[Limit hold-em] Are flush draws worth it?

[Schizoguy]

As an amateur hold-em player, I like flush draws. They're easy enough to play: you see the flop if it's cheap or if there are a lot of poeple in, and if you see two cards of the same suit, then you check your odds and decide whether to look for that fifth club or not. The math is straightforward enough, and when you make your hand, you're pretty certain it's the best (which is a relief in a game of incomplete information).

Recently, however, I have become persuaded that pure flush draws have a negative expectation. This may be due to too few of mine hitting. Nevertheless, I ran some numbers, and I didn't like what I saw, so I've decided to post them here in hopes of being corrected by people with more accurate numbers (the authors, ideally).

Okay, first we have to set the expected gain, if you make your flush and win the hand. Obviously, before the flop we don't know what the pot will eventually be; 6 players could four-bet on each round. However, from my experience at the online poker rooms (which are nice enough to post the average pot size), I find that a lenient mean pot is 10 big bets (so, $40 in a $2/4 game).

Is this figure fair?

Assuming for now that it is: It costs at least 1 small bet to see a flop with your two suited cards, and you stand to win on average 20 small bets if you make your flush. So, you would like your flush to hit at least 5% of the time, yes? And I find in the back of HEPFAP (and can corroborate with my own arithmetic) that two suited cards turn into a flush roughly 6.5% of the time. So, positive expecation.

However, that 6.5% assumes that you stay in for backdoor flush draws, and the pot odds rarely justify that. Furthermore, we are neglecting to count extra bets spent in search of that elusive fifth club.

Here, a sentence from page 310 of HEPFAP (er, 21st century edition): "If you hold two suited cards, you will flop a flush 0.8 percent of the time, and a four-flush 10.9 percent of the time." Using these numbers, and assuming that there is no raising (so you always get to see your next card for 1 bet, which is optimal when you're drawing) (unless you can get it for free) and the rule that, if you make a four-flush, you'll look for the fifth card (which isn't always the case, but it probably would be if the pot looked to reach 10 big bets, I think):

Oh, and rounding those percentages:

1% of the time, you flop a flush, and gain 20 small bets.
10% of the time, you flop a four-flush:
1/3 of those times, (or 3.33%) you will make your flush by the river (it's closer to .36, I think) and gain 20 small bets.
2/3 of those times, you will pay a total of 4 small bets to see the river (1 before the flop, 1 to see the turn, 2 to see the river)
And 89% of the time, the flop won't contain at least two cards of your suit, and you will lose your initial 1-bet investment.

(.01 * 20) + (.0333 * 20) + (.0666 * -4) + (.89 * -1) = -.2904

IE, under these rules, you will lose, on average, .29 small bets every time you see the flop with two suited cards.

Now, granted, you don't have to make your flop to win; you could certainly pair one or both of your cards, or make a straight, or so on. But I am interested specifically in hands like A2s and K2s, hands which you really only play for their flush drawing potential.

Furthermore, quite frequently you will make your flush and get less than 20 small bets in the pot.

So, I am persuaded to stay away from flush draws for the time being. However, this is contrary to what is in the literature, and the literature was written by people who know much better than myself. Hence, this post.

What, for example, is the expected value of a hand like A2s? Assuming typical, low-limit table conditions. Even with 9 people calling in front of you, is it truly worth a play? (Granted, with 9 people calling in front of you, the pot would probably end up much larger than 20 small bets).

Oh, it occurs to me that the proper question would be "At what expected pot size would seeing the flop be profitable?" And I can calculate that, but while I do, please educate me about the expected value of a flush draw.

[Schizoguy]

Okay, taking my earlier (probably oversimplistic) equation:

(.01 * 20) + (.0333 * 20) + (.0666 * -4) + (.89 * -1) = -.2904

and replacing x for the assumed pot size of 20, and setting it equal to the break-even point of 0, the new equation looks like:

.01x + .0333x + .0666*-4 +.89*-1 = 0

which simplifies:

.0433x = 1.1564
x = 26.7

So, according to this, if everything I've done is correct: if it costs 1 unit to see the flop with a flush draw, you must expect at least 27 units to go into the pot, when you make your flush, to make seeing the flop profitable.

Is this all correct?

