counting outs with an example

I am sure this question should me in the FAQ section, as it must be asked all the time. However, I would like to get a fresh answer to how many outs you can add for a back door flush draw. I have read that a back door flush gives you two outs.


Please help me understand this hand:


Heads-up AdKc vs. QsJc


Flop [Ah Qd Jd]


AKo has Ac, As, Ks, Kh, Kd, Tc, Td, Ts, Th to improve on the turn to beat the 2-pair. While QJ has only four outs to improve to the nuts and will tie if both a king and ten fall on the turn and river. This tie assumes that it is not exactly the Kd and Td.


Here is where I need help counting outs, if one of those cards misses the turn. AK can still win if a smaller card hits the turn and then pairs the river. It can also improve if two diamonds hit the turn and river. With the overall potential to be the absolute nuts, how many outs does AK have to win? What am I missing in this analysis? Thank you.

http://www.twodimes.net/poker/ gave the following result from a small sample:


Ad Kc wins 40%

Qs Jc wins 59%

tie 1%


I've heard you can count a back-door flush as about 2 outs. It's comes out to a little less than that, but when you factor in extra bets at the end, 2 outs is a rule of thumb I've heard.


Regarding the river-river pair, there are 7 cards you know about (the A Q J on the board, the AK and QJ in the hands) leaving 45 cards. Of those 45 cards, 36 are 2 through 9, so there is a 36/45 chance of getting a card that could go river-river pair on the turn. Given that, there is a 3 in 44 chance the second like card will river, making the calculation 36/45 * 3/44 = 3/55, which is between 5 and 6%, which is about the same as the backdoor flush (just a little better). Hope there's no mistakes here.

That means that AK has about 13 outs in this example? Any ace(2), king(3), ten(4), back door pair(2), and back door flush(2); does this sound right?


That gives you about 1.08:1 to connect (rec.gambling.poker FAQ) by the river. With such a huge draw and odds that good, would you want to pump this pot vs. a made hand or try to make your hand cheaply?

One reason for doing the sims is that the manual calculations can be very difficult. Sometimes your outs aren't really outs, because you have to take into account the possibility that you make a hand but your opponent makes a better one.


In a normal heads-up situation, you don't know what your opponent has. You want to play hands like this aggressively. You can win by having the best hand, forcing your opponent to fold, or improving to the best hand. If he continues to show strength in spite of your aggression, you can slow down. You probably can't get away from this hand if you don't improve because there are many hands worse than yours that your opponent could be pushing hard.