When are Flushes Profitable?

[AmericanAirlines]

Hi Everyone,
After reading the posts on Roy Cooke's article below, I was prompted to analyze flush draws.


Just trying to see how a flush draw can be profitable. As a stud player I used a lot of rules that seemed to work somewhat. Never bothered with this sort of analysis.

Now that I'm having to switch to HE AND stuck with the lame Colorado $2-5 game with $2 blind, I'm looking at the math a little more closely, as I'm not sure the game is worth fighting with. I suppose any HE newbie does some of this.

To make the math a little easier, assume everyone always bets the $5 bet. (Not too far from the truth.)

Working just with the flush draw and ignoring other sporadic
rarities on the flop I understand the odds to be:

8:1 to flop a flush draw
2:1 to hit flush by the river

so working backwards...

For every 3 flush draws I get involved in at the flop I hit 11.

To get to those 3 flush draws I have to engage in 27 flush draws from the start.

So assuming (falsely) that I always win when I hit, the following table shows what the pot would have to look like, assuming I always get out whenever two of my suit don't flop:

<pre><font class="small">code:</font><hr>
Trial first 2 flop turn river

1 1b
2 1b
3 1b
4 1b
5 1b
6 1b
7 1b
8 1b
9 1b
10 1b
11 1b
12 1b
13 1b
14 1b
15 1b
16 1b
17 1b
18 1b
19 1b
20 1b
21 1b
22 1b
23 1b
24 1b
25 1b 1b 1b 1b
26 1b 1b 1b 1b
27 1b 1b 1b 1b ---&gt; we win!</pre><hr>

That's 36 * $5 bet = $180
Add in $6 blinds for 3 orbits = 186$

So with 4 betting rounds, each player going to the river would have to shell out $20.

Divide $186 by $20 per player and you end up with 9.3 players having to chase AND lose!

So how exactly does a flush draw ever get profitable?

Beyond that, you're going to take 26 failures for each success.

Would tend to make for a crappy looking profit/loss line... in that you spend considerable time underwater before you saw a profit with these. Then started chipping down again!

So tell me what I'm missing.

Sincerely,
AA

[prospector]

Two points: First, many flush draws turn into other winning hands and having the flush draw will keep you in the pot to hit some of those other hands. The second (minor) point is that you can't charge all the blinds to flush draws.

[pudley4]

1-Ignore the times you are in the blinds. This isn't relevant to the analysis.

2-The Colorado games make the flush draw less profitable because this hand relies on implied odds. Since the betting doesn't increase on the turn, your implied odds are much worse than they would be in a normally structured game.

3-Your profit from these hands are not limited solely to flushes. When you have high suited cards (AJ, KQ, etc), you will win pots with 1 or 2 pair, or with straights.

4-In most LL games, you are getting immediate odds of 6-1 or 7-1 to see the flop - these are close enough to the 8-1 odds of flopping a flush draw that you can play Axs.

However, by looking only at flushes, you should be able to see why playing "any 2 suited" is a losing proposition. You won't win every time you make a flush, and you won't win often enough by other means to make the hands profitable.

[AmericanAirlines]

Hi Prospector,
I was factoring in the blinds I'd have to pay for the 27 flush attempts. Which is around 3 orbits, or $6 bucks in the Colorado game.

I guess I could've worked it the other way. $2 per orbit... approx $.20 per hand * 27 hands = $5.40 in blinds for the 27 attempts. I figured 27 hands = approx. 3 orbits was close enough.

Actually, you'd pay a lot more blinds waiting for 27 flush attempts to come up since you don't get 27 flush cards in a row. But I think the estimate of blinds for those 27 starting attempts is pretty close.

Sorry if my writing was unclear there.

What I don't have a good way to figure, is what the other hands that you might get would amount to. So the example was painfully sterile, in that I was only looking at the flush component part, and perhaps massively erroring by figuring the other hands you might get and win with, would be offset by the times your flush would lose.

If you know of a way to calculate it out, I'd be interested in knowing it.

The rule of thumb seem to be, "Go ahead and start your flush draw with 4-5 other callers in the pot."

I'm trying to get a handle on how to figure what the number of callers should be for any given two card starting hand.

Sincerely,
AA

[AmericanAirlines]

Hi Pudley4,
Thanks for the thoughtful reply. I agree, "any two suited" (meaning any two with only suited as it's strength) looks like a loosing proposition in the CO. game.

I suspect it'd be best not to play more than a 1-gap pair of suited cards at worst.

True enough, the straight potential is clearly important. Overlooked that pretty badly.

Unfortunately the lower implied odds plus the fact that these CO games are often loose is an interesting problem. B

Because there are often "family" pots you want to draw to big hands... but the lack of a double bet in the later streets works against you.

See any rationale for avoiding coming in unless you can limp in for the $2 bring in? Then the implied odds would return.

But it might be bad to just toss suited connectors for the $5...

Further, if someone makes it $7, what then?

So I suppose it's a matter of trying to determine when it's best to toss something like KQs or KJs etc.

Other than to say... "be more likley to stay for $2 and more likely to fold for $7" I've yet to establish any guidelines. For examples stay in against 5 or more for $2 but I need 8 callers for $7, etc.

What's your thoughts?

Sincerely,
AA

[Ed Miller]

The way you are thinking about this is flawed. The fact that you have to play blinds at some point has absolutely no bearing at all on whether a given hand is profitable in a given situation.

In your flat 2-5 structure, hands that thrive on implied odds (suited connectors, small pocket pairs, and, to a lesser extent, suited aces) drop in value. Thus, big pairs and big cards are better, in comparison.

Your opponents will not catch onto this, so you should make sure to raise with your big cards and big pairs so they make even bigger mistakes when they play their drawing (or complete trash) hands.

Having said that, you can play a lot of hands for just the $2 bring-in, including all these drawing hands.

If you want specific information about which hands are profitable in which situations... perhaps you could set up some TTH simulations to give you an idea of exactly how much the hand values change in your structure.

[Ray Zee]

you guys are looking at it the wrong way. you need to see about what the added flush draw does to the hand you are considering playing. most suited cards add somewhere in the three to five % range to a hands value. more or less as the play affects it and the chances it enables you to tag along for an extra card or two. plus the times it helps you to bluff at the pot or raise for value. overall two suited helps in more multiway pots, especially when you have bigger cards as you dont lose with your flush as often.
to answer your question, i dont think any time your hand becomes playable just because its a suited hand. your two cards and positon determines your actions. being suited though, just may put you over the threshold for coming in on a hand that was close.

[AmericanAirlines]

Hi Ray,
Thanks for the response.

Isn't the primary target I'm hoping to make with say, KQs, a flush though?

The real point of the post was that I'm trying to figure a way out to know when I have sufficient pot odds to *start* with a hand. Or perhaps to know that the starting conditions are correct to be profitable.

Every HE book out there espouses *some* starting hand suggestions. However, I've seen few explanations as to how these suggestions were arrived at.

Somewhat related to this is that I believe I should know, for any hand I start:

a) What exactly I'm trying/hoping to have happen. (An I don't mean "Flop the nuts every time... but rather something more realistic like... If I flop x x x, I should stay in if the money is $y, or a raise knocks out 3 folks... or whatever. In other words..."What is my strategy for this starting hand in all cases?"

2.) When conditions are such that I should let go.

I mean to say that conditions that come up often, I should have planned for.

I realize that there's adjustments to make to the table and a need to try to read other's hands... and thier read on me...

But I should know what the basic strategy for any hand I play is going to be, to make it profitable.

I'd go so far as to say I ought to be able to write it down and explain my rationale to someone.

Sincerely,
AA