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Figuring # of Outs, Mike Cooke, 17. Sep 2003 12:46
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When figuring how many outs you have with a particular hand, do you only use the cards you know? I'm a little confused about this. Please give me an example that accounts for all cards in the deck.

Thanks for the input-you guys that have some knowledge about this game are really helpful to us rookies.
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Re: Figuring # of Outs, Mike Caro, 17. Sep 2003 13:43
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on 17. Sep 2003 12:46 Mike Cooke wrote:
> When figuring how many outs you have with a particular hand, do you only use the
> cards you know? I'm a little confused about this. Please give me an example
> that accounts for all cards in the deck.
>
> Thanks for the input-you guys that have some knowledge about this game are
> really helpful to us rookies.

Hi, Mike --

Interesting name you have. :-)

Yes, you should take into consideration ALL cards known to you, including the board (in games where there is one), your cards, and any exposed cards of opponents (whether turned over accidentally or as part of the game, such as in stud).

Here's a simple example:

If you want to know the odds against making a flush on the river (the last community face-up card) when you hold ace of hearts and queen of clubs, with three other hearts on the board (community face-up cards) in hold 'em...

Figure there are 52 cards in the deck. You know about six of them -- the four face-up cards on the board and the two secret cards in your hand. So, there are 46 cards unknown to you, and the final card will be one of those.

Since there are 13 hearts in the deck, and you have seen four of them (three on the board and one in your hand), there are 9 remaining hearts among the 46 unknown cards.

That means there are 37 cards that are NOT hearts (46 minus 9 hearts) among the unknown cards. So, the odds against you connecting are 37 non-hearts to 9 hearts -- 37-to-9 against.

Divide the 9 into the 37 to get the odds-to-1 against. It's 4.1-to-1 against you making that nut flush.

By the way, you'd be doing us a favor if you tried to put new subjects in categories where others might expect them. This one probably should have gone in "Money and Odds," instead of tournaments.

Hope this helps.

Straight Flushes,
Mike Caro

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Re: Figuring # of Outs, mkpoker, 17. Sep 2003 14:46
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on 17. Sep 2003 13:43 Mike Caro wrote:

> Here's a simple example:
>
> If you want to know the odds against making a flush on the river (the last community
> face-up card) when you hold ace of hearts and queen of clubs, with three other hearts
> on the board (community face-up cards) in hold 'em...
>
> Figure there are 52 cards in the deck. You know about six of them -- the four
> face-up cards on the board and the two secret cards in your hand. So, there are 46
> cards unknown to you, and the final card will be one of those.
>
> Since there are 13 hearts in the deck, and you have seen four of them (three on the
> board and one in your hand), there are 9 remaining hearts among the 46 unknown
> cards.
>
> That means there are 37 cards that are NOT hearts (46 minus 9 hearts) among the
> unknown cards. So, the odds against you connecting are 37 non-hearts to 9 hearts --
> 37-to-9 against.
>
> Divide the 9 into the 37 to get the odds-to-1 against. It's 4.1-to-1 against you
> making that nut flush.
>
Mike (and Mike),

I noticed in your example that you didn't count the overcards as outs. This is probably the right decision, because in your example there were already 3 hearts on the board (so another player could already hold a lower flush). However, if the board were slightly changed, your number of outs and your odds would be quite different.

For example, let's say that you held AhQh and the board was 2c6hJh. Here, if the next card were any A, any Q or any heart, you can be pretty confident that you'd hold the best hand (assuming you didn't have reason to think someone already had a set). Hence, you'd have a total of 15 outs (9 hearts, 3 aces, and 3 queens). Your odds would then be 31 to 15 or only 2.1 to 1 against.