[Sully]

I can tell you've done a lot of work with this and are good with math, but I think you've over-analyzed it.

A couple of quick points:

1. All suited starting hands are not created equal. You seem to be lumping them all together in this analysis, and you know that just isn't right.

2. All flushes aren't winners, and all pots are not average.

For these reasons, you need to do the calculations as you play. Each bet must be analyzed and calculated using pot odds. By summarizing all of these numbers all the way through to the river, you are forgetting the basics.

In limit poker, it is all about the next bet...+EV or -EV?? That's all you need to ask. As for starting hands, it's all according to position...you don't cold call a raise with J9s in early position, but you might limp (or even raise, in the right situation) in late position.

Just go back to the basics, and remember that all suited cards are not created equal. After that, you're right...flush draws really aren't that hard to play.

[Schizoguy]

[ QUOTE ]

1. All suited starting hands are not created equal. You seem to be lumping them all together in this analysis, and you know that just isn't right.

[/ QUOTE ]Well, yes, I'm focusing on hands like Axs. Hands where you definitely wouldn't play their non-suited equivalent.

[ QUOTE ]
In limit poker, it is all about the next bet...+EV or -EV?? That's all you need to ask.

[/ QUOTE ]That's a difficult question before the flop. Or, at least, I'm having trouble with it.

[Monty Cantsin]

The two biggest problems I see with your calculations are:

1. Average pot size needs to big much bigger, because you only play Axs/Kxs when you know the pot is going to be multiway.

2. You can't disregard the times you win with non-flush hands because this number is more significant than you think.

In short, you can fold my A2s with 3 limpers ahead of me when you pry it out of my cold, dead hands.

/mc

[Hermes]

[ QUOTE ]
The two biggest problems I see with your calculations are:

1. Average pot size needs to big much bigger, because you only play Axs/Kxs when you know the pot is going to be multiway.

2. You can't disregard the times you win with non-flush hands because this number is more significant than you think.

In short, you can fold my A2s with 3 limpers ahead of me when you pry it out of my cold, dead hands.

/mc

[/ QUOTE ]
I agree with 2. Don't disregard your odds of flopping two pair, trips, full-house, or quads. I think the odds work out to something like 30:1 against. Although your odds of flopping these hands with any 2 non-paired hole cards are a bit remote, they do need to be factored in to your equation. Just last night I twice flopped top two pair (rainbow board) with my Axs.

[astroglide]

i'm only skimming this thread, but a large point of value for suited hands is catching top pair, running 2 pair, etc while chasing a draw when the offsuit counterpart would have folded

[LinusKS]

You've put a lot of good thought into it, and I appreciate the nature of the question you're asking.

Thanks for posting.

I'm not going to be able to say a lot about your math - unfortunately - I'm not that good at it. But it looks right to me.

Personally, I don't like to play less than Ax suited, and I think the "any-two-suited-cards" style of play is a beginner's mistake.

The big problem with it is *losing when you make your flush.* This sometimes happens when a set fills up, but more often when you come up against a bigger flush. When that happens you stand to lose ten small bets or more.

I think Ax suited is questionable as well - as your math shows. But the others are right. You make that up, not only by hitting other kinds of hands, but by successfully bluffing from position as well.

[Nottom]

Are flush draws worth it ... damn skippy.

Are little suited cards worth it ... usually not.

[Schizoguy]

[ QUOTE ]
I think Ax suited is questionable as well - as your math shows. But the others are right. You make that up, not only by hitting other kinds of hands, but by successfully bluffing from position as well.

[/ QUOTE ]

Which is a big weakness in my 10-player game; I never bluff. Just can't bring myself to do it. Semi-bluffing when I'm on a draw, I can do, but a pure bluff, I can't do it when the table's full, I'm just certain that somebody has something worth staying in with.

Recently I've started playing six-max and doing incredibly well, 25 or more big bets an hour. And I don't understand why. But for some reason, I'm in there bluffing, and it's working like it never does in the full games, and the only difference is that there are 4 less people at the table. I don't understand it.

