basic odds question.

[Yort Mada]

i was counting my outs for my flush draw on the flop to hit on the turn.

i've seen 5 cards (3 on the flop and my 2)

that leaves 47 unseen cards

i have 9 outs to hit my flush draw

47 divided by 9 = 5.2.

So i would need better pot odds than 5.2 to 1 to call profitably. I realize almost never fold the nut flush draw or a strong one, i'm just using this as an example for my question.

with that said and i'm assuming my math is correct. I was surfing the micro-limit FAQ's and found a pot odd chart. Well according to the pot odd chart, it says i need 4.1 to 1 for the call to be profitable.

Now my question(s) i think what the pot odds chart is saying is its 4.1 to 1 to hit your flush draw by the river. Could someone show me the formula to calculate 'by the river'?

and also, which odd is correct? 5.2 or 4.1 to call profitably?

Thanks for your time.

[Quicksilvre]

You have nine outs on the turn, and then nine outs on the river, too. The 5.2 that you're getting is the chance you'll hit on the turn only.

[Pov]

You're confused because 47/9 is not a statement of odds. Your odds on the flop are actually 38:9 meaning you need pot odds of 4.2:1 to peel off the next card if you ignore the river. From the turn to the river you know one more card so now the necessary pot odds are 37:9 to get the 4.1:1 you cited in your post.

When you think 9 out of 47 cards help me you're thinking in percentages. Odds are a ratio. 38/47 are bad and 9/47 cards are good = 38:9 ~ 4.2:1 good to bad cards. Your pot odds are a statement of odds. $22 in the pot and $4 to call = 22:4 = 5.5:1 pot odds. 5.5:1 pot odds > 4.2:1 odds of making your hand resulting in an easy call.

On the flop there are actually two cards to come so you don't necessarily need the full 4.2:1 to see the turn because your odds of making your flush in the next two cards are roughly twice as good as just making them in one, though presumably your opponent will bet again. And then there are implied odds, etc. etc. so there is a lot more to it, but this should get you started.

Check out this odds chart for a better explanation.

edit: clarity

you are dividing 47 by 9 and this is not correct.
instead think of it as 47 :9 reduced to 4:1

like 10:2 reduced to 5:1

[AKQJ10]

[ QUOTE ]
you are dividing 47 by 9 and this is not correct.
instead think of it as 47 :9 reduced to 4:1

like 10:2 reduced to 5:1

[/ QUOTE ]

No! This method only reinforces the confusion. If you reduce 47 (total unseen cards) : 9 (unseen flush cards) byt dividing both sides by 9, you get 5.222:1, same as the OP!

The conceptual difference between probability and odds is that probability is:

successful outcomes / ALL total outcomes

or

successful outcomes / (successful outcomes + failure outcomes)

Odds are expressing the same relationship in a different way:

Failure outcomes : Successful outcomes .

So you do not want to reduce 46:9 unless you want to find the probability of a flush, which would be written 9/46 = 1/5.222222 = 0.191489 = 19.1%.

For odds, you want to reduce

non-flush cards : flush cards

which is

all unseen cards - unseen flush cards : flush cards

which is

47 - 9 : 9 or 38:9 or 4.2222222 : 1

to hit your flush ON THE TURN CARD.

Note that the odds against are always one less than the inverse of the probability. If p is 1/5, odds are 4:1. If p is 1/23, odds are 22:1.

Now I'm going to put this on the wiki so someone else can improve upon my explanation (even though I pretty much repeated what Pov said).

[Quicksilvre]

Ick, ignore this, I was confused too.