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