Outs after the flop Part II

[sgfried]

From what I have read I am NOT looking for implied odds or effective odds. In the paragraph below I am looking at how they came up with 36% after the flop to hit the flush. With one card you have 9 outs, 9/47 is roughly 1:4. Yet, 36% is obviously better than 1:3, how do you figure out that the flush draw with 2 cards is a 1:3 chance NOT a 1:4 chance. I have seen equations that are fine on paper but no way am I doing that at the table in my head. Thanks, please see paragraph below.


So, here's an example:
You are heads up. You have a flush draw on the flop, giving you roughly a 36% chance of hitting.....

[Tom1975]

Sounds like you're looking for something like the rule of four, which is very easy to use, though not deadly accurate. If you know your number of outs and there are two cards to come, multiple your number of outs by four to get the percent of hitting. This works nicely for your flush draw example, e.g. 9 * 4 = 36%. If you have only one card to come, multiple by two instead of four.

[aargh57]

Multiplying fractions we get:

(38/47)*(37/46)=.6503

This is how often we miss our flush so we will make it about 35% of the time.

I just memorize the postflop quick outs odds instead of doing the calculations in my head otherwise I couldn't do them. Just memorize the table and compare them to the pot to see if the pot justifies calling. For example, if you know that the break even point on the turn is 4.1 to one to make your flush (ignoring implied odds) and there are 5 BB in the pot and there's no one behind you to act you're getting proper odds to chase. If there are 5 BB and it's 2 bets to you now you're only getting 2.5 to one so it's incorrect to chase.

[AKQJ10]

Note: After rereading your OP, I think you're looking for a simple rule such as other respondents have given. So feel free to ignore the last several paragraphs of this post.

That said, are you certain you're not confusing probability and odds? http://poker.wikicities.com/wiki/Odds
You seem to be confusing the odds against a flush with one card to come (approximately 4:1) with the probability of a flush with two cards to come (approximately 1/3). Although odds and probability are closely related, failure to distinguish between them will lead you to all kinds of estimation errors.

Your expression "1:3 chance" probably is intended to mean "a probability of 1/3", not "3:1 odds" (i.e., a 1/4 probability), but is likely to breed confusion. I would only use the colon for odds.

OK, the rest of this post is minutiae you probably don't care about. [img]/images/graemlins/smile.gif[/img]

[ QUOTE ]
From what I have read I am NOT looking for implied odds or effective odds.

[/ QUOTE ]

I beg to differ -- if this isn't a classic question on effective odds, then I don't understand effective odds properly. (EDIT: I just remembered that effective odds also accounts for the extra turn bet, so that's extraneous to your question -- still, your question is very much an effective odds question, or I don't understand effective odds.)

But if you're looking for the specific math:

Turn: 9 [img]/images/graemlins/spade.gif[/img] remain, 47 unseen cards.
River -- provided you didn't catch a [img]/images/graemlins/spade.gif[/img] on the turn: 9 [img]/images/graemlins/spade.gif[/img] remain, 46 unseen cards

Probability of a OR b (or both) =
P(a) + P(not a) * P(b)

In our case, P( [img]/images/graemlins/spade.gif[/img] on turn, river, or both turn and river) =
9/47 + (38 / 47) * (9 / 46) =
0.191 + 0.809 * 0.195 =
0.349

A probability of 0.349 can be expressed as 34.9% or "odds of 1.865 : 1 against".

(NOTE: My original post had a small error, now corrected.)

[jb9]

Learn to count outs then memorize this outs and odds chart (or this one if you prefer).

A few quick outs totals to remember:

If you have 4 to a flush, you have 9 outs
If you have an open ended straight draw, you have 8 outs
If you have 2 overcards, you have 6 outs to make a pair
If you have a pair, you have 5 outs to 2 pair or 3 of a kind
If you have a gutshot straight, you have 4 outs

Note that not all of your outs will always be good. For example, if you have an open ended straight draw, but there is a flush draw on the board, 2 of your 8 outs will complete the flush, so if someone else is drawing to the flush, you really only have 6 outs.