “real poker”! You don’t have enough time to record sufficient hands to get a statistically valid set and trying to so will, almost certainly, lead you to draw wrong conclusions.

If you want to know, as a certain person continuously and pointlessly asks, “what are the chances?”, the answer is in the maths.

Regarding point 3, that is a concept called “bluffing” and is discussed in detail in several other threads.

Regards,
TA

Perfect example of how I can limp-miss for an hour and a half and the first time I catch top pair of course it’s a two tone to four flush run out. I even manage to river two pair, for added irony. Bet-fold.

I don’t care that it happens, I just want to understand why it’s so frequent, when I have a pair.

https://www.replaypoker.com/hand/replay/772562052

I will write this in easy words just for you.

Learn maths. Do sums. Get answer.

You haven’t, that I have seen, asked any question that you can not answer for yourself just by following those simple steps.

https://www.mathsisfun.com/data/probability.html

Hope this helps.
TA

Oh look what it is, some nice math.

https://www.replaypoker.com/hand/replay/772565654

So why is the probability 100%?

Just for the record: Replay is “real poker”!

If it isn’t for real money, it isn’t real poker. It’s a reasonably close approximation and lots of fun, but real poker it is not.

Gosh, really?

I don’t wish to be impolite and personal, but if we’re going to start patronizing people, your chip total of 1,191,439 since December 2019 is poor.

To be fair, I have been wasting all of his time lately. Between that, and inventing mathematics, and constant rehearsals for the Sophocles theatre revival, I doubt that he’s had much time to actually play any poker.