/tangent

[daryn]

</font><blockquote><font class="small">In risposta di:</font><hr />
Recently I've started playing six-max and doing incredibly well, 25 or more big bets an hour. And I don't understand why. But for some reason, I'm in there bluffing, and it's working like it never does in the full games

[/ QUOTE ]


/images/graemlins/grin.gif /images/graemlins/grin.gif /images/graemlins/grin.gif


it won't last /images/graemlins/frown.gif

[PittRounder]

"Recently I've started playing six-max and doing incredibly well, 25 or more big bets an hour."

This has to be damn near impossible. Well it is impossible, except over the smallest samples. That's $100 an hour at 2/4.

Anyway, you forget to mention pre-flop raises in your post. It's very hard to consistantly limp A2s UTG and see a flop for one bet. It's also very easy, although probably not too much in 2/4, to get isolated with A2 junk vs. the PFR, which usually is a 2 sb check/fold.

[jess72]

[ QUOTE ]
[ QUOTE ]
Recently I've started playing six-max and doing incredibly well, 25 or more big bets an hour. And I don't understand why. But for some reason, I'm in there bluffing, and it's working like it never does in the full games

[/ QUOTE ]


/images/graemlins/grin.gif /images/graemlins/grin.gif /images/graemlins/grin.gif


it won't last /images/graemlins/frown.gif

[/ QUOTE ]


Very true!!!

Jess

[The Armchair]

You're right in saying that, in late position in a multi-way pot, you'd not play A2o, but you would play A2s. The reason: The flush.

But while that is the primary reason, you have to be aware of additional values. Let's take a look at two hands -- A2s (hearts) and 72s (hearts). You are on the button and, to not make anyone look bad, you posted a blind. There are three other callers and you check, as do the "real" blinds. (Six way flop.)

The flop comes down:
J/images/graemlins/heart.gif 4/images/graemlins/spade.gif 5/images/graemlins/diamond.gif

If you have the 72, you're losing, and you have virtually no outs. You can't call a bet here.

If you have A2, you have at least 4 (the gut-shot 3s) and probably 7 (the other aces) as outs, plus you can make the runner-runner nut flush.

The only way 72s wins is the flush or the miracle hand. That's not true for "flush-plus" hands like A2s or 76s.

[SheridanCat]

[ QUOTE ]
Which is a big weakness in my 10-player game; I never bluff. Just can't bring myself to do it. Semi-bluffing when I'm on a draw, I can do, but a pure bluff, I can't do it when the table's full, I'm just certain that somebody has something worth staying in with.


[/ QUOTE ]

Then you're leaving money on the table. This is weak tight thinking that is costing you.

Regards,

T

[Duke]

[ QUOTE ]
Recently I've started playing six-max and doing incredibly well, 25 or more big bets an hour. And I don't understand why. But for some reason, I'm in there bluffing, and it's working like it never does in the full games, and the only difference is that there are 4 less people at the table. I don't understand it.

[/ QUOTE ]

Wow. You're THAT guy.

THAT guy doesn't win long term.

~D

[Senor Choppy]

[ QUOTE ]
But I am interested specifically in hands like A2s and K2s, hands which you really only play for their flush drawing potential.

[/ QUOTE ]

The reason A2s is playable isn't solely because of it's suitedness. It's because of this + the fact that you have an ace. Just because A2o isn't playable doesn't mean the A doesn't have value, it's just not enough by itself to justify paying 1 sb preflop.

(K2s is pretty bad normally, and most of the other smaller suited hands are usually overrated by most people.)

[Ed Miller]

Now, granted, you don't have to make your flop to win; you could certainly pair one or both of your cards, or make a straight, or so on. But I am interested specifically in hands like A2s and K2s, hands which you really only play for their flush drawing potential.

Your problem is that you assume that A2s and K2s are only worthwhile if you make a flush. That's just plain wrong. To see why, think about how often A2o and K2o will win. It's definitely not 0% of the time.

Here's something specifically to break you of a psychological hurdle here:

You will win a lot of pots with a pair of aces or a pair of kings when you start with A2s or K2s.

[LoveNh8]

sure, but if he takes a 75% hit, he's still making 6bb an hour or so! 8)

I could live with dat.

[Cerril]

If I get your math correctly, I'm probably miming the rest of the board here with a short reply - basically what you figured showed that you need a very, very loose table to play 'any two suited' -and- somehow know that if you make your flush you won't get beaten by a better flush.

