I need some clarification

[WalkAmongUs]

After doing some reading I was looking over odds and probablities. Most books say you should get around 4:1 pot odds when drawing to a four flush. The flush supposedly should come in 35% of the time. If thats a tiny bit over 1/3 of the time wouldn't you only need 2:1 odds to break even? Also, I was looking over the probablities in the back of Hold Em Poker (not HPFAP) and It tells how to convert the probablities to odds. So with 47 unseen cards the 35% flush draw probablitity gives you odds of 1.857:1 (or about 2:1). I was just wondering how this relates to the calculation of having 9 cards out of 47 make your flush (47/9 = 5.2-1 = odds of 4:1)What calculation gives you the 35% chance of making a flush by the river with four of a suit on the flop? And how do the 2:1 odds (35%) relate to the 4:1 odds (47/9-1 claculation)?

[dtbog]

[ QUOTE ]
Most books say you should get around 4:1 pot odds when drawing to a four flush.

[/ QUOTE ]

I'm not sure, but...

4:1 just happens to be (about) the probability of hitting a flush with one card to come; the 35% figure is assuming you get to see two more cards.

If it's an all-in situation where you don't need to do any more betting, then feel free to use 35% for your chance of hitting your flush, but remember that your opponent will have redraw outs if he has at least one pair on the flop. (If he has a set, he gets one 7-outer and one 10-outer... pretty significant.)

Otherwise... almost 20% of the time (there's the 4-1), you'll hit your flush on the turn.

-DB

[dtbog]

To get the 35% figure:

chance of missing flush on the turn: 38/47
chance of missing flush on the river, given that you missed on the turn: 37/46

(38 * 37) / (47 * 46) = ~0.65

This is the chance that you missed your flush. (Does that make sense?)

Now.. since you want the chance that you MAKE your flush, subtract from 1. 1 - 0.65 = 0.35, or 35%.

-DB

[WalkAmongUs]

With four to the flush on the flop you have 9 out 47 cards to make the flush. 47/9 = 5.22. Subtract 1 for the odds and you get 4.22. On the turn 46/9 = 5.11 minus and you get 4.11. I'm assuming this is why the pot odds of 4:1 are suggested when drawing to your four flush by the river (with four to the flush on the flop). I see where the 35% chance of making the flush with 2 cards to come is gotten. But this translates to ~2:1 odds. So why do you need 4:1 pot odds? To be safe? I'm just wondering.

[WalkAmongUs]

SSH states that break even pot odds for 9 outs is 4.11:1 with one card left. For two cards left the footnote says to see Hold Em Poker. Well in Hold Em Poker its gives the 35% chance of making the flush with 2 cards to come. Following the formula for translating percentages to odds stated in the book: (100-35)/35 = 1.857:1. So is it safe to assume that you only need pott odds of 2:1 to draw to a four flush on the flop but then you need 4:1 after seeing the turn?

[dtbog]

[ QUOTE ]
So is it safe to assume that you only need pott odds of 2:1 to draw to a four flush on the flop but then you need 4:1 after seeing the turn?

[/ QUOTE ]

Reverse the scenario for a second. Say you have two pair, on a board that contains two spades. You bet on the flop, and your opponent calls. You think he might be on a flush draw.

The turn comes, and it's not a spade. What do you do?

Obviously, bet again.

This is what will happen against you, too... so you're not paying once to see if you make your flush, but twice.

4:1 on the flop ensures that you have the odds to either A) make your flush on the turn or B) have a favorable proposition if you miss the flush on the turn, where you can still call a bet with justified odds of hitting a flush. I haven't done the calculations here, but I'm sure the author of the book has.

It is, of course, always worth thinking about how many of your flush cards pair the board, and what your opponent may be holding.

This all ignores the concept of implied odds... but strict pot-odds-wise, 2:1 on the flop isn't really enough, unless you KNOW you will get to see the turn and river for free.

-DB

[WalkAmongUs]

Ok cool. That makes sense. Getting 4:1 pot odds on the flop betting round ensures you can stay for the river as long as it is only one bet back to you on the turn betting round. I guess I was confused because Hold Em Poker didn't explicitly explain this. It might be in HPFAP but I haven't read it yet.

[dtbog]

[ QUOTE ]
Getting 4:1 pot odds on the flop betting round ensures you can stay for the river as long as it is only one bet back to you on the turn betting round.

[/ QUOTE ]

It definitely doesn't -ensure- it, but it makes it more likely.

This is the sort of thing that you'd really need to be able to think about on the fly. It really depends on how many players are in the pot, what their likely holdings are, what card comes on the turn, etc. 4:1 on the flop in a heads-up pot won't give you odds on the turn, but in a three-way pot, it will... unless the card pairs the board, or unless you get the feeling that someone is drawing to a higher flush -- you have to factor the chance of you making your flush and still losing. There isn't anything that's true 100% of the time.

Rather than worrying about memorizing situations in which you probably will and will not have the odds to call a bet, it's better to learn how to figure it out at the time the bet is made. This will pay off greatly in the long run.

-DB

[gaming_mouse]

[ QUOTE ]
Rather than worrying about memorizing situations in which you probably will and will not have the odds to call a bet, it's better to learn how to figure it out at the time the bet is made. This will pay off greatly in the long run.

[/ QUOTE ]

This is good advice, and DB gave a good discussion on all the factors to consider, when exceptions come up, etc.

However, as WalkAmongUs is new, I would like to emphasize that usually you should be seeing the river with your flush draws, and almost always you should be seeing a turn.

As noted, the most common exceptions to this rule occur in small unraised pots (especially pots which get checked through on the flop) and hands with heavy action on a paired board.

While anaylzing every situation on a case-by-case basis is the best approach, I think general guidelines are also important when you're learning.

HTH,
gm