Novice With Outs Problem

Just started learning Hold Em. The books say if you flop a flush draw there are 9 outs to make the flush. In a ten-handed game, however, 20 cards have been dealt, five of which should be of the suit (on average). You hold two and three by other players. That leaves only 6 outs. Right? [img]/images/graemlins/confused.gif[/img]

[jba]

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Just started learning Hold Em. The books say if you flop a flush draw there are 9 outs to make the flush. In a ten-handed game, however, 20 cards have been dealt, five of which should be of the suit (on average). You hold two and three by other players. That leaves only 6 outs. Right? [img]/images/graemlins/confused.gif[/img]

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forget about the cards that have been dealt to other players - with no other information about their cards, we have to assume they will have the same % of your outs as the unused cards in the deck.

[Catt]

This is a common logical misunderstanding for new players. In your example, there are 47 unknown cards (some in the deck, some in others' hands). 9 of those cards represent outs for us. We treat all unknown cards as "available" cards despite the fact that some cards (we don't know which) are not available because they've been dealt out already. The chances that we'll see one of our 9 outs is 9/47 or 19.15%. The way you're looking at it makes some intuitive sense, but it is needlessly complicating the situation. Sometimes all 9 of our outs are still available, sometimes less (or none) are available. Since you can't know, you intuitively assume that the suits have been distributed in line with statistical expectations. 18 of the 47 unknwon cards are in others' hands. 18/47 = 38.30%. 38.30% of our 9 outs is 3.447 outs, meaning we should expect that we only have 5.553 outs still available to use (9 outs - 3.447 outs assumed already dealt to others). However, since we have assumed that 3.447 outs are among the 18 unknown cards held by others, we must treat those "unknown" cards as "known" in this approach. So we have 5.553 outs out of 29 unknown cards (3 flop, 20 dealt cards). 5.553 / 29 = 19.15% chance to hit an out.

Long story short = any unseen card is truly unknown. Count your outs as if all are available and count all unseen cards as "available." Doing it the other way is way more complicated and yields precisely the same chance of seeing an out on the next card dealt.

Well written