Do You Really Have 9 OutsTo A Flush Draw??

If 20 cards are dealt, then on average 5 of each suit will be dealt. If you are suited then you can assume that on average 3 other cards of your suit were already dealt. So once you flop a flush draw you would only have 6 outs in reality on average.

Is it better to assume we have 6 outs to a flush instead of 9??

[pokerjunky]

If you're going to count the cards that are already dealt, you are drawing to 6 out of 29 cards, which is still roughly 4:1 odds.

[slavic]

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If 20 cards are dealt, then on average 5 of each suit will be dealt. If you are suited then you can assume that on average 3 other cards of your suit were already dealt. So once you flop a flush draw you would only have 6 outs in reality on average.

Is it better to assume we have 6 outs to a flush instead of 9??

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It doesn't matter what those other 18 cards are because they are unknown. We assume 9 outs because of the 47 unknown card on the flop 9 of them improve us. Now as known cards come up we can certainly discount outs along with reduce the number of unknown cards.

[SNOWBALL138]

post this in probability or poker theory.

[W. Deranged]

This is a very important idea which is particularly important in stud.

The main point is simply that since we can't see the other cards, we have to count them in "the deck." We basically just consider the likelihood that a card of our desired suit is at a specific position (the top of the deck) among the 46 cards we don't know.

Another way to think of it is this. In general, our odds of drawing to a flush are about 4:1. We should only adjust this based on the cards that have been dealt if we have a reason to believe that there are a disproportionate amount of our suit among the cards that have already been dealt. In stud, this is obviously an important concept; we can see what's been dealt and adjust. (Interestingly, pot limit Omaha also makes use of a concept like this; often times it becomes correct to draw to slightly thin draws--like calling a pot size bet on the turn with 13 outs-- because you can reasonably presume that cards in your opponent's hand are not ones that you need. Similarly, in 2-7 triple draw, we often need to consider how "heavy" or "light" the deck is by considering how many good, low card are contained in our opponents hands).

In hold'em, occassionally there are times you can make this sort of adjustment. Specifically, if hand reading tells you that an opponent is likely to also have a (hopefully lower) flush draw, you should probably slightly discount your outs. The thing is, though, since so few cards are held by our opponents in comparison to the number of the cards in the deck (as compared to other games), such adjustments tend to have a much smaller effect on odds calculations and so you can play very effective limit hold'em without ever considering such things (at least at the small stakes level).

To assume there are still 9 cards of the same suit still left in the deck (28 cards) is wrong. On average there will only be 6. You can not ignore that over the long term there simply will not be 9 outs.

However 6 outs in 28 cards left to come is still close to 4:1 ( about 4.5 : 1)

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To assume there are still 9 cards of the same suit still left in the deck (28 cards) is wrong. On average there will only be 6. You can not ignore that over the long term there simply will not be 9 outs.

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Wrong. Barring any compelling clues about unseen cards, the likelihood of hitting an out = total outs / number of unseen cards. If you make a different long-term calculation, you are making an error.

Consider a hypothetical hold 'em game: you are all-in with a flush draw. Your cards are visible to everyone, but your opponent who has you outchipped wants to wait until showdown to show his.

The dealer burns a card and is about to flip over the river, but pauses after you make a comment about having approximately "six outs". He asks what you mean, and you repeat your theory about outs in the deck (countable) vs. outs in opponents' hands (not countable).

So he says, "okay, buddy. I'll let you choose any face-down card on the table, including mucked cards, live cards in opponents' hands, burn cards, and the whole deck," which he proceeds to spread across the table, "and we will let whatever card you choose be 'the river'." Out of pure curiosity and astonishment, everyone at the table agrees.

So now every unseen card is 'live' to you. You have 'more' outs.

Do you believe your likelihood of rivering a flush has changed?

[TaintedRogue]

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If 20 cards are dealt, then on average 5 of each suit will be dealt. If you are suited then you can assume that on average 3 other cards of your suit were already dealt. So once you flop a flush draw you would only have 6 outs in reality on average.

Is it better to assume we have 6 outs to a flush instead of 9??

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When you assume you have 8 outs, the odds of getting your flush by the River, when two have flopped, is 1.86:1

Ok, let's assume 4 of our suit was dealt out and we have two of them, leaving 6 in the deck. We assume now, that we have "seen" the cards dealt to our opponents.

The Flop comes with 2 of our suit. We have now "seen" 23 cards in the deck, leaving 29.

29*28 = 812 total possible turn/river variations

23*22 = 506 variations that won't give us the flush

812 - 506 = 306 that will

506/306 = 1.65:1 odds. You've increased the chances of you getting your flush.

[fluff]

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If 20 cards are dealt, then on average 5 of each suit will be dealt. If you are suited then you can assume that on average 3 other cards of your suit were already dealt. So once you flop a flush draw you would only have 6 outs in reality on average.

Is it better to assume we have 6 outs to a flush instead of 9??

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Holy Ephipany Batman!

Let's extend your logic: After dealing 20 cards, the burn card, and the flop, there are only 28 cards left in the deck. Since the dealer only deals from the top of the deck, the cards in the bottom of the deck can never come out. Well, since there are only 4 more cards coming out (burn, turn, burn, river), and 2 of those are burn cards, that means 26 cards in the back of the deck won't help you. That means on average, 6.5 of the cards of your suit are in the back of the deck, where they are useless.

Substracting those out from the remaining 6 outs you had after the flop is dealt, 6 outs - 6.5 outs = -0.5 outs.

Clearly flush draws are hugely -EV. Fold please.

Does anyone doubt that on average there will be 6 outs left?
If so, do you really beleive that on average there are 9 outs left in the 28 remaining cards??

So if you are only going to see 2 more cards, then how often will one of your suits fall? Well you will average 6 outs in 28 cards..so the chances that one of your suits will fall is 6:28 or about 4.5:1.