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I'm reading Poker Math that matters by Owen Gaines and I'm struggling to calculate outs in certain situations. For instance, I could not understand fully this example in the book:

Hero: Jh7s Villain: AdQs Board: Ah9sTd

I can see clearly that 4 8's would give Hero a straight. In the book he explains that he disregards the KQ backdoor straight because it villain has a Q. I get it.

On the other hand, there's another possibility that I do not understand why it's not been considered: a J and 7 appearing at the turn and river respectively, thus giving Hero 2 pairs against villain's A's top pair.

In this scenario, when a stronger hand depends on a specific pair of cards, they are not counted as outs ?

  • good read, this book helped introduce me to poker math as well – Clarko Mar 17 '18 at 22:28
  • also when you refer to the turn and river, it is misleading to use the term "pair". running cards is the correct term – Clarko Mar 17 '18 at 22:30
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Outs are counted as single cards not "running" cards, although running cards do have an effect on the hero's probability of winning the hand. in this example the Hero currently has 4 outs (the 4 8's left in the deck), which means that if the next card is an 8, the hero will have a better hand than the villain.

If one of the running cards (like J, 7, K, Q) comes on the turn, the hero still has a hand that is worse than the villain but he has more outs on the river. For example, if a a J came on the turn, the hero now has 9 outs (another j, a 7, or an 8).

An out is any card that could come on the next street that would make the Hero's hand better than the villain's. possibilities of running cards (like a queen then a king -or- a jack then a 7) add around 1% to the hero's probability of winning the hand but do not count as outs.

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In real life you do not know the opponent's hole cards.

Outs are cards to improve and likely beat your opponent.

If your opponent has an ace then 4 outs.

The 7 is probably not good here. So you have you have like 7 outs.

You don't count runner runner as outs. JJ, 77, and J7 are runouts that are probably good but not likely enough to even count as one out on the flop.

In real life you do not know one Q is blocked. Without a block runner runner KQ is worth about .7 out. (8/47 * 4/46) * 47

If you add up all the runner runner you get about 1.6 outs. It is better to just go with outs based on one card. You are facing one bet to see one card.

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