When your looking for outs and odds, don't forget to look for all the possible ways you can make the best hand!
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Re: Figuring # of Outs, Mike Caro, 17. Sep 2003 17:59
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on 17. Sep 2003 14:46 mkpoker wrote:
> on 17. Sep 2003 13:43 Mike Caro wrote:
>
> > Here's a simple example:
> >
> > If you want to know the odds against making a flush on the river (the last community
> > face-up card) when you hold ace of hearts and queen of clubs, with three other hearts
>
> > on the board (community face-up cards) in hold 'em...
> >
> > Figure there are 52 cards in the deck. You know about six of them -- the four
> > face-up cards on the board and the two secret cards in your hand. So, there are 46
> > cards unknown to you, and the final card will be one of those.
> >
> > Since there are 13 hearts in the deck, and you have seen four of them (three on the
> > board and one in your hand), there are 9 remaining hearts among the 46 unknown
> > cards.
> >
> > That means there are 37 cards that are NOT hearts (46 minus 9 hearts) among the
> > unknown cards. So, the odds against you connecting are 37 non-hearts to 9 hearts --
> > 37-to-9 against.
> >
> > Divide the 9 into the 37 to get the odds-to-1 against. It's 4.1-to-1 against you
> > making that nut flush.
> >
> Mike (and Mike),
>
> I noticed in your example that you didn't count the overcards as outs. This is probably
> the right decision, because in your example there were already 3 hearts on the board (so
> another player could already hold a lower flush). However, if the board were slightly
> changed, your number of outs and your odds would be quite different.
>
> For example, let's say that you held AhQh and the board was 2c6hJh. Here, if the next
> card were any A, any Q or any heart, you can be pretty confident that you'd hold the best
> hand (assuming you didn't have reason to think someone already had a set). Hence, you'd
> have a total of 15 outs (9 hearts, 3 aces, and 3 queens). Your odds would then be 31 to
> 15 or only 2.1 to 1 against.
>
> When your looking for outs and odds, don't forget to look for all the possible ways you
> can make the best hand!

Hi, mkpoker --

That's very good advice. You should always consider all the ways you can win, as well as all the ways you can lose. And with more that one card to come, the odds are more difficult to calculate, but remain basically the same as in my simple example. You just count the combinations that will fail, equate that by ratio to the number that will succeed, reduce the odds by dividing the success into the failure, and you get your odds-to-one against whatever you're weighing.

By the way, my example was only targeted to the odds of making the flush -- not the odds of winning. As you point out, that's really what you need to measure in a game.

Straight Flushes,
Mike Caro
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Re: Figuring # of Outs, Mike Cooke, 18. Sep 2003 02:06
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Thanks for the example-that was just what I needed.
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Re: Figuring # of Outs, Urban Chaos, 18. Sep 2003 03:22
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My basic math skills suck and I think that could be a huge hindrance to my poker improvement (except that I'm planning on improving my basic math).

....thank you Mike and mkpoker for making that easy to understand!

-Urban

"If you're dumb, surround yourself with smart people; and if you're smart, surround yourself with smart people who disagree with you. "
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Re: Figuring # of Outs, Bungus, 18. Sep 2003 20:31
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Ok, all you guys seem pretty smart, especially mkpoker for using the word fundamental in a sentence (and I've heard Caro guy ain't so dumb either).
Now lets say in your AhXoff example, shooting for that nut flush of hearts (ignoring overcards in this case), with the same 3 hearts on the board, you say you have nine outs because there are nine spades unaccounted for in the deck. But, hearts comprised of one quarter of the deck at the time you and your opponents hands were dealt, so statistically, shouldn't you calculate that (in a 8 person game) one fourth of your opponents cards are also hearts? Technically then, as 16 cards were dealt, odds are 4 of them should be hearts. You have 1heart, so wouldn't it be prudent to factor in your opponents have 3 hearts amongst them (in addition to the ones on the board), so you probably only have 6 outs?
Ps. this little relavation seems out of place in the tourny section
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Re: Figuring # of Outs, mkpoker, 18. Sep 2003 22:10
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First, thanks for the compliment. I'm genuinely pleased that my posts have helped. I've "taken" a lot from the better players on this board, so I'm glad I can "give" a little occasionally.

The short answer to your question is no, you do not adjust pot odds to account for cards that are in the muck or in other people's hands. You should base pot odds calculations on the number of cards that are unknown TO YOU.