So if you have an incredibly loose table (especially passive) then Axs and Kxs are the first contenders. In fact, in late position those are often playable for precisely that reason in highly passive/loose games.

Outside of those (games and draws), generally to get the sort of odds you want you really need a few more ways to win than just flopping a flush or two-pair (straights or high pairs). That's why most of the time the suggested hands are suited connectors, many one-offs, and very high cards in general (assuming you haven't already, there are an ample number of charts and such to give you a better idea).

-Cerril

[Leavenfish]

[ QUOTE ]
So if you have an incredibly loose table (especially passive) then Axs and Kxs are the first contenders. In fact, in late position those are often playable for precisely that reason in highly passive/loose games.



[/ QUOTE ]

So, I am curious...in these sort of tables, why should not one play Axs and Kxs from first position as well? Calling simply gives more people more reason to passively call in and play...making the pot bigger and making your decision to simply limp in with Axs or Kxs all the more correct.

[Cerril]

The simple reason is that you need better than just good odds at the moment, you need to stand to get paid off pretty well once you make it. If you're paying two bets or three to see the flop it is slightly less worth it even if everyone comes in (because as a rule, the number of bets you can get out of the table postflop is similar, so you're paying 2x or 3x as much up front if things don't work out to get a similar payoff later).

Worse, and more directly, a raise partway around the table is likely to scare out some people that might have seen one bet, so instead of having seven people in to see the flop with you, you only have four (or in particularly bad cases, one or two).

Now I have found, as it seems you're implying, that limping from early position does tend to get people in later position who might have raised to either steal or just for value to sometimes limp themselves, especially if they respect your limp. THe problem is that if they really do respect your bet (figuring 'he wouldn't come in there without premium cards) they might toss out hands they would have called with. You're now having a similar affect on the table as a raise would have. You'd need to have the table wrapped around your little finger to play a hand like that and get away with it in early position. (and if you're that psychic, poker may very well be the game for you but there are probably still more profitable options)

Even then, you really just don't want to play these hands against cards worth raising with. So at the vast, vast majority of tables you want to get everyone else's reaction. If you bet and get raised with those cards you really wouldn't want to be in this hand anyway, but unless it becomes two more bets to you it can be hard to get away.

And, of course, position in later rounds can't be denied either. If you get yourself a draw it's still not going to be worth paying too much on, say, the turn to see if it comes through on the river. Again, the table would need to be half asleep for it to be a good move to try to complete a flush draw with no other outs.

[Cry Me A River]

[ QUOTE ]

1% of the time, you flop a flush, and gain 20 small bets.
10% of the time, you flop a four-flush:
1/3 of those times, (or 3.33%) you will make your flush by the river (it's closer to .36, I think) and gain 20 small bets.


[/ QUOTE ]

I think this is quite incorrect. When a flop is single suited, unless you're playing against super-fish, everyone thinks flush and looks for excuses to fold. You seldom get paid anywhere near as well as when you catch your flush on later streets unless someone caught a second-best flush.

I also think you're oversimpifying and ignoring all the cases where your flush is no good or where you have to tread cautiously and can't build the pot as big as normal due to a tricky board - ie: bigger flushes (particularly when 4 of your suit are on the board) and houses.

In late position hands like Axs and Kxs can be very profitable in the right table conditions (enough loose limpers) but you have to be carefull with them since you're most likely to wind up with top pair crap kicker which can be dangerous, particularly against passive opponents who'll give no indication they're sitting on TPTK and not just being their good 'ol calling station selves.

They're also great when you flop 2 pair with a couple overcards on the board (ie: You have K4s and flop is AK4) as these can pay off really well against fish with TPGK who never see it coming. But it isn't exactly a common occurance.

[ChipWrecked]

Theory of Sucking Out According to Abdul (http://www.posev.com/poker/holdem/strategy/outs-abdul.html)

Izmet's 'Playing With the Fishes' (http://slicer.headsupclub.com:3455/16/Home)

Gary Carson dot com (http://garycarson.com/)

Oh, alright. The last one was just to bug Mason. /images/graemlins/wink.gif

But I still like Gary's book and explanation of odds.