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Old 07-14-2016, 02:53 PM   #1
Manchineel
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Should I account for opponents hand (when flopping a flush draw)?

If I'm trying to calculate the odds for flush.

And i have two hearts. If I'm alone there is 50 cards left in the deck and 11 of them are hearts. So it's easy to calculate the odds.

But in a game of heads up there will be 48 cards in the deck and 2 unknown in opponents hand.

Are the odds still 11/50 or 11/48 or something else.

Forget about hand-ranges. Just two random cards in opponents hand.

Thanks in advance.
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Old 07-14-2016, 03:08 PM   #2
RustyBrooks
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re: Should I account for opponents hand (when flopping a flush draw)?

The denominator in these calculations in the number of unknown cards. The cards in your opponent's hand are still unknown, even though he has them.

I see how it can see kind of weird, but consider this: once the flop is dealt, the turn is going to be one specific card. In a live game, you'll burn one and then deal the turn, so the turn card will be the 2nd card in the deck. It is impossible to get a turn that is any other card. So what difference does it make if those 2 cards in your opponents hand are in his hand, or at the bottom of the deck? Either way, they won't be on the turn

You're not going to adjust your calc because you can't get dealt the bottom card in the deck, right? Or the 2nd to the bottom, etc?
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Old 07-14-2016, 03:26 PM   #3
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Thumbs up re: Should I account for opponents hand (when flopping a flush draw)?

Quote:
Originally Posted by RustyBrooks View Post
The denominator in these calculations in the number of unknown cards. The cards in your opponent's hand are still unknown, even though he has them.

I see how it can see kind of weird, but consider this: once the flop is dealt, the turn is going to be one specific card. In a live game, you'll burn one and then deal the turn, so the turn card will be the 2nd card in the deck. It is impossible to get a turn that is any other card. So what difference does it make if those 2 cards in your opponents hand are in his hand, or at the bottom of the deck? Either way, they won't be on the turn

You're not going to adjust your calc because you can't get dealt the bottom card in the deck, right? Or the 2nd to the bottom, etc?
Thanks very much, No. It felt reasonable that you would not account for it. But i felt that i had to be sure(doh).

Your example were on point and shows the point without a doubt. Thank you very much!
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Old 07-17-2016, 09:48 PM   #4
asymbacguy
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re: Should I account for opponents hand (when flopping a flush draw)?

So if I'd flop a flush draw having 9 outs to hit my flush, do I have to assume that I'm always taking this perfect scenario, that is no one flush card I need was dealt on opponents' hands?
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Old 07-17-2016, 10:41 PM   #5
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re: Should I account for opponents hand (when flopping a flush draw)?

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Originally Posted by asymbacguy View Post
So if I'd flop a flush draw having 9 outs to hit my flush, do I have to assume that I'm always taking this perfect scenario, that is no one flush card I need was dealt on opponents' hands?
ZOMG but what if one of your flush cards is dealt to the 2 bottom cards of the deck! You can't get dealt those either. So it's the same as if it's in your opponent's hand. There is only one card you can get dealt on the turn.
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Old 07-18-2016, 01:23 AM   #6
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re: Should I account for opponents hand (when flopping a flush draw)?

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Originally Posted by asymbacguy View Post
So if I'd flop a flush draw having 9 outs to hit my flush, do I have to assume that I'm always taking this perfect scenario, that is no one flush card I need was dealt on opponents' hands?
You don't assume anything. The 9 out calculation is how often you will actually hit, on average, including the times some of those cards are dead. If we KNOW all 9 are available, the chance is greater than the average, because you have reduced the unknowns in the denominator.
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Old 07-18-2016, 05:25 AM   #7
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re: Should I account for opponents hand (when flopping a flush draw)?

You said this in OP "Forget about hand-ranges. Just two random cards in opponents hand. "

Therefore the posters above are correct.

In reality, you can draw some small inference on the flop about the suits in an opponents hand, but that's not what you asked.
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Old 07-18-2016, 07:46 AM   #8
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re: Should I account for opponents hand (when flopping a flush draw)?

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Originally Posted by asymbacguy View Post
So if I'd flop a flush draw having 9 outs to hit my flush, do I have to assume that I'm always taking this perfect scenario, that is no one flush card I need was dealt on opponents' hands?
What are the odds one of your flush cards was in another hand? Two cards? Three? ... All? None? In each scenario what are the odds that the flush card will come on the turn? What is the result when all scenarios are combined?

Show your work.
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Old 07-18-2016, 04:36 PM   #9
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re: Should I account for opponents hand (when flopping a flush draw)?

Yep, thanks for the answers.
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Old 08-15-2016, 01:20 AM   #10
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re: Should I account for opponents hand (when flopping a flush draw)?

I have also wondered about this. If the game is 9 handed and I have (had) 8 opponents and each opponent was dealt two cards, this makes 16 cards that will never come on the board. If an average of 1 in 4 cards are a flush card, should I assume that instead of nine outs to make my flush, I have less than this since odds are that some of my outs were dealt to other players?

