Calculating Outs part 2

Lets look at another example:
We are holding: A♥, K♥
Our opponent holds: J♣, J♠
Flop: 7♥,3♣,9♥

In this case the AK of hearts is the weaker hand.To win we have following options:
A pair with either the King or the Ace.
A double pair with King and Ace.
A triple with King or the Ace.
A flush.

You can categorize the first three options.
For all of them you need at least one King or one Ace. There are 3 remaining Kings and 3 remaining Aces in the deck. That gives us 6 outs for the first three options.

For the flush we need another card of hearts. There are 9 remaining heart cards left in the deck. So that gives us another 9 outs.
=> total of 15 outs for that situation

We know now that there is a maximum of 15 winning cards left in the deck. But some cards may have been already folded or some could be in our opponent's hand.
But since we don't know what cards have been folded we have to proceed under the assumption that all of our potential outs are available.


Common "outs" Situations:
- Flop a flush draw => 9 outs
- Flop a flush draw with two over cards (seen in example above) => 15 outs
- Flop an open-ended straight draw => 8 outs
- Flop a gut-shot straight draw => 4  outs (i.e. 5,6,8,9: you need the 7, only 4 7s left)
- Under-pair to your opponents over-pair => 2 outs
- If neither you or your opponent have a pair, but he is still ahead => 6 outs
(i.e. he has A,K; you have Q,J => 3 Jacks, 3 Queens)
- Flop a straight flush draw => 15 outs

Remember tho, you usually don't have all your outs to come and improve your hand.

Calculating outs part 3