Let's turn back to our example, with one card to come. If you hold AhKh and the board is 2h7hJd5c, there are 9 "unaccounted for" hearts (they may be in the deck, they may be in your opponents hands--you don't know). In total, there are 46 cards unknown TO YOU (namely, all the cards except those on the board [4]and in your hand [2]). Because 9 cards (the hearts) will make your flush and 37 (the non-hearts) will not, your odds of making the flush are 37 to 9 (or 4.1 to 1) against.

Of course, if by some freakish shuffle all the hearts had been dealt out pre-flop and are currently sitting in players hands, you actually have no chance of making the flush. **But there's no way you can know that, so you always calculate your odds on the basis of cards unknown TO YOU.**

If you actually know about other cards (if, for example, an opponent turned his cards face up before mucking--a terrible breach of etiquette--and he held 3h4h), it would dramatically reduce your chances of making the flush. Then, there would be 44 cards unknown to you, but only 7 would make the flush. Hence, your odds would be 37 to 7 (or 5.25 to 1) against.

--matt

P.S. You're right about the location of this thread--it should be in "money and odds," but it started here and I don't think it's moveable.
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Re: Figuring # of Outs, shorn, 19. Sep 2003 05:10
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Bungus-

I understand the logic behind your question, but this is flawed thinking. As an example, using your logic if you started with a 52 card deck and drew 1 spade, 1 club, and 1 diamond, you would assume that the next card off the top would be a heart (which i think you will agree is not true). In fact, the chances of you drawing a heart on the next card are 13/49 or 26.5%.

Similarly, in a poker hand the cards are not distributed "equally" in terms of suit. So, you cannot adjust for the fact that your opponents might or might not be holding any of the remianing 9 hearts that you need. It could be that all of the remaining 9 are still in the deck OR all of them are in the muck, folded in others hands. But, you still need to count 9 in terms of the odds to draw.

Hope this helps clear things up.

Steve
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Re: Figuring # of Outs, shorn, 18. Sep 2003 06:01
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mk-

Don't want to be picky, but in your overcard example, I don't think you can be certain that either an Ace or Queen is a clean out for you because of the Jack on the board (many players could hold QJ or AJ as they are reasonable starting cards). What a friend of mine suggested doing in cases such as these is to give yourself 1 extra out for each overcard so that you take into account the fact that you could win if they hit, but you aren't necessarily making a bad call by counting all 6 cards as outs. Granted, in the flush example, it wouldn't matter too much because the main draw is to the nuts.

Steve
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Re: Figuring # of Outs, mkpoker, 18. Sep 2003 17:20
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on 18. Sep 2003 06:01 shorn wrote:
> mk-
>
> Don't want to be picky, but in your overcard example, I don't think you can be certain that
> either an Ace or Queen is a clean out for you because of the Jack on the board (many players
> could hold QJ or AJ as they are reasonable starting cards). What a friend of mine suggested
> doing in cases such as these is to give yourself 1 extra out for each overcard so that you take
> into account the fact that you could win if they hit, but you aren't necessarily making a bad
> call by counting all 6 cards as outs. Granted, in the flush example, it wouldn't matter too
> much because the main draw is to the nuts.
>
> Steve

I don't think that's picky at all...It's a very important point. It's pretty easy to calculate pot odds when drawing to the nut hand (e.g. with a 2-flush on an unpaired board when you're holding Axs of the flush suit). It's also pretty easy to adjust those odds when your outs are clearly "tainted" (e.g. when you're drawing to the straight, but 2 of your 8 outs might make someone else a flush).

It's quite a bit harder when the situation is somewhat ambiguous, as in my example (drawing to overcards as well as the nut flush). I think your solution of counting only one additional out per overcard is a bit too strong (effectively, it predicts only a 1 in 3 chance that an overpair will be good). I agree that some "discounting" is in order, but I wouldn't go that far. If an A or Q came up in my example, I'd still be pretty confident that I had the best hand--not 100% confident, but more than 33% confident.

Nonetheless your fundamental point is well-taken: **When drawing to a non-nut hand, you must consider the fact that your "outs" might not make your hand the winner. Accordingly, you need better pot odds to justify the call.**

--matt
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