In a nine handed game, 18 cards are dealt ( two per player), on average, 4.5 of these 18 cards will be of the same suit, if I have 2 of them, then shouldn't I assume that 2.5 of the same suit aren't left available to hit the board (on average)?
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Old 08-15-2016, 04:37 AM   #11
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re: Should I account for opponents hand (when flopping a flush draw)?

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Originally Posted by kb5zcr View Post
I have also wondered about this. If the game is 9 handed and I have (had) 8 opponents and each opponent was dealt two cards, this makes 16 cards that will never come on the board.
If this were true, you could also ignore the twenty cards at the bottom of the deck, as they will absolutely never come on the board either.

"In a nine handed game, 18 cards are dealt ( two per player), on average, 4.5 of these 18 cards will be of the same suit, if I have 2 of them, then shouldn't I assume that 2.5 of the same suit aren't left available to hit the board (on average)?"

Sure you can do that. But you then don't count those unseen opponents cards when working out the chance of hitting.

So the chance of the next card being a heart normally calculated is 11 / 50
(11 = the number of hearts in the deck)
(50 = the number of unseen cards)

So the chance of the next card being a heart calculating it your way is 8.5 / 34
(8.5 = the number of hearts you estimate are in the stub on average)
(34 = the number of cards in the stub)

These two come out with the same answer (not exactly the same because your 2.5 number is not exactly correct). This should show you that you don't have to do those interim calculations... just use the total 'unseen' cards method and it saves a lot of effort.




Alternatively think of it this way... you deal the hands out and get two hearts in your hand. Then lets say one of the other players just simply swaps his hand with the bottom two cards on the deck. Would that affect the probabilities of hearts on the flop? Obviously not. So why do you need to consider what's in the other players hand at all?
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Old 08-15-2016, 07:37 AM   #12
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re: Should I account for opponents hand (when flopping a flush draw)?

Quote:
Originally Posted by kb5zcr View Post
I have also wondered about this. If the game is 9 handed and I have (had) 8 opponents and each opponent was dealt two cards, this makes 16 cards that will never come on the board. If an average of 1 in 4 cards are a flush card, should I assume that instead of nine outs to make my flush, I have less than this since odds are that some of my outs were dealt to other players?

In a nine handed game, 18 cards are dealt ( two per player), on average, 4.5 of these 18 cards will be of the same suit, if I have 2 of them, then shouldn't I assume that 2.5 of the same suit aren't left available to hit the board (on average)?
.

Quote:
Originally Posted by Didace View Post
What are the odds one of your flush cards was in another hand? Two cards? Three? ... All? None? In each scenario what are the odds that the flush card will come on the turn? What is the result when all scenarios are combined?

Show your work.
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Old 08-15-2016, 08:51 AM   #13
kb5zcr
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re: Should I account for opponents hand (when flopping a flush draw)?

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Originally Posted by David Lyons View Post
Sure you can do that. But you then don't count those unseen opponents cards when working out the chance of hitting.

So the chance of the next card being a heart normally calculated is 11 / 50
(11 = the number of hearts in the deck)
(50 = the number of unseen cards)

So the chance of the next card being a heart calculating it your way is 8.5 / 34
(8.5 = the number of hearts you estimate are in the stub on average)
(34 = the number of cards in the stub)

These two come out with the same answer (not exactly the same because your 2.5 number is not exactly correct). This should show you that you don't have to do those interim calculations... just use the total 'unseen' cards method and it saves a lot of effort.

David Lyons,
You sir, should be a math teacher, you explained it perfectly so that my brain can understand. When you compared both methods it clicked in my head.

Thanks, Tim from Texas
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Old 08-15-2016, 04:29 PM   #14
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re: Should I account for opponents hand (when flopping a flush draw)?

Since this question comes up quite often, I will sticky the thread. Thanks for the questions and the great answers.
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Old 11-03-2016, 06:43 PM   #15
Talladega
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Re: Should I account for opponents hand (when flopping a flush draw)?

Grave digging!


Nobody expanded on if we should try to infere something about our opponents hand and account for that in calculating the number of outs? Looking at ranges should let you low ball some approximation of discounting outs?
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Old 11-03-2016, 06:57 PM   #16
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Re: Should I account for opponents hand (when flopping a flush draw)?

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Originally Posted by Talladega View Post
Looking at ranges should let you low ball some approximation of discounting outs?
You can determine suits from someone's range?
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Old 11-04-2016, 03:46 PM   #17
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Re: Should I account for opponents hand (when flopping a flush draw)?

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Originally Posted by Didace View Post
You can determine suits from someone's range?

Nope I was just thinking more generally.
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Old 11-04-2016, 05:26 PM   #18
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Re: Should I account for opponents hand (when flopping a flush draw)?

Then it's just your hand vs your opponents range, not the specific question in this thread.
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