When should you not chase a flush in HE?
 

Ok so I've been thinking about this a little. Game is limit Hold'Em:

The odds that after you flop a 4-flush that you will get your flush are: 35% according to HEFAP (probability chart in the back - 9 outs)... that gives you odds of 1.85714 to 1. (To calculate that you do (100-35)/(35)=65/35=1.85714, right?)

If there were only 2 people in the pot (let's say a 5/10 limit game). You could even be the small blind and complete giving $20 into the pot (the smallest it will ever be). You flop a 4-flush. You check, they bet. Now the bet to you is $10 for a $30 pot... 3 to 1 right? Even if I'm wrong and the odds are 2 to 1... that's still better than your 1.85714 to 1 so you should call.

Let's say that 2 other people came in with you. For the smallest starting pot possible, they were the blinds. You call from MP somewhere. (3 players * $10 = $30 pot) Flop comes and gives you a 4-flush. Small blind bets... big blind raises... bet is now $20 to you for a $60 pot ($30 preflop + $10 from SB + $20 from BB). Again here is your 3 to 1 (or 2 to 1 even) which is better than your 1.85714 to 1.

3 other people? $40 PF + $10 SB bet + $20 BB raise + $30 UTG reraise = $100. So $30 for a $100 pot = 3 1/3 to 1 ... again higher than our 1.85714 to 1. (and even higher than if you were head's up)

Heck let's try the family pot! Everyone calls at a 10 seated table! YAY! 10*10=$100 PF then theoretically(which I know can't happen)everone raised on the flop! ($100 + 10 + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90 + 100 = $650) $650 for a $100 bet. That is 6.5 to 1 which is still higher than the 1.85714 to 1 odds you need.

Am I right on this?? Cause that means if you EVER flop a 4-flush in a limit game, then it is always statistically correct to chase it no matter how many people raise. (If everyone checks then you don't even worry about it cause you get to chase for free so you don't care)

And then in NLHE... you and one other guy stay in PF at .25/.5 NLHE for $.50 each. ($1 pot) You flop a 4-flush... for you to not get proper odds to call, your opponent would need to bet at least 117% of the pot - in this case $1.17 for you to not call. ( Pot Size ~ (1+x), Bet Size ~ x, odss of making hand are (100-35)/35 : therefore the equation should be (1+x)/x = (100-35)/35 , solve for x and you get x = 1.16667)

Am I calculating something wrong in any of this, or is it really proper for you to call even with these crazy statistics?

Re: When should you not chase a flush in HE?
 

don't forget that if you flop a four flush you will hit it 35% of the time by the river

things change a little because there is a betting round on the turn

Re: When should you not chase a flush in HE?
 

You need to consider several additional factors:

[img]/images/graemlins/diamond.gif[/img] How often will you win if you miss the flush?
Most of the time, you have other ways to win. An overcard might provide 3 outs. Against someone with ace high, you might have 6 extra pairing outs. You can get a runner-runner straight or trips. Your opponent's low pair might be counterfeited, e.g., your opponent has 33 on a board of 78872. You might be ahead of someone with no pair. These possibilities add up. A flush draw with no obvious other draws often wins about 38% of the time against a high pair.

[img]/images/graemlins/diamond.gif[/img] How often will you make the flush and still lose?
Someone could have the nut flush draw. Someone could have just one high card of that suit, and the turn and river could put a 4-flush on the board. The board might pair, and your flush could lose to a full house. Flush draws typically win only about 25% of the time against someone with trips or a set.

If the flop is monotone, you can't treat a low card of that suit as a flush draw against multiple opponents.

[img]/images/graemlins/diamond.gif[/img] How much will you put in on the turn if you miss?
This is a serious consideration both in limit and NL. If you raise on the flop, you may get a free card in limit, and you may win the pot in NL. The free card is not free, but it is better than half-price because if you are behind with a flush draw on the flop, you are often only a slight underdog, so you don't mind seeing a lot of money go in on the flop.

In NL, if your opponents routinely bet a lot on the turn after you call on the flop, then fail to pay off if a flush card comes on the river, they succeed in making flush draws unprofitable. However, they will pay too much when you have a straight draw or slow-play strong made hand, and you can play weak draws with the added value of being able to bluff on a flush card.

[img]/images/graemlins/diamond.gif[/img] How much extra will you win after you make your flush?
If you have position on your opponent, it is much easier to charge your opponent after you make your flush, particularly if you make your flush on the turn.

In conclusion, some flush draws are stronger than others. If your flush draw is too weak (you are out of position, you may be drawing dead, it will be hard to win other than by hitting the flush, you are drawing to a low flush), you won't have the odds to play it in a large multi-way pot. A strong flush draw (you are in position, you have the nut flush draw, many other potential outs, your hand might be good already) can be played heads-up even when the pot is small.

Re: When should you not chase a flush in HE?
 

3/6 game, I am the BB with K [img]/images/graemlins/spade.gif[/img] 3 [img]/images/graemlins/spade.gif[/img].

One player opens, all fold to me.
Pot: $7

Flop A [img]/images/graemlins/spade.gif[/img] 9 [img]/images/graemlins/diamond.gif[/img] 2 [img]/images/graemlins/spade.gif[/img]

I check and tight opponent bets $3.

$10 in pot, $3 to call. I do not call.

Why?

A. Odds next card is a [img]/images/graemlins/spade.gif[/img] is roughly 1 in 5. I am not getting pot odds to draw just one cards. Opponenet is tight and will not pay off my flush, hence no implied odds.

B. If I do call and turn card not a [img]/images/graemlins/spade.gif[/img]. I check, opponent bets $6. $19 in pot and I am not getting odds to draw to a 1 in 5 shot on the river.

Bottom line: will cost me $9 to see the river. Flop pot plus opponents bets: $7 + $3 + $6 = $16. Does not justify calling.

And please do not tell me this would never happen in a real game. Because it did.

Re: When should you not chase a flush in HE?
 

If your opponent is that tight, you should check-raise and your opponent will fold too much, or will fail to bet the turn. Perhaps you should have bet out.

You can always imagine that your opponent will act optimally given your precise holdings, but your opponent does not know what you have.

Re: When should you not chase a flush in HE?
 

Your K outs could be good here,
If a tight player is never paying off your flush, you can bluff-raise in a situation where you are not drawing to a flush but a flush draw comes in.
If you bet or raise the flop, the tight player will be more likely to pay off your flush draw if he does not fold immediately.